an investigation on speed control of a spindle cluster...

Research ArticleAn Investigation on Speed Control of a Spindle Cluster Drivenby Hydraulic Motor Application to Metal Cutting Machines

Ngoc Hai Tran1 Cung Le 1 and Anh Dung Ngo2

1University of Science and Technology University of Danang Vietnam2Ecole de Technologie Superieure (ETS) Canada

Correspondence should be addressed to Cung Le lcungdutudnvn

Received 27 August 2018 Revised 21 December 2018 Accepted 31 January 2019 Published 19 February 2019

Academic Editor Ryoichi Samuel Amano

Copyright copy 2019 Ngoc Hai Tran et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In this article we present an experimental study on the speed stability of a spindle driven by a hydraulic motor which is controlledby a proportional valve through a V-belt transmission The research includes the dynamic modeling of the transmission clusterand the transmission from the hydraulic motor to the working shaft via V-belt mechanism together with the establishment of amathematical model and fuzzy self-tuning PID controller model In the model the V-belt is assumed as an elastic module andthe friction coefficient and mass inertia moment of the hydraulic motor are considered as constant The Matlab software is used tosimulate the speed response of the hydraulic motor to the working shaft Based on theoretical study we resemble the experimentalsystem and determine the parameters for the fuzzy self-tuning PID controller We conduct experiment and investigate the speedstability of the working shaft from 300 to 1100 (rpm) based on transient response parameters such as the time delay the setting timethe overshoot and the rotation error at steady stateThereby in this study the simulation and the experiment results are comparedand evaluated regarding the speed stability of the working shaft driven by hydraulic motor transmitted through V-belt mechanismThe findings show the speed controllability by using proportional valve to manipulate the oil flow and applying a self-tuning PIDcontroller to achieve very good results such as the error difference of 0001 to 0036 the delay of 001 to 002 seconds no overshootand the settling error less than 5 compared to the set values On the other hand we include the effect of the oil temperature of 40to 80∘C on the working shaft speed (500 900 rpm) in this study and derive that the system works well at temperature range of 40to 70∘C On these findings we propose the applicability of this system on the current machinery cutters In addition we verify theeffects of the hydraulic drive for main shaft controlled by fuzzy PID by comparison of the roughness of the machining work piecewith respect to the one using the 3-phase motor drive

1 Introduction

Automatic transmission and control of hydraulic systems(ATACOHS) is one among the high technology developmentdirections in machining and equipment industry Due toits outstanding features such as compact structure greattorque transmission fast response speed self-lubricatingand heat transfer properties of liquid and good system life theresearch on ATACOHS has got very high attention recently[1] Indeed in industrial applications ATACOHS has beenapplied to cutting tools movement system by several cuttingmachinesmanufacturers [2ndash6] Currently there are twomainapproaches in the stepless speed control of a hydraulic motorThe first approach is to change theworkingmode of the pump

and the hydraulic motor which can vary the volume of thepump and the motor [7] or change the speed of the pumpthrough changing the speed of the three-phase electric motorusing an inverter [8]The other one is to change the resistanceon the oil path by a proportional valve or a servo valveThis method is more commonly used because the closedloop control system has a strong relationship between theinputoutput response signals and the feedback signal to thecontroller for minimize the system errors [1 8ndash13]

However there is almost no application to the spindlecluster driven by hydraulic motors because there are manydesign challenges for ATACOHS the dynamic process isa nonlinear relationship due to many factors such as theelasticity of the fluid the relationship between the flow and

HindawiInternational Journal of Rotating MachineryVolume 2019 Article ID 4359524 17 pageshttpsdoiorg10115520194359524

2 International Journal of Rotating Machinery

the pressure the change in viscosity due to oil temperature [114ndash17] the pressure loss in the pipeline the oil leakage insidethe hydraulic elements and the influence of other nonlinearparameters during operation Therefore for simplicity theyusually linearized such nonlinear systems in the controllerdesign process for an ATACOHS [9 18]

With the rapid development of control technology andthe application of that technique to ATACOHS control [19]it is possible to mention some of the applicable controlmethods which are feedback control adaptive control fuzzylogic control neural network control and genetic algorithmcontrol Thus the problems encountered in the precisecontrol of the ATACOHS system are no longer a concernfor designers Each controller has different characteristicsand depending on the actual requirements of the system thedesigner selects a suitable control method However throughthe literature study there are two controllers commonly usedtoday classic PID controllers and fuzzy PID controllers

Classic PID controllers [1 10 16 20 21] are the most com-mon control tools in many industrial applications becausethey can improve response times and steady state errorsOn the other hand the structure of the PID sets is simpleand intuitive with the KPKIKD parameter sets Howeverthe KPKIKD parameter sets are usually fixed during theoperation of the system so it is usually applied to control thehydraulic actuator operating at a fixed output value Ming Xuet al [10] introduced an experimental model for controllingthe velocity of a hydraulic cylinder by using proportionalvalve in combination with a method of controlling the inputspeed of the pump via controlling the speed of three-phaseelectric motor using converter (energy saving solution) Theclassic PID controller was used for processing and speedcontrolling The results of this study indicated accuracy inhigh-speed control fast feedback and good energy efficiencyof the designed controller (at the same condition of 02ms)This approach derived a very good result and can be appliedin practice but its drawback is the high cost Furthermore aspeed control model for a conveyor belt driven by hydraulicmotor through rack and pinion mechanism was introducedby Rong Li and his colleges [20] Through the static anddynamic properties of simulation and initial system analysisthey found that the system was difficult to achieve therequired control accuracy From there they designed the PIDcontroller The results show that the system response hasbeen improved the overshoot from over 312 decreased to184 the response time from 1146s decreased to 00143s theoscillation frequency from 74Hz decreased to 7Hz the erroramplitude is less than 005 and the phase error is less than02 K Dasgupta et al reported the reasonable simulationresults of a hydraulic motor at a value of 50 rads with the PIparameter set (KI = 100 KP = 10)

With the consideration of the effect of oil temperature onthe dynamic properties of servo valves and hydraulic motors[1 17] AAMH AL-Assady et al designed and analyzedthe speed controller for hydraulic motors using proportionalvalves and a PID controller with various parameter sets ofKPKIKD which was established by using the Trial and errormethod Ziegler and Nichols method and Self-turn param-eters by Matlab package Experimental results showed that

when using a classical PID controller the desired dynamicquality is achieved when the temperature range of 60∘C to70∘C at a rotational speed of 700 hydraulic rpm and the loadvaries on the output shaft of the hydraulic motor Fouly Aet al reported the effects of oil temperature on the servomotorrsquos dynamic properties The experiments were carriedout in the case of no load and load of 5560N The effect ofhydraulic oil temperature changes on system performancewas investigated starting from 28 to 500∘C The result at load(5560N) and pressure (50bar) the higher the temperaturesthe faster the flow of oil through the valve (at 280∘C the flowthrough the valve is 4855mls at 400∘C the flow through thevalve is 5669mls and at 500∘C the flow through the valve is6634mls) On the other hand when the temperature risesthe pressure across the valve decreases The above statementsshow that the PID controllers is only suitable for fixed outputsystems and for systems with variable output PID control isno longer suitable

Applying fuzzy PID controllers [9 12 13 22] significantlyimproves the disadvantages of classical PID controllers itgave faster response time no overshoot and less steady stateerror The highlight is KPKIKD automatically adjusted inthe process of operation In particular Kwanchai Sinthip-somboon et al control servohydraulic valve assemblies byapplying a self-adjusting fuzzy PID controller ie the param-eters and PID controller were adjusted using the fuzzy ruleset (Zhang et al 2004 Song and Liu 2010 Zulfatman andRahmat 2006 Feng et al 2009) the results of motor speedcontrol of 100 rpm which was much better than that whenusing PID control

Through the analysis of the above studies we choose theself-adjusting fuzzy PID controller on the proposed modelPrevious publications have studied only one spin volumeand one elastic segment which are not unique but in realsituations there are structures with multiple spin volumesandmultiple elastic properties inmany practical applications

Our difference is that we have two rotational massesand two elastic stages in the proposed model of the speedcontrol of the hydraulic transmission work shaft The fuzzyPID controller is design to control at various setting speedsand takes into account the oil temperature changeThe resultsof the study are verified on the speed response of lathe axis

The main shaft of metal cutting machine plays an impor-tant role in the machining process as it provides cuttingspeeds for the cutting tools and is a part of the transmissionmechanism between the machine and the cutting tools orthe parts When manufacturing on metal cutting machinemanufacturers have studied this problem However eachdesigned model of spindle has different characteristics Thespindle drive is the transmission mechanism of the spindleincluding the drive motor Typically there are two main typesof spindle depending on the type of drive mechanism directdrive and indirect drive (via a belt mechanism or gear drive)In this study we chose the belt mechanism for transmittingthe motion from the hydraulic motor to the main shaft

Based on the analysis of these studies different researchhypothesis will result in different mathematical models anddifferent control applications lead to variation in quality ofthe system dynamics Also as the authors aware there is

International Journal of Rotating Machinery 3

M

Pressure Gauge Filter

Filter

Electrical Motor

Gas-loaded Accumulator with

separatorPr

essu

re

Relie

f Val

ve

Pump

Belt

p0

Belt p Q

Filter Belt

Pressure Gauge

Pres

sure

Re

lief V

alve

Variable rottle Valve

Pump

Directional Valve(22)

Belt

Belt

Belt nt

Belt

ＪＮ

1(Ω1 n1)

0(Ω0 n0)

Load Generation System

Working shaTachometer

Fuzzy self-tuning PID controller

Amplification

Power Unit Proportional Valve

Motor 2-Direction

Figure 1 System configuration

currently no publication on the application of ATACOHSdrive for machinery cutters Thus in this study we proposea model of spindle speed control that simulates the lathespindle assembly In our proposed model we also takeinto account the elastic deformation of the transmissionbelt from hydraulic motors to working shaft the frictionand the value of momentum inertia on the working shaftand also on the rotary axis of the hydraulic motors Theprocedure is as follows Firstly we develop a theoreticalmodel of spindle control set up a dynamic computationalmodel with assumptions mathematical description of thesystem and define the structural parameters of the systemSecondly we fabricate and resemble the working shaft andthe hydraulic transmission Then we develop a self-tuningPID control model define the experimental range of thePID control parameter set and program the system controlprogram on the IDE software [23] and build the interface onMatlabGuide [24 25] The results of the transient responseof the speed stability of the work axes of the theoretical andexperimental are shown graphically The results are verifiedby an application in a machining equipment test

2 Method

21 Research Model The research model of the speed controlof transmission cluster includes the hydraulic motor and V-belt mechanism Figures 1 and 2 show the system configura-tion and experimental model of our study respectively In themodel three-phase electric motor drives the gear of the oilpump through a V-belt the working pressure as well as theoverflow prevention is controlled by an overflow valve and asafety valveThe speed of a hydraulicmotor is regulated by the

Electrical Motor

Belt Pump

Pressure Gauge

Filter

Accumulator

Pump

Proportional valve Motor

Pressure Gauge

Figure 2 Experimental model

oil flow which is controlled by proportional valve [1 10 26]On the oil line from the pump to the proportional valve thereare a high-pressure filter and the battery to accumulate andcompensate for the oil potential energy [10 27 28]

In addition a hydraulic motor transmits rotation to theworking shaft through a V-belt the speedometer of theworking shaft is used as a speed sensor to measure the speedThe speedometer receives the speed signal of the workingshaft through the transmission belt We use the oil pump asthe load equipmentThe load can be changed by changing thepressure (pt) by using overflow valve and safety valve


123

4

5 6 8 9 117 10 12

Figure 3 Picture of experimental system (1 pressure gauge 2 overflow valve and safety valve (maximum pressure 31106Nm2 maxiumumflow rate 567lmin Taiwan) 3 hydraulic power with three-phase motor (22 kW 1420 rpm) operating with the V-belt (transmission ratio is11) to supply oil for gears (volume is 12lowast10minus6m3rev maximum pressure is 20lowast106Nm2) flow rate supplying for the system is 1704lmin 4amplification (Festo Didactic) 5 load generation system 6 working shaft 7 tachometer (Pittman USA no F8412G591 2VKrpm) 8 high-pressure filter Using to filter debris of oil (Parker USA) 9 Hydraulic motor (12lowast10minus6m3rad Rockford illinois Model 16-Z-3) 10 hydraulicaccumulator (34lowast106Nm2 volume 095l) 11 proportional valve (Q = 0divide233lowast10minus4m3s 119901max = 1598lowast106Nm2 119868max = 100mA input voltage0divide24 VDC linear error lt 4 Festo Didactic Proportional valve 43) 12 Arduino (MEGA 2560) digital-to-analog converter (DAC 4921))

Based on the theory mentioned before the test-rig for theexperimental tests is built and shown in Figure 3

22 Mathematical Model The mathematical model of ATA-COHS system is established based on linear system assump-tion [9 18] Both the elastic deformation of the transmissionbelt from the rotary shaft of the hydraulic motor to theworking axis and the friction and the moment of inertia onthe rotor of the hydraulic motor are included (the values inthe hypothesis are chosen from the manufacturer catalog orby measurements) Due to a very small load and nonelasticof belt the transmission of the belt conveyor from workingshaft to speed sensor is considered as a proportional moduleThe analysis model of ATACOHS is shown in Figure 4 andthe system parameters are shown in Table 1

With the established mathematical model and thehypotheses of the system dynamics we describe the math-ematical formulation of the system as follows

On the working shaft

(i) The moment on the working shaft [29]

(1198791 minus 1198792) 1199031 = 1198691 119889212057911198891199052 + 1198911

1198891205791119889119905 +119872119871(119872119871 = 119901119905119863119905119887)

(1)

(ii) Belt horsepower [29]

1198791 = 119896 (11990301205790 minus 11990311205791) 1198792 = 119896 (11990311205791 minus 11990301205790) (2)

(iii) Feedback

119865 = 119870119899119899119905 = 1198701198991198991 119899119905 = 1198991 ( 1198991199051198991 = 1) (3)

On the hydraulic motor [1 8 9 18]

(i) The moment of rotor of the hydraulic motor

1198630119898119901 = 1198690 119889

212057901198891199052 + 11989101198891205790119889119905 + (1198791 minus 1198792) 1199030 (4)

(ii) Flow

Hydraulic motor

119876 = 119863119898 1198891205790119889119905 + 119888119889119901119889119905 + 120582119901

(119888 = 1198811 + 11988122119861 119863119898 = 1198630

1198982120587 )(5)

Proportional valve

119876 = 119870119881119868 (neglecting the flow loss of the valve) (6)

From (1) to (6) we can obtain

21198961199031 (11990301205790 minus 11990311205791) = 1198691 119889212057911198891199052 + 1198911

1198891205791119889119905 + 1198721198711198630119898119901 = 1198690 119889

212057901198891199052 + 11989101198891205790119889119905

+ 21198961199030 (11990301205790 minus 11990311205791)119876 = 119863119898 1198891205790119889119905 + 119888

119889119901119889119905 + 120582119901


Belt

J1

J0

T2

r0

r1

T1T1T2

k k

ML

f1

f0

0mD


Q V1

p

C

Q V2

Kn

-F

u 0E

I

I

Proportional valve

KVAmplification

0

1(Ω1 n1)

0(Ω0 n0)

1

Ｃ =ＨＮ

Ｈ1

= 1

ＨＮ

+

Figure 4 Mathematical model

Table 1 System parameters

Symbol Specifications of the (ATACOHS)Description Source of Information Unit Value

Dm Motor displacement Manufacturer data m3rad 12lowast10minus6V1+ V2

Total fluid volume in pipes Calculated m3 205lowast10minus5B Hydraulic bulk modulus Manufacturer data Nm2 14lowast108120582 Leakage coefficient of motor Calculated experimentally m5Ns 25lowast10minus11k Stiffness of the V-belt Calculated experimentally Nm 20r1

Radius of driven pulley Manufacturer data m 009r0 Radius of drive pulley Manufacturer data m 009J1 Inertia of load Calculated Nms2rad 45lowast10minus3J0

Inertia of motor Calculated Nms2rad 35lowast10minus3T1T2

Tension on the belt Calculated N -Q Input and output flow rate of the hydraulic motor From experimental m3s -p Supply pressure From experimental Nm2 49lowast105I Current of proportional vales (maximum) Manufacturer data mA 100n0

Rotor speed experimentally rpm -n1

Working shaft speed experimentally rpm -KV Valve flow gain Manufacturer data (m3s)mA 115lowast10minus31205790

Rotation angle of rotor Manufacturer data rad -1205791

Rotation angle of working shaft Manufacturer data rad -Kn Tachogenerat or gain Calculated experimentally Vrpm 00167u0

Control voltage Manufacturer data vDC 0divideplusmn10u1 Valve control voltage Manufacturer data vDC 0divideplusmn24f0

equivalent viscous coefficient of motor Calculated experimentally Nmsrad 295lowast10minus4f1

Friction coefficient of working shaft Calculated experimentally Nmsrad 0118ML Load on working shaft Calculated experimentally Nm -


F(s)

u0(s)

200

20 rk2sfsJ

1++

Fuzzy self-tuning PID controller KV

+sc

0mD

E(s) I(s) Q(s)

Dms

2kr0r1

2kr0r1

211

21 rk2sfsJ

1++

ML(s)

Kn

θ1(s) n1(s)0(s)30Ｍ

minus

minus minus+

+

Figure 5 Block diagram

119876 = 119870119881119868119865 = 11987011989911989911198991 = 30120587 Ω1Ω1 = 1198891205791119889119905 119864 = 1199060 minus 119865

(7)

From (7) we have

21198961199031 [11990301205790 (119904) minus 11990311205791 (119904)]= (11986911199042 + 1198911119904) 1205791 (119904) + 119872119871 (119904) lArrrArr

2119896119903111990301205790 (119904) = (11986911199042 + 1198911119904 + 211989611990321) 1205791 (119904) + 119872119871 (119904)1198630119898119901 (119904)= (11986901199042 + 1198910119904) 1205790 (119904) + 21198961199030 [11990301205790 (119904) minus 11990311205791 (119904)] lArrrArr

1198630119898119901 (119904)= (11986901199042 + 1198910119904 + 211989611990320) 1205790 (119904) minus 2119896119903011990311205791 (119904)

119876 (119904) = 1198631198981199041205790 (119904) + (119888119904 + 120582) 119901 (119904)119876 (119904) = 119870119881119868 (119904) 119865 = 1198701198991198991 (119904) 1198991 (119904) = 30120587 Ω1 (119904) Ω1 (119904) = 1199041205791 (119904) 119864 (119904) = 1199060 (119904) minus 119865 (119904)

(8)

From (8) we can build the block diagram of the system asshown in Figure 5

In the theoretical model we just indicate the relationshipbetween the output signal n1 with input signal u0

23 Application of Self-Tuning Fuzzy PID Controller In thispaper the authors used the fuzzy self-tuning PID controllersuch as KPKIKD parameters of the classical PID controllerare adjusted by using the fuzzy detector [9] The cconfigu-ration of the fuzzy self-tuning PID controller is presented

e

+

Fuzzy tuner

KP KI KD

PID Controller

(ATACOHS) Set-point Output

Δe

Sensor

Figure 6 Block diagram of a fuzzy self-tuning PID controller

in Figure 6 Where e is the error between input and outputΔe = dedt is the derivative of e as a function of timeFor the configuration of the fuzzy self-tuning PID con-

troller there are two inputs 119890 and 119890 and three corre-sponding outputs K1015840P K

1015840

I and K1015840D Mamdanirsquos fuzzy law andprocessor are used to obtain the optimal values for KP KIand KD The range of parameters of the PID controller is(KPminKPmax) (KIminKImax) (KDminKDmax) and is obtainedexperimentally on the classical PID controller of ATACOHSThe process of finding the PID controller parameter isconducted at the temperature varying from 40∘C to 80∘CInitially we assumeKI =0KD =0 and then gradually increasethe KP value until satisfying the set limit of the interval ofthe speed (within an error of 5 of the set values) Thenwe choose the average of KP and adjust KD With the samemethod we conduct the experiment with KP and KD sothat it is within the acceptable range Then we choose theaverage of KP KD and continue to adjust KI According tothe experiments the ranges of parameters are obtained asKP isin (0033 0153) KI isin (0 00001) KD isin (0 004) Sothese parameters can be adjusted in the range (01) as [30]

1198701015840119875= 119870119875 minus 119870119875min119870119875max minus 119870119875min

= 119870119875 minus 00330153 minus 0033 119870119875 = 0121198701015840119875 + 0033

1198701015840119868= 119870119868 minus 119870Im119894119899119870Im119886119909 minus 119870Im119894119899

= 119870119868 minus 000001 minus 0 119870119868 = 0000111987010158401198681198701015840119863= 119870119863 minus 119870119863min119870119863max minus 119870119863min

= 119870119863 minus 0004 minus 0 119870119863 = 0041198701015840119863

(9)


Table 2 Fuzzy rules of KP gain

e eNB N Z P PB

NB S S S MS MN S MS MS MS MZ S MS M MB BP M MB MB MB BPB M MB B B B

Table 3 Fuzzy rules of KI gain

e eNB N Z P PB

NB B B B MS SN B MB MB M SZ MB MB M MS SP M MB MS MS SPB M MS S S S

The input variables e and e are symbolized as NB(Negative Big) N (Negative) Z (Zero) P (Positive) and PB(Positive Big) Based on our repeated tests on the PID setthese values are retained Each test will have different rangesof e and Δe values and we choose the range of values thatmostly appear According to characteristics of ATACOHS theinput range of e and e is from -50 to 50 and from -600 to600 respectively The output variables KP KI and KD areseparated as S (Small) MS (Medium Small) M (Medium)MB (Medium Big) and B (Big) with the range from 0 to 1

Next the fuzzy rules [9] of the KP KI and KD variablesare established as shown in Tables 2 3 and 4 respectivelyWe will choose the coefficients that match our ATACOHSThe fuzzy self-tuning PID controller is illustrated in Figures7 and 8

By using MatlabSimulink the fuzzy self-tuning PIDcontroller is plotted in Figure 9

3 Experimental Procedure

31 Control System In order to control the system theArduino Mega 2560 is used The Arduino Mega 2560 is anATmega2560 based microcontroller that allows users to writeand upload control programs to it using IDE programmingsoftware [23 31] The power supply we use in this systemis Elenco Electronics XP-620 For the controller to driveFesto Didactic proporional valve a DAC4921 circuit is usedto converts from digital format with 12bit resolution TheDAC4921 amplifies voltage from -5vDC to + 5vDC fromArduino to voltage from -10vDC to +10vDC The controlblock diagram of the system is shown in Figure 10 Based onthe selection equipment the assembly circuit diagram of thecontrol system is shown in Figure 11

32 Experiments As discussed in previous parts for sim-ulation the system parameters and the block diagram are

shown in Table 1 and Figure 4 respectively In the study theMatlabSimulink is used for the simulation [24 25] Figure 12shows the Matlabrsquos interface of the simulation and then thedata is saved as mat format

For experiments the PID controller automatically adjuststhe control parameters by the algorithm with the programThe control program is written to the Arduino board byIDE programming software The Arduino board connects tothe computer via the virtual COM port and a physical USBconnection The MatlabGuide interface is built-in functionsand procedures for data communication via COM ports [2425] as shown in Figure 13 At least five experiments wereexamined under each condition and the results were averagedto reduce the experimental error and to get reliable resultsFinally the control and feedback signals are stored inmatformat

4 Simulation and Experimental Tests

41 Results andDisscussions Figure 14 represents the result ofa theoretical and empirical investigation of the speed controlof the working shaft driven by a hydraulic motor whose speedis controlled by a proportional valve The results show thedifference of velocity response for setting point simulationand experiment at five setting speeds 300 500 700 900and 1100 rpm Indeed the experimental results for the spindlespeed control work absolutely in line with the theoreticalsurvey results We observe that the difference between thecorresponding values are in the range of 0001 to 0036the difference is very small indicating that the experimentalresults are well consistent with the theoretical conclusionFurthermore the comparison between the simulation andexperimental results at five setting speeds is shown in Table 5From the table the KP KI and KD self-tuning parametersof the controller work very well which means that the speedcontrol range from 300 to 1100 rpm of the working shaft


Table 4 Fuzzy rules of KD gain

e eNB N Z P PB

NB S S S MB BN S MS MS M BZ MS MS M MB BP M MS MB MB BPB M MB B B B

NB1

0

N Z P PB

minus50 50100minus10e

NB1

0

N Z P PB

minus600 0 600minus300 300

S1

0

MS M MB B

0033 0093KP

01530063 0123

S1

0

MS M MB B

0 5E-5KI

25E-5 75E-5

S1

0

MS M MB B

0 002KD

004001 003

1E-4

Δe

Figure 7 Fuzzy sets of a fuzzy self-tuning PID controller

ensures no overshoot and the steady state error is less than5

Compared to our result in the previous research [32]when using fixed PID parameters the system worked wellfor the set point of 2200 rpm (KP = 006 KI = 001 KD =004) However with the set points of 600 rpm and 1000 rpmthe system has overshot This indicated that the classic PIDparameters only work well for certain value

To confirm that the self-tuning fuzzy PID parameter onour system is working well when one of the uncertaintyfactors such as the increase of the temperature of the oil thechange of oil viscosity during the operation period the oillosses in the pipeline oil leaks inside the hydraulic elementsIn this paper we only consider the effect of temperature onthe response of the system

In addition in this study in order to demonstrate thatthe self-tuning fuzzy PID controller works well for the largetemperature range in comparison with [1] the effect ofthe oil temperature is investigated The temperature variesfrom 40 to 80∘C on the work shaft when it rotates at 500900 rpm on the experimental model In this paper we onlychange the oil temperature to investigate speed stability of theworking shaft and other parameters of working oil such asviscosity chemical and physical stability lubrication abilityand foaming are neglected

The transient responses of the speed of the working shaftat 5 difference temperatures (40∘C 50∘C 60∘C 70∘C and80∘C) and 2 speed values (500rpm and 900 rpm) are shownin Figures 15ndash19 Also in order to investigate the effect of oiltemperature on velocity response some comparison valuessuch as set speed actual speed overshoot delay settling timeand error are provided in Table 6The results show that at lowtemperature from 40∘C to 50∘C the delay time is greater thanwhen controlled at temperatures above 50∘C 002 comparedwith 001sec at temperature lower and higher than 50∘Crespectively Also at temperature from 50∘C to 70∘C it showsa very good response in particular the delay time is 001 secand fast response time increases from 253 to 257 seconds at500 rpm and decreases from 272 to 261 seconds at 900 rpmThe error in number of revolutions for the upper and lowerlimits is lower than that in the other temperature range (le50∘C and ge 80∘C) When the temperature is greater than80∘C the rotation error at the steady state increases Thisis suitable because the viscosity of oil is reduced at hightemperatures thus it results in higher loss Figures 14ndash19show that the working shaft speed has little oscillates at steadystate However the range of fluctuation is still less than 5which is the criterion of the transient response of the systemIt is clear that the velocity response of the working shaft isstill good when the fuzzy self-tuning PID controller is used


Table 5 Theoretical and experimental results

Setting speed(rpm) Methodology

ResultsAcutal speed

(rpm) Overshoot () Delay time (s) Setting time (s) Upper bounderror ()

Lower bounderror ()

300 Theory 3001 0 0 253 15 0Experiment 300plusmn10 0 002 263 33 36





08

06

04

02

08

06

04

02

08

06

04

02

de

de

deminus500

minus500

minus600minus400

minus200

e

e

e

KpF

KiF

KdF

200

600400

500

500

minus50

minus50

minus50

0

0

0

0

0 0

50

50

50

Figure 8 The ouput variables of the fuzzy self-tuning PID controller


1Out1

Product2

Product1

Product

Integrator

004Gain2

00001

Gain1

012Gain

dudtDerivative1

dudt

Derivative

0033Constant

Add

1In1

1

Ｍ

times

times

times

+

++

+

+

Figure 9 Fuzzy self-tuning PID simulation in MatlabSimulink


Matlab IDE soware

V-Belt

V-Belt

Synchronous Belts

-5vDC to +5vDC

-10vDC to

+10vDC

Oil

Oil

Oil

Oil

Amplification Hydraulic

Motor

Arduino(Mega 2560)

DAC(4921)Proportional

Valve

Tachometer

working sha Load

Generation System

HydraulicSource

Computer

Power XP-620

USB

Filter accumulator

Figure 10 Control block diagram

Table 6 Experimental results as a function of the oil temperature

Oil temperature(∘C)

Setting speed(rpm)

ResultsActual speed


Lower bounderror ()

40(plusmn2) 500 500plusmn10 0 002 35 26 28900 900plusmn10 0 002 32 22 16





On the other hand in practice the Kp Ki Kd coefficients aregood but vary exponentially (asymptotic to the input signal)Therefore at high temperatures the viscosity of the oil andthe oil friction on the tube wall decreases the opening of thevalve also decreases leading to the oil flow through the valveto the hydraulic motor increases so the response time of thesystem is faster (shown in the dynamic properties of Figures15ndash19 and Table 6)This issue fits in with the findings of FoulyA and Guy [17]

According to the results of Ali Abdul Mohsin Hassan etal [1] the response at 700 rpm with the temperature rangeof 60-70∘C is the best result From their results and ourprevious results [32] it has been confirmed that classicalPID control with fixed parameter is only suitable to workon a certain speed and corresponds to a variable range ofparameters during the operation This is a limitation whenapplied on the spindle of a metal cutting machine becausewhen machining a workpiece with multiple surfaces each


32 3334 3536 3738 3940 4142 4344 4546 4748 4950 5152 53

GND

RESE

T3V

35V G

ND

VIN 0

PWM COMMUNICATION

POWERANALOG

DIG

ITA

L

LM7805

C3104

C11000uF

C2470uF

C4104

R11K

LED1234

8765

5V

22 2324 2526 2728 2930 31

1234

8765 C4

104

R210K

R320K

R610K R7

20K

R8 10K

C6104

R6 10K

R320K

DACMCP4921

OP072

0V

-12V

+12V

OUT

CS

SCK

SDI

1 MATLAB2 ARDUINO IDE

USB

VAC 110V

+12V-12V 0V

+24V

0V

A

B

IN

GN

D

1 2 3 4 5 6 7 9 10 11 12 13 14 15815 17 18 19 20 2116144 3 2 1 05678910111213

GN

DA

REF

COMPUTER

ARDUINO MEGA 2560

DAC4921AMPLIFICATION

POWER XP-620

Figure 11 Assembly circuit

Figure 12 Simulating result on MatlabGuide

of which has a different machining size the cutting speedmust be appropriate to ensure the quality of the final productThus in the machining process it is necessary to change therotation speed of the spindle corresponding to each size ofworkTherefore the PID self-adjusting controller applicationfully complies with our proposed system

42 Application to Metal Cutting Machine The test machinewe propose is a lathe machine which uses hydraulic drive forthe spindle The system is compared to the one that has the

Table 7 Machining parameters selection

Spindle drive Machining parameterThree-phase electric motorsdrive

ntc = 1100(rpm)S = 30(mmmin)t = 02(mm)Hydraulic motor drive

spindle driven by a 3-phase electric motor via an inverter Aphoto of the test machine is shown in Figure 20

The size and details of the workpiece are shown inFigure 21 the selected material is CT38 steel

Choose cutting tool andmachining parameters accordingto Mitsubishi standard as shown in Table 7

The machining of 3 different samples on each systemie a total of 6 samples was taken where the samples 1-3are machined with hydraulic drive system and the samples4-6 machined with three-phase electric motor system Themeasurement of 6 specimenswas processed on themeasuringmachine Mitutoyo Surftest SJ-301 The details of specimentsand of the measurement are shown in Figure 22

The results of the samples 1 2 and 3 are shown in Table 8and the values for Rz and its graphs are on Figure 23



Figure 13 Experimental result on MatlabGuide

0 100 200 300 400 500 600 700 800 900 1000minus200

0

200

400

600

800

1000

1200

Time (numberlowast001sec)

setpointsimulateexperimentally

n1 (r

pm)

Figure 14 Velocity respone of the working shaft

0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000


setpointexperimentally n1=500(rpm)experimentally n1=900(rpm)

n1 (r

pm)

Figure 15 Velocity respone of the working shaft at oil temperature of 40∘C


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000


experimentally n1=900(rpm)setpointexperimentally n1=500(rpm)

n1 (r

pm)


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)

Figure 17 Velocity response of the working shaft at oil temperature of 60∘C

Table 8 Surface roughness results for samples 1 2 and 3

Machining parameters SampleSurface

roughness Rz(120583m)

Average of Rz(120583m) Roughness Grade

ntc= 1100(rpm) 1 2142721381 sim 5S= 30(mmmin) 2 21331

t= 02(mm) 3 21385


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)


On Table 8 we found that the 3 samples had the sameroughness and the average was 21381 (120583m) On the otherhand the profile in the graph (Figure 23) was relativelyuniform according to the corresponding standard (grade 5)

Similarly on Table 9 with the same machining parame-ters we find that the 3 machined samples have the averageroughness value of 26535 (120583m) The profile for each sampleis almost the same and the roughness grade is 5 as shown inFigure 24

Based on the above results we found that with the samemachining process on the two spindle drive systems thesurface roughness was in the same grade (grade 5)

5 Conclusions

In this paper a newmodel for the working shaft transmissionwas designed and built Then the mathematical equations







t= 02(mm) 6 24933

Hydraulic Power ree-phase motor

Hydraulic motor Spindle

Figure 20 Picture of experimental equipment

for the signals of the system can be obtained Furthermorethe fuzzy self-tuning PID controller with the KP KI andKD parameters is chosen for the velocity response of theworking shaft (at different setting speed)This study took intoaccount the set of influenced parameters such as the momentof mass inertia of the work shaft assembly the friction onthe work axis the moment of mass inertia of rotor andviscous friction on the rotational axis of hydraulic engineand the elastic deformation of the transmission belt from thehydraulic motor to the work axis The test-rig of ATACOHSis built and the control program is developed Based on theexperimental results the following conclusions can be made

(1) We proposed a model of two rotational masses andtwo elastic stages with mathematical descriptionsshowing the relationship between the input and out-put signals in the system

(2) Fuzzy PID parameters have been found to control thesystem at different setting speeds

(3) The effect of oil temperature (from 40∘C to 80∘C)to the velocity response of the working shaft isconsidered (this is to confirm that the PID self-adjusting controller is appropriate for our particularapplication) The transient response of ATACOHSshows a good trend However it is better if thetemperature of the oil is not higher than 70∘C

(4) The highlight of this paper is that we have appliedATACOHS on the spindle of the lathe with the mostly

Table 10 Abbreviation

Symbol Description

ATACOHS Automatic transmission and controlof hydraulic systems

WETHK Controller

PID Proportional-Integral-Derivativecontroller

DAC Digital-to-analog converter

IDE Integreted DevelopmentEnvironment

KPis the proportional gain a tuningparameter

KIis the integral gain a tuningparameter

KDis the derivative gain a tuningparameter

e ErrorNB Negative bigN NegativeZ ZeroP PositivePB Positive bigS SmallMS Medium SmallM MediumMB Medium BigB Big

same results of surface roughness with reference tothe three-phase electric system This result will applythe new transmission system for the spindle of themetal cutting tool and the hydraulicmotor system forthe spindle will be synchronous with the tool-feederhydraulic cylinder drive that the manufacturers arecurrently used

(5) The ATACOHS can be developed to apply for con-trolling the spindle of metal cutting machines andspecialized high capacity CNC machines becauseit has many oustanding features such as compactstructure simple to operate and stepless controls ofthe spindle speed without the need of a gearbox

(6) In the next publication we will introduce the rela-tionship between the output signal n1 and the input


70100

26

30

60

28

70100

26

30

profin RZ

Figure 21 Workpiece configuration for machining (CT38)

Figure 22 Details and RZ profiling process of 06 detailed samples

Figure 23 Pictures of Rz and profin graph of samples 123

Figure 24 Pictures of Rz and profin graphs of samples 4 5 6

signal ML The proposed experimental model is thehydraulic spindle lathe driven by hydraulic motorsThe next study will include the investigation ofATACOHS dynamics through the quality of surfaceroughness of machined parts in which the refer-ence spindle drive system is a three-phase electricmotor

Appendix

See Table 10

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The authors would like to extend their sincere thanks tostaffs at the Institute of Mechanical and Automation Danang


University of Science and Technology Vietnam for thesupports and experimental tests

References

[1] A A M H AL-Assady and T J A Mohammad ldquoDesign andanalysis of electro-hydraulic servo system for speed control ofhydraulic motorrdquo Journal of Engineering vol 5 pp 562ndash5732013

[2] M E Graham Jr and L Ronnie ldquoElectro-Hydraulic positioncontrol for amachine tool with actual and commanded positionfeedbackrdquo International Journal of Machine Tool Design andResearch vol 26 1986

[3] A M Minar A Gullu and S Taskin ldquoStatistical investigationof hydraulic driven circular interpolation motionsrdquo IndianAcademy of Sciences vol 37 pp 557ndash568 2012

[4] C C Mbaocha Lakpah E A and A E Jonathan ldquoA numericalmachine tool controller for servomechanismsrdquo InternationalJournal of Scientific and Research Publications vol 5 pp 1ndash42015

[5] httpwwwsendaycomtwenfeeding01html[6] httpmtfujicojpeproductshardturning[7] A C Kong X Zhang andG L Hao ldquoSimulation study on con-

stant speed output control of fixed displacement pump-variabledisplacement motor hydraulic systemrdquo in Proceedings of theInternational Conference on Fluid Power andMechatronics FPM2011 pp 276ndash281 China August 2011

[8] H W Wu and C B Lee ldquoInfluence of a relief valve on theperformance of a pumpinverter controlled hydraulic motorsystemrdquoMechatronics vol 6 no 1 pp 1ndash19 1996

[9] I Sohail N Boumella and C F G Jua A Hybrid of Fuzzy andFuzzy Self-Tuning PID Controller for Servo Electro-HydraulicSystem InTech 2012

[10] M Xu B Jin G Chen and J Ni ldquoSpeed-control of energy reg-ulation based variable-speed electrohydraulic driverdquo StrojniskiVestnik Journal of Mechanical Engineering vol 59 no 7-8 pp433ndash442 2013

[11] R-F Fung Y-C Wang R-T Yang and H-H Huang ldquoAvariable structure control with proportional and integral com-pensations for electrohydraulic position servo control systemrdquoMechatronics vol 7 no 1 pp 67ndash81 1997

[12] A A Ayman ldquoSelf tuning fuzzy logic control of an electrohy-draulic servomotorrdquoACSE Journal vol 5 no 4 pp 67ndash76 2005

[13] P Pornjit T Siripun and T Surapun ldquoA hybrid of fuzzyand proportional-integral-derivative controller for electro-hydraulic position servo systemrdquo Energy Research Journal vol1 no 2 pp 62ndash67 2010

[14] K Majid N Farid S Hossein and S Mozafar ldquoApplicationof a flexible structure artificial neural network on a servo-hydraulic rotary actuatorrdquo International Journal of AdvancedManufacturing Technology vol 39 pp 559ndash569 2008

[15] H M Khalil and M El-Bardini ldquoImplementation of speedcontroller for rotary hydraulic motor based on LS-SVMrdquoExpertSystems with Applications vol 38 no 11 pp 14249ndash14256 2011

[16] M F Rahmat S M Rozali N A Wahab Zulfatman and KJusoff ldquoModeling and controller design of an electro-hydraulicactuator systemrdquo American Journal of Applied Sciences vol 7no 8 pp 1100ndash1108 2010

[17] A Fouly T W Sadak et al Effect of Oil Temperature onthe Performance of A Hydraulic Linear System Controlled with

Electro Hydraulic Servo Valve Department of Production andDesign Engineering Minia University 2015

[18] H E Merritt Hydraulic Control Systems Wiley New York NYUSA 1967

[19] E J Mohieddine and K Andreas Hydraulic Servo-SystemsSpringer London UK 2004

[20] L Rong L Jing S Chun-geng and L Sen ldquoAnalysis of electro-hydraulic proportional speed control system on conveyerrdquoProcedia Engineering vol 31 pp 1185ndash1193 2012

[21] K Dasgupta and H Murrenhoff ldquoModelling and dynamicsof a servo-valve controlled hydraulic motor by bondgraphrdquoMechanism and Machine Theory vol 46 no 7 pp 1016ndash10352011

[22] B B Ghosh B K Sarkar and R Saha ldquoRealtime performanceanalysis of different combinations of fuzzy-PID and bias con-trollers for a two degree of freedom electrohydraulic parallelmanipulatorrdquo Robotics and Computer-Integrated Manufactur-ing vol 34 pp 62ndash69 2015

[23] httpswwwarduinoccenGuideWindows[24] httpsukmathworkscomproductsMATLABhtml[25] httpplaygroundarduinoccInterfacingMATLAB[26] B Eryilmaz and B H Wilson ldquoUnified modeling and analysis

of a proportional valverdquo Journal of The Franklin Institute vol343 no 1 pp 48ndash68 2006

[27] C Peter Principles of Hydraulic Systems Design MomentumPress LLC New York NY USA 2015

[28] K C Gustavo and S Nariman Hydrostatic Transmissions andActuators Wiley 2015

[29] C D Richard and H B Robert Modern Control SystemsPearson Prentice Hall Upper Saddle River 12th edition 2010

[30] N Tran C Le and A Ngo ldquoExperimental investigation ofspeed control of hydraulic motor using proportional valverdquo inProceedings of the International Conference on System Scienceand Engineering (ICSSE) pp 330ndash335 Ho Chi Minh CityVietnam July 2017

[31] httpbinaryupdatescomhow-to-setup-and-program-arduino-board

[32] N H Tran C Le and A D Ngo ldquoExperimental study onspeed stability of lathe spindle driven by hydraulic motorrdquo inProceedings of the 6th National Conference on Mechatronics pp494ndash499 Vietnam 2016

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the pressure the change in viscosity due to oil temperature [114ndash17] the pressure loss in the pipeline the oil leakage insidethe hydraulic elements and the influence of other nonlinearparameters during operation Therefore for simplicity theyusually linearized such nonlinear systems in the controllerdesign process for an ATACOHS [9 18]

With the rapid development of control technology andthe application of that technique to ATACOHS control [19]it is possible to mention some of the applicable controlmethods which are feedback control adaptive control fuzzylogic control neural network control and genetic algorithmcontrol Thus the problems encountered in the precisecontrol of the ATACOHS system are no longer a concernfor designers Each controller has different characteristicsand depending on the actual requirements of the system thedesigner selects a suitable control method However throughthe literature study there are two controllers commonly usedtoday classic PID controllers and fuzzy PID controllers

Classic PID controllers [1 10 16 20 21] are the most com-mon control tools in many industrial applications becausethey can improve response times and steady state errorsOn the other hand the structure of the PID sets is simpleand intuitive with the KPKIKD parameter sets Howeverthe KPKIKD parameter sets are usually fixed during theoperation of the system so it is usually applied to control thehydraulic actuator operating at a fixed output value Ming Xuet al [10] introduced an experimental model for controllingthe velocity of a hydraulic cylinder by using proportionalvalve in combination with a method of controlling the inputspeed of the pump via controlling the speed of three-phaseelectric motor using converter (energy saving solution) Theclassic PID controller was used for processing and speedcontrolling The results of this study indicated accuracy inhigh-speed control fast feedback and good energy efficiencyof the designed controller (at the same condition of 02ms)This approach derived a very good result and can be appliedin practice but its drawback is the high cost Furthermore aspeed control model for a conveyor belt driven by hydraulicmotor through rack and pinion mechanism was introducedby Rong Li and his colleges [20] Through the static anddynamic properties of simulation and initial system analysisthey found that the system was difficult to achieve therequired control accuracy From there they designed the PIDcontroller The results show that the system response hasbeen improved the overshoot from over 312 decreased to184 the response time from 1146s decreased to 00143s theoscillation frequency from 74Hz decreased to 7Hz the erroramplitude is less than 005 and the phase error is less than02 K Dasgupta et al reported the reasonable simulationresults of a hydraulic motor at a value of 50 rads with the PIparameter set (KI = 100 KP = 10)

With the consideration of the effect of oil temperature onthe dynamic properties of servo valves and hydraulic motors[1 17] AAMH AL-Assady et al designed and analyzedthe speed controller for hydraulic motors using proportionalvalves and a PID controller with various parameter sets ofKPKIKD which was established by using the Trial and errormethod Ziegler and Nichols method and Self-turn param-eters by Matlab package Experimental results showed that

when using a classical PID controller the desired dynamicquality is achieved when the temperature range of 60∘C to70∘C at a rotational speed of 700 hydraulic rpm and the loadvaries on the output shaft of the hydraulic motor Fouly Aet al reported the effects of oil temperature on the servomotorrsquos dynamic properties The experiments were carriedout in the case of no load and load of 5560N The effect ofhydraulic oil temperature changes on system performancewas investigated starting from 28 to 500∘C The result at load(5560N) and pressure (50bar) the higher the temperaturesthe faster the flow of oil through the valve (at 280∘C the flowthrough the valve is 4855mls at 400∘C the flow through thevalve is 5669mls and at 500∘C the flow through the valve is6634mls) On the other hand when the temperature risesthe pressure across the valve decreases The above statementsshow that the PID controllers is only suitable for fixed outputsystems and for systems with variable output PID control isno longer suitable

Applying fuzzy PID controllers [9 12 13 22] significantlyimproves the disadvantages of classical PID controllers itgave faster response time no overshoot and less steady stateerror The highlight is KPKIKD automatically adjusted inthe process of operation In particular Kwanchai Sinthip-somboon et al control servohydraulic valve assemblies byapplying a self-adjusting fuzzy PID controller ie the param-eters and PID controller were adjusted using the fuzzy ruleset (Zhang et al 2004 Song and Liu 2010 Zulfatman andRahmat 2006 Feng et al 2009) the results of motor speedcontrol of 100 rpm which was much better than that whenusing PID control

Through the analysis of the above studies we choose theself-adjusting fuzzy PID controller on the proposed modelPrevious publications have studied only one spin volumeand one elastic segment which are not unique but in realsituations there are structures with multiple spin volumesandmultiple elastic properties inmany practical applications

Our difference is that we have two rotational massesand two elastic stages in the proposed model of the speedcontrol of the hydraulic transmission work shaft The fuzzyPID controller is design to control at various setting speedsand takes into account the oil temperature changeThe resultsof the study are verified on the speed response of lathe axis

The main shaft of metal cutting machine plays an impor-tant role in the machining process as it provides cuttingspeeds for the cutting tools and is a part of the transmissionmechanism between the machine and the cutting tools orthe parts When manufacturing on metal cutting machinemanufacturers have studied this problem However eachdesigned model of spindle has different characteristics Thespindle drive is the transmission mechanism of the spindleincluding the drive motor Typically there are two main typesof spindle depending on the type of drive mechanism directdrive and indirect drive (via a belt mechanism or gear drive)In this study we chose the belt mechanism for transmittingthe motion from the hydraulic motor to the main shaft

Based on the analysis of these studies different researchhypothesis will result in different mathematical models anddifferent control applications lead to variation in quality ofthe system dynamics Also as the authors aware there is


M


Filter

Electrical Motor


separatorPr

essu

re

Relie

f Val

ve

Pump

Belt

p0

Belt p Q

Filter Belt

Pressure Gauge

Pres

sure

Re

lief V

alve


Pump


Belt

Belt

Belt nt

Belt

ＪＮ

1(Ω1 n1)

0(Ω0 n0)




Amplification


Motor 2-Direction



2 Method


Electrical Motor

Belt Pump

Pressure Gauge

Filter

Accumulator

Pump


Pressure Gauge





123

4

5 6 8 9 117 10 12







(1198791 minus 1198792) 1199031 = 1198691 119889212057911198891199052 + 1198911

1198891205791119889119905 +119872119871(119872119871 = 119901119905119863119905119887)

(1)


1198791 = 119896 (11990301205790 minus 11990311205791) 1198792 = 119896 (11990311205791 minus 11990301205790) (2)

(iii) Feedback

119865 = 119870119899119899119905 = 1198701198991198991 119899119905 = 1198991 ( 1198991199051198991 = 1) (3)



1198630119898119901 = 1198690 119889

212057901198891199052 + 11989101198891205790119889119905 + (1198791 minus 1198792) 1199030 (4)

(ii) Flow

Hydraulic motor

119876 = 119863119898 1198891205790119889119905 + 119888119889119901119889119905 + 120582119901

(119888 = 1198811 + 11988122119861 119863119898 = 1198630

1198982120587 )(5)

Proportional valve



21198961199031 (11990301205790 minus 11990311205791) = 1198691 119889212057911198891199052 + 1198911

1198891205791119889119905 + 1198721198711198630119898119901 = 1198690 119889

212057901198891199052 + 11989101198891205790119889119905

+ 21198961199030 (11990301205790 minus 11990311205791)119876 = 119863119898 1198891205790119889119905 + 119888

119889119901119889119905 + 120582119901


Belt

J1

J0

T2

r0

r1

T1T1T2

k k

ML

f1

f0

0mD


Q V1

p

C

Q V2

Kn

-F

u 0E

I

I

Proportional valve

KVAmplification

0

1(Ω1 n1)

0(Ω0 n0)

1

Ｃ =ＨＮ

Ｈ1

= 1

ＨＮ

+

















F(s)

u0(s)

200

20 rk2sfsJ

1++


+sc

0mD

E(s) I(s) Q(s)

Dms

2kr0r1

2kr0r1

211

21 rk2sfsJ

1++

ML(s)

Kn

θ1(s) n1(s)0(s)30Ｍ

minus

minus minus+

+


119876 = 119870119881119868119865 = 11987011989911989911198991 = 30120587 Ω1Ω1 = 1198891205791119889119905 119864 = 1199060 minus 119865

(7)

From (7) we have

21198961199031 [11990301205790 (119904) minus 11990311205791 (119904)]= (11986911199042 + 1198911119904) 1205791 (119904) + 119872119871 (119904) lArrrArr

2119896119903111990301205790 (119904) = (11986911199042 + 1198911119904 + 211989611990321) 1205791 (119904) + 119872119871 (119904)1198630119898119901 (119904)= (11986901199042 + 1198910119904) 1205790 (119904) + 21198961199030 [11990301205790 (119904) minus 11990311205791 (119904)] lArrrArr

1198630119898119901 (119904)= (11986901199042 + 1198910119904 + 211989611990320) 1205790 (119904) minus 2119896119903011990311205791 (119904)

119876 (119904) = 1198631198981199041205790 (119904) + (119888119904 + 120582) 119901 (119904)119876 (119904) = 119870119881119868 (119904) 119865 = 1198701198991198991 (119904) 1198991 (119904) = 30120587 Ω1 (119904) Ω1 (119904) = 1199041205791 (119904) 119864 (119904) = 1199060 (119904) minus 119865 (119904)

(8)




e

+

Fuzzy tuner

KP KI KD

PID Controller


Δe

Sensor




1015840



= 119870119875 minus 00330153 minus 0033 119870119875 = 0121198701015840119875 + 0033



= 119870119863 minus 0004 minus 0 119870119863 = 0041198701015840119863

(9)



e eNB N Z P PB



e eNB N Z P PB














e eNB N Z P PB


NB1

0

N Z P PB


NB1

0

N Z P PB

minus600 0 600minus300 300

S1

0

MS M MB B

0033 0093KP

01530063 0123

S1

0

MS M MB B

0 5E-5KI

25E-5 75E-5

S1

0

MS M MB B

0 002KD

004001 003

1E-4

Δe










ResultsAcutal speed


Lower bounderror ()






08

06

04

02

08

06

04

02

08

06

04

02

de

de

deminus500

minus500

minus600minus400

minus200

e

e

e

KpF

KiF

KdF

200

600400

500

500

minus50

minus50

minus50

0

0

0

0

0 0

50

50

50



1Out1

Product2

Product1

Product

Integrator

004Gain2

00001

Gain1

012Gain

dudtDerivative1

dudt

Derivative

0033Constant

Add

1In1

1

Ｍ

times

times

times

+

++

+

+



Matlab IDE soware

V-Belt

V-Belt

Synchronous Belts

-5vDC to +5vDC

-10vDC to

+10vDC

Oil

Oil

Oil

Oil


Motor

Arduino(Mega 2560)


Valve

Tachometer

working sha Load

Generation System

HydraulicSource

Computer

Power XP-620

USB

Filter accumulator




Setting speed(rpm)

ResultsActual speed


Lower bounderror ()









32 3334 3536 3738 3940 4142 4344 4546 4748 4950 5152 53

GND

RESE

T3V

35V G

ND

VIN 0

PWM COMMUNICATION

POWERANALOG

DIG

ITA

L

LM7805

C3104

C11000uF

C2470uF

C4104

R11K

LED1234

8765

5V

22 2324 2526 2728 2930 31

1234

8765 C4

104

R210K

R320K

R610K R7

20K

R8 10K

C6104

R6 10K

R320K

DACMCP4921

OP072

0V

-12V

+12V

OUT

CS

SCK

SDI


USB

VAC 110V

+12V-12V 0V

+24V

0V

A

B

IN

GN

D

1 2 3 4 5 6 7 9 10 11 12 13 14 15815 17 18 19 20 2116144 3 2 1 05678910111213

GN

DA

REF

COMPUTER

ARDUINO MEGA 2560


POWER XP-620
















0 100 200 300 400 500 600 700 800 900 1000minus200

0

200

400

600

800

1000

1200



n1 (r

pm)


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)



0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)







t= 02(mm) 3 21385


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)





5 Conclusions








t= 02(mm) 6 24933










Symbol Description


WETHK Controller












70100

26

30

60

28

70100

26

30

profin RZ






Appendix

See Table 10

Data Availability




Acknowledgments




References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



M


Filter

Electrical Motor


separatorPr

essu

re

Relie

f Val

ve

Pump

Belt

p0

Belt p Q

Filter Belt

Pressure Gauge

Pres

sure

Re

lief V

alve


Pump


Belt

Belt

Belt nt

Belt

ＪＮ

1(Ω1 n1)

0(Ω0 n0)




Amplification


Motor 2-Direction



2 Method


Electrical Motor

Belt Pump

Pressure Gauge

Filter

Accumulator

Pump


Pressure Gauge





123

4

5 6 8 9 117 10 12







(1198791 minus 1198792) 1199031 = 1198691 119889212057911198891199052 + 1198911

1198891205791119889119905 +119872119871(119872119871 = 119901119905119863119905119887)

(1)


1198791 = 119896 (11990301205790 minus 11990311205791) 1198792 = 119896 (11990311205791 minus 11990301205790) (2)

(iii) Feedback

119865 = 119870119899119899119905 = 1198701198991198991 119899119905 = 1198991 ( 1198991199051198991 = 1) (3)



1198630119898119901 = 1198690 119889

212057901198891199052 + 11989101198891205790119889119905 + (1198791 minus 1198792) 1199030 (4)

(ii) Flow

Hydraulic motor

119876 = 119863119898 1198891205790119889119905 + 119888119889119901119889119905 + 120582119901

(119888 = 1198811 + 11988122119861 119863119898 = 1198630

1198982120587 )(5)

Proportional valve



21198961199031 (11990301205790 minus 11990311205791) = 1198691 119889212057911198891199052 + 1198911

1198891205791119889119905 + 1198721198711198630119898119901 = 1198690 119889

212057901198891199052 + 11989101198891205790119889119905

+ 21198961199030 (11990301205790 minus 11990311205791)119876 = 119863119898 1198891205790119889119905 + 119888

119889119901119889119905 + 120582119901


Belt

J1

J0

T2

r0

r1

T1T1T2

k k

ML

f1

f0

0mD


Q V1

p

C

Q V2

Kn

-F

u 0E

I

I

Proportional valve

KVAmplification

0

1(Ω1 n1)

0(Ω0 n0)

1

Ｃ =ＨＮ

Ｈ1

= 1

ＨＮ

+

















F(s)

u0(s)

200

20 rk2sfsJ

1++


+sc

0mD

E(s) I(s) Q(s)

Dms

2kr0r1

2kr0r1

211

21 rk2sfsJ

1++

ML(s)

Kn

θ1(s) n1(s)0(s)30Ｍ

minus

minus minus+

+


119876 = 119870119881119868119865 = 11987011989911989911198991 = 30120587 Ω1Ω1 = 1198891205791119889119905 119864 = 1199060 minus 119865

(7)

From (7) we have

21198961199031 [11990301205790 (119904) minus 11990311205791 (119904)]= (11986911199042 + 1198911119904) 1205791 (119904) + 119872119871 (119904) lArrrArr

2119896119903111990301205790 (119904) = (11986911199042 + 1198911119904 + 211989611990321) 1205791 (119904) + 119872119871 (119904)1198630119898119901 (119904)= (11986901199042 + 1198910119904) 1205790 (119904) + 21198961199030 [11990301205790 (119904) minus 11990311205791 (119904)] lArrrArr

1198630119898119901 (119904)= (11986901199042 + 1198910119904 + 211989611990320) 1205790 (119904) minus 2119896119903011990311205791 (119904)

119876 (119904) = 1198631198981199041205790 (119904) + (119888119904 + 120582) 119901 (119904)119876 (119904) = 119870119881119868 (119904) 119865 = 1198701198991198991 (119904) 1198991 (119904) = 30120587 Ω1 (119904) Ω1 (119904) = 1199041205791 (119904) 119864 (119904) = 1199060 (119904) minus 119865 (119904)

(8)




e

+

Fuzzy tuner

KP KI KD

PID Controller


Δe

Sensor




1015840



= 119870119875 minus 00330153 minus 0033 119870119875 = 0121198701015840119875 + 0033



= 119870119863 minus 0004 minus 0 119870119863 = 0041198701015840119863

(9)



e eNB N Z P PB



e eNB N Z P PB














e eNB N Z P PB


NB1

0

N Z P PB


NB1

0

N Z P PB

minus600 0 600minus300 300

S1

0

MS M MB B

0033 0093KP

01530063 0123

S1

0

MS M MB B

0 5E-5KI

25E-5 75E-5

S1

0

MS M MB B

0 002KD

004001 003

1E-4

Δe










ResultsAcutal speed


Lower bounderror ()






08

06

04

02

08

06

04

02

08

06

04

02

de

de

deminus500

minus500

minus600minus400

minus200

e

e

e

KpF

KiF

KdF

200

600400

500

500

minus50

minus50

minus50

0

0

0

0

0 0

50

50

50



1Out1

Product2

Product1

Product

Integrator

004Gain2

00001

Gain1

012Gain

dudtDerivative1

dudt

Derivative

0033Constant

Add

1In1

1

Ｍ

times

times

times

+

++

+

+



Matlab IDE soware

V-Belt

V-Belt

Synchronous Belts

-5vDC to +5vDC

-10vDC to

+10vDC

Oil

Oil

Oil

Oil


Motor

Arduino(Mega 2560)


Valve

Tachometer

working sha Load

Generation System

HydraulicSource

Computer

Power XP-620

USB

Filter accumulator




Setting speed(rpm)

ResultsActual speed


Lower bounderror ()









32 3334 3536 3738 3940 4142 4344 4546 4748 4950 5152 53

GND

RESE

T3V

35V G

ND

VIN 0

PWM COMMUNICATION

POWERANALOG

DIG

ITA

L

LM7805

C3104

C11000uF

C2470uF

C4104

R11K

LED1234

8765

5V

22 2324 2526 2728 2930 31

1234

8765 C4

104

R210K

R320K

R610K R7

20K

R8 10K

C6104

R6 10K

R320K

DACMCP4921

OP072

0V

-12V

+12V

OUT

CS

SCK

SDI


USB

VAC 110V

+12V-12V 0V

+24V

0V

A

B

IN

GN

D

1 2 3 4 5 6 7 9 10 11 12 13 14 15815 17 18 19 20 2116144 3 2 1 05678910111213

GN

DA

REF

COMPUTER

ARDUINO MEGA 2560


POWER XP-620
















0 100 200 300 400 500 600 700 800 900 1000minus200

0

200

400

600

800

1000

1200



n1 (r

pm)


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)



0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)







t= 02(mm) 3 21385


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)





5 Conclusions








t= 02(mm) 6 24933










Symbol Description


WETHK Controller












70100

26

30

60

28

70100

26

30

profin RZ






Appendix

See Table 10

Data Availability




Acknowledgments




References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



123

4

5 6 8 9 117 10 12







(1198791 minus 1198792) 1199031 = 1198691 119889212057911198891199052 + 1198911

1198891205791119889119905 +119872119871(119872119871 = 119901119905119863119905119887)

(1)


1198791 = 119896 (11990301205790 minus 11990311205791) 1198792 = 119896 (11990311205791 minus 11990301205790) (2)

(iii) Feedback

119865 = 119870119899119899119905 = 1198701198991198991 119899119905 = 1198991 ( 1198991199051198991 = 1) (3)



1198630119898119901 = 1198690 119889

212057901198891199052 + 11989101198891205790119889119905 + (1198791 minus 1198792) 1199030 (4)

(ii) Flow

Hydraulic motor

119876 = 119863119898 1198891205790119889119905 + 119888119889119901119889119905 + 120582119901

(119888 = 1198811 + 11988122119861 119863119898 = 1198630

1198982120587 )(5)

Proportional valve



21198961199031 (11990301205790 minus 11990311205791) = 1198691 119889212057911198891199052 + 1198911

1198891205791119889119905 + 1198721198711198630119898119901 = 1198690 119889

212057901198891199052 + 11989101198891205790119889119905

+ 21198961199030 (11990301205790 minus 11990311205791)119876 = 119863119898 1198891205790119889119905 + 119888

119889119901119889119905 + 120582119901


Belt

J1

J0

T2

r0

r1

T1T1T2

k k

ML

f1

f0

0mD


Q V1

p

C

Q V2

Kn

-F

u 0E

I

I

Proportional valve

KVAmplification

0

1(Ω1 n1)

0(Ω0 n0)

1

Ｃ =ＨＮ

Ｈ1

= 1

ＨＮ

+

















F(s)

u0(s)

200

20 rk2sfsJ

1++


+sc

0mD

E(s) I(s) Q(s)

Dms

2kr0r1

2kr0r1

211

21 rk2sfsJ

1++

ML(s)

Kn

θ1(s) n1(s)0(s)30Ｍ

minus

minus minus+

+


119876 = 119870119881119868119865 = 11987011989911989911198991 = 30120587 Ω1Ω1 = 1198891205791119889119905 119864 = 1199060 minus 119865

(7)

From (7) we have

21198961199031 [11990301205790 (119904) minus 11990311205791 (119904)]= (11986911199042 + 1198911119904) 1205791 (119904) + 119872119871 (119904) lArrrArr

2119896119903111990301205790 (119904) = (11986911199042 + 1198911119904 + 211989611990321) 1205791 (119904) + 119872119871 (119904)1198630119898119901 (119904)= (11986901199042 + 1198910119904) 1205790 (119904) + 21198961199030 [11990301205790 (119904) minus 11990311205791 (119904)] lArrrArr

1198630119898119901 (119904)= (11986901199042 + 1198910119904 + 211989611990320) 1205790 (119904) minus 2119896119903011990311205791 (119904)

119876 (119904) = 1198631198981199041205790 (119904) + (119888119904 + 120582) 119901 (119904)119876 (119904) = 119870119881119868 (119904) 119865 = 1198701198991198991 (119904) 1198991 (119904) = 30120587 Ω1 (119904) Ω1 (119904) = 1199041205791 (119904) 119864 (119904) = 1199060 (119904) minus 119865 (119904)

(8)




e

+

Fuzzy tuner

KP KI KD

PID Controller


Δe

Sensor




1015840



= 119870119875 minus 00330153 minus 0033 119870119875 = 0121198701015840119875 + 0033



= 119870119863 minus 0004 minus 0 119870119863 = 0041198701015840119863

(9)



e eNB N Z P PB



e eNB N Z P PB














e eNB N Z P PB


NB1

0

N Z P PB


NB1

0

N Z P PB

minus600 0 600minus300 300

S1

0

MS M MB B

0033 0093KP

01530063 0123

S1

0

MS M MB B

0 5E-5KI

25E-5 75E-5

S1

0

MS M MB B

0 002KD

004001 003

1E-4

Δe










ResultsAcutal speed


Lower bounderror ()






08

06

04

02

08

06

04

02

08

06

04

02

de

de

deminus500

minus500

minus600minus400

minus200

e

e

e

KpF

KiF

KdF

200

600400

500

500

minus50

minus50

minus50

0

0

0

0

0 0

50

50

50



1Out1

Product2

Product1

Product

Integrator

004Gain2

00001

Gain1

012Gain

dudtDerivative1

dudt

Derivative

0033Constant

Add

1In1

1

Ｍ

times

times

times

+

++

+

+



Matlab IDE soware

V-Belt

V-Belt

Synchronous Belts

-5vDC to +5vDC

-10vDC to

+10vDC

Oil

Oil

Oil

Oil


Motor

Arduino(Mega 2560)


Valve

Tachometer

working sha Load

Generation System

HydraulicSource

Computer

Power XP-620

USB

Filter accumulator




Setting speed(rpm)

ResultsActual speed


Lower bounderror ()









32 3334 3536 3738 3940 4142 4344 4546 4748 4950 5152 53

GND

RESE

T3V

35V G

ND

VIN 0

PWM COMMUNICATION

POWERANALOG

DIG

ITA

L

LM7805

C3104

C11000uF

C2470uF

C4104

R11K

LED1234

8765

5V

22 2324 2526 2728 2930 31

1234

8765 C4

104

R210K

R320K

R610K R7

20K

R8 10K

C6104

R6 10K

R320K

DACMCP4921

OP072

0V

-12V

+12V

OUT

CS

SCK

SDI


USB

VAC 110V

+12V-12V 0V

+24V

0V

A

B

IN

GN

D

1 2 3 4 5 6 7 9 10 11 12 13 14 15815 17 18 19 20 2116144 3 2 1 05678910111213

GN

DA

REF

COMPUTER

ARDUINO MEGA 2560


POWER XP-620
















0 100 200 300 400 500 600 700 800 900 1000minus200

0

200

400

600

800

1000

1200



n1 (r

pm)


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)



0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)







t= 02(mm) 3 21385


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)





5 Conclusions








t= 02(mm) 6 24933










Symbol Description


WETHK Controller












70100

26

30

60

28

70100

26

30

profin RZ






Appendix

See Table 10

Data Availability




Acknowledgments




References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Belt

J1

J0

T2

r0

r1

T1T1T2

k k

ML

f1

f0

0mD


Q V1

p

C

Q V2

Kn

-F

u 0E

I

I

Proportional valve

KVAmplification

0

1(Ω1 n1)

0(Ω0 n0)

1

Ｃ =ＨＮ

Ｈ1

= 1

ＨＮ

+

















F(s)

u0(s)

200

20 rk2sfsJ

1++


+sc

0mD

E(s) I(s) Q(s)

Dms

2kr0r1

2kr0r1

211

21 rk2sfsJ

1++

ML(s)

Kn

θ1(s) n1(s)0(s)30Ｍ

minus

minus minus+

+


119876 = 119870119881119868119865 = 11987011989911989911198991 = 30120587 Ω1Ω1 = 1198891205791119889119905 119864 = 1199060 minus 119865

(7)

From (7) we have

21198961199031 [11990301205790 (119904) minus 11990311205791 (119904)]= (11986911199042 + 1198911119904) 1205791 (119904) + 119872119871 (119904) lArrrArr

2119896119903111990301205790 (119904) = (11986911199042 + 1198911119904 + 211989611990321) 1205791 (119904) + 119872119871 (119904)1198630119898119901 (119904)= (11986901199042 + 1198910119904) 1205790 (119904) + 21198961199030 [11990301205790 (119904) minus 11990311205791 (119904)] lArrrArr

1198630119898119901 (119904)= (11986901199042 + 1198910119904 + 211989611990320) 1205790 (119904) minus 2119896119903011990311205791 (119904)

119876 (119904) = 1198631198981199041205790 (119904) + (119888119904 + 120582) 119901 (119904)119876 (119904) = 119870119881119868 (119904) 119865 = 1198701198991198991 (119904) 1198991 (119904) = 30120587 Ω1 (119904) Ω1 (119904) = 1199041205791 (119904) 119864 (119904) = 1199060 (119904) minus 119865 (119904)

(8)




e

+

Fuzzy tuner

KP KI KD

PID Controller


Δe

Sensor




1015840



= 119870119875 minus 00330153 minus 0033 119870119875 = 0121198701015840119875 + 0033



= 119870119863 minus 0004 minus 0 119870119863 = 0041198701015840119863

(9)



e eNB N Z P PB



e eNB N Z P PB














e eNB N Z P PB


NB1

0

N Z P PB


NB1

0

N Z P PB

minus600 0 600minus300 300

S1

0

MS M MB B

0033 0093KP

01530063 0123

S1

0

MS M MB B

0 5E-5KI

25E-5 75E-5

S1

0

MS M MB B

0 002KD

004001 003

1E-4

Δe










ResultsAcutal speed


Lower bounderror ()






08

06

04

02

08

06

04

02

08

06

04

02

de

de

deminus500

minus500

minus600minus400

minus200

e

e

e

KpF

KiF

KdF

200

600400

500

500

minus50

minus50

minus50

0

0

0

0

0 0

50

50

50



1Out1

Product2

Product1

Product

Integrator

004Gain2

00001

Gain1

012Gain

dudtDerivative1

dudt

Derivative

0033Constant

Add

1In1

1

Ｍ

times

times

times

+

++

+

+



Matlab IDE soware

V-Belt

V-Belt

Synchronous Belts

-5vDC to +5vDC

-10vDC to

+10vDC

Oil

Oil

Oil

Oil


Motor

Arduino(Mega 2560)


Valve

Tachometer

working sha Load

Generation System

HydraulicSource

Computer

Power XP-620

USB

Filter accumulator




Setting speed(rpm)

ResultsActual speed


Lower bounderror ()









32 3334 3536 3738 3940 4142 4344 4546 4748 4950 5152 53

GND

RESE

T3V

35V G

ND

VIN 0

PWM COMMUNICATION

POWERANALOG

DIG

ITA

L

LM7805

C3104

C11000uF

C2470uF

C4104

R11K

LED1234

8765

5V

22 2324 2526 2728 2930 31

1234

8765 C4

104

R210K

R320K

R610K R7

20K

R8 10K

C6104

R6 10K

R320K

DACMCP4921

OP072

0V

-12V

+12V

OUT

CS

SCK

SDI


USB

VAC 110V

+12V-12V 0V

+24V

0V

A

B

IN

GN

D

1 2 3 4 5 6 7 9 10 11 12 13 14 15815 17 18 19 20 2116144 3 2 1 05678910111213

GN

DA

REF

COMPUTER

ARDUINO MEGA 2560


POWER XP-620
















0 100 200 300 400 500 600 700 800 900 1000minus200

0

200

400

600

800

1000

1200



n1 (r

pm)


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)



0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)







t= 02(mm) 3 21385


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)





5 Conclusions








t= 02(mm) 6 24933










Symbol Description


WETHK Controller












70100

26

30

60

28

70100

26

30

profin RZ






Appendix

See Table 10

Data Availability




Acknowledgments




References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



F(s)

u0(s)

200

20 rk2sfsJ

1++


+sc

0mD

E(s) I(s) Q(s)

Dms

2kr0r1

2kr0r1

211

21 rk2sfsJ

1++

ML(s)

Kn

θ1(s) n1(s)0(s)30Ｍ

minus

minus minus+

+


119876 = 119870119881119868119865 = 11987011989911989911198991 = 30120587 Ω1Ω1 = 1198891205791119889119905 119864 = 1199060 minus 119865

(7)

From (7) we have

21198961199031 [11990301205790 (119904) minus 11990311205791 (119904)]= (11986911199042 + 1198911119904) 1205791 (119904) + 119872119871 (119904) lArrrArr

2119896119903111990301205790 (119904) = (11986911199042 + 1198911119904 + 211989611990321) 1205791 (119904) + 119872119871 (119904)1198630119898119901 (119904)= (11986901199042 + 1198910119904) 1205790 (119904) + 21198961199030 [11990301205790 (119904) minus 11990311205791 (119904)] lArrrArr

1198630119898119901 (119904)= (11986901199042 + 1198910119904 + 211989611990320) 1205790 (119904) minus 2119896119903011990311205791 (119904)

119876 (119904) = 1198631198981199041205790 (119904) + (119888119904 + 120582) 119901 (119904)119876 (119904) = 119870119881119868 (119904) 119865 = 1198701198991198991 (119904) 1198991 (119904) = 30120587 Ω1 (119904) Ω1 (119904) = 1199041205791 (119904) 119864 (119904) = 1199060 (119904) minus 119865 (119904)

(8)




e

+

Fuzzy tuner

KP KI KD

PID Controller


Δe

Sensor




1015840



= 119870119875 minus 00330153 minus 0033 119870119875 = 0121198701015840119875 + 0033



= 119870119863 minus 0004 minus 0 119870119863 = 0041198701015840119863

(9)



e eNB N Z P PB



e eNB N Z P PB














e eNB N Z P PB


NB1

0

N Z P PB


NB1

0

N Z P PB

minus600 0 600minus300 300

S1

0

MS M MB B

0033 0093KP

01530063 0123

S1

0

MS M MB B

0 5E-5KI

25E-5 75E-5

S1

0

MS M MB B

0 002KD

004001 003

1E-4

Δe










ResultsAcutal speed


Lower bounderror ()






08

06

04

02

08

06

04

02

08

06

04

02

de

de

deminus500

minus500

minus600minus400

minus200

e

e

e

KpF

KiF

KdF

200

600400

500

500

minus50

minus50

minus50

0

0

0

0

0 0

50

50

50



1Out1

Product2

Product1

Product

Integrator

004Gain2

00001

Gain1

012Gain

dudtDerivative1

dudt

Derivative

0033Constant

Add

1In1

1

Ｍ

times

times

times

+

++

+

+



Matlab IDE soware

V-Belt

V-Belt

Synchronous Belts

-5vDC to +5vDC

-10vDC to

+10vDC

Oil

Oil

Oil

Oil


Motor

Arduino(Mega 2560)


Valve

Tachometer

working sha Load

Generation System

HydraulicSource

Computer

Power XP-620

USB

Filter accumulator




Setting speed(rpm)

ResultsActual speed


Lower bounderror ()









32 3334 3536 3738 3940 4142 4344 4546 4748 4950 5152 53

GND

RESE

T3V

35V G

ND

VIN 0

PWM COMMUNICATION

POWERANALOG

DIG

ITA

L

LM7805

C3104

C11000uF

C2470uF

C4104

R11K

LED1234

8765

5V

22 2324 2526 2728 2930 31

1234

8765 C4

104

R210K

R320K

R610K R7

20K

R8 10K

C6104

R6 10K

R320K

DACMCP4921

OP072

0V

-12V

+12V

OUT

CS

SCK

SDI


USB

VAC 110V

+12V-12V 0V

+24V

0V

A

B

IN

GN

D

1 2 3 4 5 6 7 9 10 11 12 13 14 15815 17 18 19 20 2116144 3 2 1 05678910111213

GN

DA

REF

COMPUTER

ARDUINO MEGA 2560


POWER XP-620
















0 100 200 300 400 500 600 700 800 900 1000minus200

0

200

400

600

800

1000

1200



n1 (r

pm)


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)



0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)







t= 02(mm) 3 21385


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)





5 Conclusions








t= 02(mm) 6 24933










Symbol Description


WETHK Controller












70100

26

30

60

28

70100

26

30

profin RZ






Appendix

See Table 10

Data Availability




Acknowledgments




References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




e eNB N Z P PB



e eNB N Z P PB














e eNB N Z P PB


NB1

0

N Z P PB


NB1

0

N Z P PB

minus600 0 600minus300 300

S1

0

MS M MB B

0033 0093KP

01530063 0123

S1

0

MS M MB B

0 5E-5KI

25E-5 75E-5

S1

0

MS M MB B

0 002KD

004001 003

1E-4

Δe










ResultsAcutal speed


Lower bounderror ()






08

06

04

02

08

06

04

02

08

06

04

02

de

de

deminus500

minus500

minus600minus400

minus200

e

e

e

KpF

KiF

KdF

200

600400

500

500

minus50

minus50

minus50

0

0

0

0

0 0

50

50

50



1Out1

Product2

Product1

Product

Integrator

004Gain2

00001

Gain1

012Gain

dudtDerivative1

dudt

Derivative

0033Constant

Add

1In1

1

Ｍ

times

times

times

+

++

+

+



Matlab IDE soware

V-Belt

V-Belt

Synchronous Belts

-5vDC to +5vDC

-10vDC to

+10vDC

Oil

Oil

Oil

Oil


Motor

Arduino(Mega 2560)


Valve

Tachometer

working sha Load

Generation System

HydraulicSource

Computer

Power XP-620

USB

Filter accumulator




Setting speed(rpm)

ResultsActual speed


Lower bounderror ()









32 3334 3536 3738 3940 4142 4344 4546 4748 4950 5152 53

GND

RESE

T3V

35V G

ND

VIN 0

PWM COMMUNICATION

POWERANALOG

DIG

ITA

L

LM7805

C3104

C11000uF

C2470uF

C4104

R11K

LED1234

8765

5V

22 2324 2526 2728 2930 31

1234

8765 C4

104

R210K

R320K

R610K R7

20K

R8 10K

C6104

R6 10K

R320K

DACMCP4921

OP072

0V

-12V

+12V

OUT

CS

SCK

SDI


USB

VAC 110V

+12V-12V 0V

+24V

0V

A

B

IN

GN

D

1 2 3 4 5 6 7 9 10 11 12 13 14 15815 17 18 19 20 2116144 3 2 1 05678910111213

GN

DA

REF

COMPUTER

ARDUINO MEGA 2560


POWER XP-620
















0 100 200 300 400 500 600 700 800 900 1000minus200

0

200

400

600

800

1000

1200



n1 (r

pm)


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)



0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)







t= 02(mm) 3 21385


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)





5 Conclusions








t= 02(mm) 6 24933










Symbol Description


WETHK Controller












70100

26

30

60

28

70100

26

30

profin RZ






Appendix

See Table 10

Data Availability




Acknowledgments




References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




e eNB N Z P PB


NB1

0

N Z P PB


NB1

0

N Z P PB

minus600 0 600minus300 300

S1

0

MS M MB B

0033 0093KP

01530063 0123

S1

0

MS M MB B

0 5E-5KI

25E-5 75E-5

S1

0

MS M MB B

0 002KD

004001 003

1E-4

Δe










ResultsAcutal speed


Lower bounderror ()






08

06

04

02

08

06

04

02

08

06

04

02

de

de

deminus500

minus500

minus600minus400

minus200

e

e

e

KpF

KiF

KdF

200

600400

500

500

minus50

minus50

minus50

0

0

0

0

0 0

50

50

50



1Out1

Product2

Product1

Product

Integrator

004Gain2

00001

Gain1

012Gain

dudtDerivative1

dudt

Derivative

0033Constant

Add

1In1

1

Ｍ

times

times

times

+

++

+

+



Matlab IDE soware

V-Belt

V-Belt

Synchronous Belts

-5vDC to +5vDC

-10vDC to

+10vDC

Oil

Oil

Oil

Oil


Motor

Arduino(Mega 2560)


Valve

Tachometer

working sha Load

Generation System

HydraulicSource

Computer

Power XP-620

USB

Filter accumulator




Setting speed(rpm)

ResultsActual speed


Lower bounderror ()









32 3334 3536 3738 3940 4142 4344 4546 4748 4950 5152 53

GND

RESE

T3V

35V G

ND

VIN 0

PWM COMMUNICATION

POWERANALOG

DIG

ITA

L

LM7805

C3104

C11000uF

C2470uF

C4104

R11K

LED1234

8765

5V

22 2324 2526 2728 2930 31

1234

8765 C4

104

R210K

R320K

R610K R7

20K

R8 10K

C6104

R6 10K

R320K

DACMCP4921

OP072

0V

-12V

+12V

OUT

CS

SCK

SDI


USB

VAC 110V

+12V-12V 0V

+24V

0V

A

B

IN

GN

D

1 2 3 4 5 6 7 9 10 11 12 13 14 15815 17 18 19 20 2116144 3 2 1 05678910111213

GN

DA

REF

COMPUTER

ARDUINO MEGA 2560


POWER XP-620
















0 100 200 300 400 500 600 700 800 900 1000minus200

0

200

400

600

800

1000

1200



n1 (r

pm)


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)



0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)







t= 02(mm) 3 21385


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)





5 Conclusions








t= 02(mm) 6 24933










Symbol Description


WETHK Controller












70100

26

30

60

28

70100

26

30

profin RZ






Appendix

See Table 10

Data Availability




Acknowledgments




References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





ResultsAcutal speed


Lower bounderror ()






08

06

04

02

08

06

04

02

08

06

04

02

de

de

deminus500

minus500

minus600minus400

minus200

e

e

e

KpF

KiF

KdF

200

600400

500

500

minus50

minus50

minus50

0

0

0

0

0 0

50

50

50



1Out1

Product2

Product1

Product

Integrator

004Gain2

00001

Gain1

012Gain

dudtDerivative1

dudt

Derivative

0033Constant

Add

1In1

1

Ｍ

times

times

times

+

++

+

+



Matlab IDE soware

V-Belt

V-Belt

Synchronous Belts

-5vDC to +5vDC

-10vDC to

+10vDC

Oil

Oil

Oil

Oil


Motor

Arduino(Mega 2560)


Valve

Tachometer

working sha Load

Generation System

HydraulicSource

Computer

Power XP-620

USB

Filter accumulator




Setting speed(rpm)

ResultsActual speed


Lower bounderror ()









32 3334 3536 3738 3940 4142 4344 4546 4748 4950 5152 53

GND

RESE

T3V

35V G

ND

VIN 0

PWM COMMUNICATION

POWERANALOG

DIG

ITA

L

LM7805

C3104

C11000uF

C2470uF

C4104

R11K

LED1234

8765

5V

22 2324 2526 2728 2930 31

1234

8765 C4

104

R210K

R320K

R610K R7

20K

R8 10K

C6104

R6 10K

R320K

DACMCP4921

OP072

0V

-12V

+12V

OUT

CS

SCK

SDI


USB

VAC 110V

+12V-12V 0V

+24V

0V

A

B

IN

GN

D

1 2 3 4 5 6 7 9 10 11 12 13 14 15815 17 18 19 20 2116144 3 2 1 05678910111213

GN

DA

REF

COMPUTER

ARDUINO MEGA 2560


POWER XP-620
















0 100 200 300 400 500 600 700 800 900 1000minus200

0

200

400

600

800

1000

1200



n1 (r

pm)


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)



0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)







t= 02(mm) 3 21385


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)





5 Conclusions








t= 02(mm) 6 24933










Symbol Description


WETHK Controller












70100

26

30

60

28

70100

26

30

profin RZ






Appendix

See Table 10

Data Availability




Acknowledgments




References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Matlab IDE soware

V-Belt

V-Belt

Synchronous Belts

-5vDC to +5vDC

-10vDC to

+10vDC

Oil

Oil

Oil

Oil


Motor

Arduino(Mega 2560)


Valve

Tachometer

working sha Load

Generation System

HydraulicSource

Computer

Power XP-620

USB

Filter accumulator




Setting speed(rpm)

ResultsActual speed


Lower bounderror ()









32 3334 3536 3738 3940 4142 4344 4546 4748 4950 5152 53

GND

RESE

T3V

35V G

ND

VIN 0

PWM COMMUNICATION

POWERANALOG

DIG

ITA

L

LM7805

C3104

C11000uF

C2470uF

C4104

R11K

LED1234

8765

5V

22 2324 2526 2728 2930 31

1234

8765 C4

104

R210K

R320K

R610K R7

20K

R8 10K

C6104

R6 10K

R320K

DACMCP4921

OP072

0V

-12V

+12V

OUT

CS

SCK

SDI


USB

VAC 110V

+12V-12V 0V

+24V

0V

A

B

IN

GN

D

1 2 3 4 5 6 7 9 10 11 12 13 14 15815 17 18 19 20 2116144 3 2 1 05678910111213

GN

DA

REF

COMPUTER

ARDUINO MEGA 2560


POWER XP-620
















0 100 200 300 400 500 600 700 800 900 1000minus200

0

200

400

600

800

1000

1200



n1 (r

pm)


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)



0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)







t= 02(mm) 3 21385


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)





5 Conclusions








t= 02(mm) 6 24933










Symbol Description


WETHK Controller












70100

26

30

60

28

70100

26

30

profin RZ






Appendix

See Table 10

Data Availability




Acknowledgments




References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



32 3334 3536 3738 3940 4142 4344 4546 4748 4950 5152 53

GND

RESE

T3V

35V G

ND

VIN 0

PWM COMMUNICATION

POWERANALOG

DIG

ITA

L

LM7805

C3104

C11000uF

C2470uF

C4104

R11K

LED1234

8765

5V

22 2324 2526 2728 2930 31

1234

8765 C4

104

R210K

R320K

R610K R7

20K

R8 10K

C6104

R6 10K

R320K

DACMCP4921

OP072

0V

-12V

+12V

OUT

CS

SCK

SDI


USB

VAC 110V

+12V-12V 0V

+24V

0V

A

B

IN

GN

D

1 2 3 4 5 6 7 9 10 11 12 13 14 15815 17 18 19 20 2116144 3 2 1 05678910111213

GN

DA

REF

COMPUTER

ARDUINO MEGA 2560


POWER XP-620
















0 100 200 300 400 500 600 700 800 900 1000minus200

0

200

400

600

800

1000

1200



n1 (r

pm)


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)



0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)







t= 02(mm) 3 21385


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)





5 Conclusions








t= 02(mm) 6 24933










Symbol Description


WETHK Controller












70100

26

30

60

28

70100

26

30

profin RZ






Appendix

See Table 10

Data Availability




Acknowledgments




References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




0 100 200 300 400 500 600 700 800 900 1000minus200

0

200

400

600

800

1000

1200



n1 (r

pm)


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)



0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)







t= 02(mm) 3 21385


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)





5 Conclusions








t= 02(mm) 6 24933










Symbol Description


WETHK Controller












70100

26

30

60

28

70100

26

30

profin RZ






Appendix

See Table 10

Data Availability




Acknowledgments




References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)







t= 02(mm) 3 21385


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)





5 Conclusions








t= 02(mm) 6 24933










Symbol Description


WETHK Controller












70100

26

30

60

28

70100

26

30

profin RZ






Appendix

See Table 10

Data Availability




Acknowledgments




References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000



n1 (r

pm)





5 Conclusions








t= 02(mm) 6 24933










Symbol Description


WETHK Controller












70100

26

30

60

28

70100

26

30

profin RZ






Appendix

See Table 10

Data Availability




Acknowledgments




References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








t= 02(mm) 6 24933










Symbol Description


WETHK Controller












70100

26

30

60

28

70100

26

30

profin RZ






Appendix

See Table 10

Data Availability




Acknowledgments




References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



70100

26

30

60

28

70100

26

30

profin RZ






Appendix

See Table 10

Data Availability




Acknowledgments




References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


an investigation on speed control of a spindle cluster...

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