designassignment#3_fall2010

8/8/2019 DesignAssignment#3_Fall2010

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ELE 440 Fall 2010 Dr. Gao Design Assignment #3 Due Dec. 3, 2010

Overview:

You are to design and simulate a positioning control system for an industrial application. The system

consists of a digital controller, a DC motor drive (motor and power amplifier), and a load of 235 lbs that is to be

moved linearly by 12 inches in 0.3 second with an accuracy of 1% or better. A belt and pulley mechanism is used

to convert the motor ration to a linear motion. The design process involves:

1. Selection of components including: motor, power amplifier, the belt-and-pulley, the feedback devices

(position sensor and/or speed sensor)2. Modeling of the plant

3. Control design and simulation

4. Implementation and tuning

The step 1 and 2 have been completed by Prof. Don and Jack Zeller with the results shown below. You are to

complete step 3. Hopefully, you will get a chance to do step 4 as part of your job later on. Here we address step 3.

System Parameters:

1) Electrical:

Winding resistance and inductance: Ra=.4 om La= 8 mH (the transfer function of armature voltage tocurrent is (1/Ra)/((La/Ra)s+1) ;

back emf constant:KE=1.49 v/(rad/sec),

power amplifier gain:Kpa=80, current feedback gain: Kcf=.075 v/amp;2) Mechanical:

Torque constant: Kt=13.2 in-lb/amp; motor inertiaJm=.05 lb-in-sec2; Pulley radius Rp=1.25 in; load weight: W=235 lbs (including the assembly);

total inertia Jt=Jm+Jl=.05 +(W/g)Rp2=1.0 lb-in-sec2.With the maximum armature current set at 100 amp, the Maximum Torque = K tIa,max=13.2x100 = 1320 in-

lbs; the maximum angular acceleration = 1320/Jt=1320 rad/sec2, and the maximum linear acceleration =

1320*Rp=1650 in/sec2=4.27 gs(1650/386). As it turned out, they are sufficient for this application.

Simulation Model:

1) Plant model: From the above discussion, the Simulink model of the plant is constructed as follows:

I a

t o t a l

t o r q u e

a n g u l a r

a c c e l a t i o n

a n g u l a r

v e l o c i t rya r m a t u r e

v o l t a g e

c o n t ro l

s i g n a l b a c k e m f e f fe c t

l i n e a r

v e l o c i t ry

l i n e a r

p o s i t i o n

3

I a

2

d X o u t / d t

1

X o u ts

1

v e l t o p o s

s

1

a c c t o v e l

1 . 2 5

R p

8 0

P o w e r a m p

K p a

1 3 . 2

K t

1 . 4 9

K e

. 0 7 5

K c f

. 0 2 s+ 1

2 . 5

A rm a t u re D y n a m i c s

1 . 0

1 / J t+ / -8 V

+ / -1 6 0 V

2

t o rq u e

d i st u rb a n c e

1

V [ c ]

Figure 1 PlantIn Simulink, this can be defined as a single block subsystem: plant, as shown below. Theclosed-loop control with a PID controller can now be simulated.


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dXout/dt

XoutStep

PID

Position PID

V[c]

torque disturbance

Xout

dXout/dt

Ia

Plant Ia

0

Constant

Xout

Figure 2 Closing the loop with a PID controller

Control Design and Simulation: Part I

1) Design a PID controller so that the load is moved 12 inches in .3 second with noovershoot;

2) Employ an industry-standard Trapezoidal Profile, defined as follows:

1 / 0 . 3

no rm a l i z i ng

g a i n

1 2

f i n a l

pos i t i onT rapezo id

S c o p e

s

1

I n t eg ra t o rC loc k

where the trapezoid is defined using the Simulink 1-D lookup table with the inputvector as [0 .1 .2 .3 .4] and the output vector as [0 1.5 1.5 0 0]. Repeat step 3) usingthis profile. What changes do you see in motor voltage and current?

3) Introduce a small (e.g .01%) measurement noise in your simulation (white noise)and observe if the system is still within the specs; gradually increase the level ofnoise and determine the maximum level of noise this system can handle;

4) Determine how much constant torque disturbance this system can tolerate;

5) Introduce a sinusoidal torque disturbance with an amplitude equal to 10% ofmaximum torque, find the highest disturbance frequency this system can handle;

6) Determine the largest tolerable transport delay in the output before the systembecomes unstable.

7) Draw the Nyquist diagram, analyze stability characteristics, and determine the gainand phase margins of the PID loop. Discuss analytically the connection between thephase margin and tolerable transport delay.

8) Determine how much inertia change the control system can handle before itbecomes unstable;

9) Now add a resonant mode, 2

1

( ) 2 1n n

s s

+ + with = .05 and n unknown, to the model

between torque and acceleration as shown below. Determine the lowest resonant frequency the systemcan handle.


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Ia

total

torque

angular

accelat ion

angular

veloci t ryarmature

vol tage

control

signal back emf ef fect

l i near

veloci t ry

l i near

posi t ion

dXo

Xs

1

vel to pos

*.0

1

resonancem ode

s

1

acc to vel

1.25

Rp

80

Power amp

Kp a

13.2

Kt

1.49

Ke

.075

Kc f

.02s+1

2. 5

Armature Dynamics

1. 0

1/Jt+/-8V

+/-160V

2

torque

disturbance

1

V[c]


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Control Design and Simulation: Part II

Repeat Part I using the looping shaping method, compare it with the PID controllerperformance benchmarked in part I; document the design process, the controllerobtained and the improvements, if any, in performance and energy consumption interms of percentage and put the results side by side in a table.

Control Design and Simulation: Part III (Optional, but recommended)

Repeat Part II using the Active Disturbance Rejection Control method. A motion controlexample can be found at http://cact.csuohio.edu/index.php?option=com_content&view=article&id=63&Itemid=78under Materials of ADRC motion controlexample. (Im looking for a flash video showing how ADRC works for the problem in our design project).To understand the general concept of ADRC, see http://cact.csuohio.edu/index.php?option=com_docman&task=doc_download&gid=3&Itemid=54 )

Preliminary Report:

1. Nov. 22nd: Submit a preliminary report on the frequency response analysis of yourprevious PID design, including the open loop Bode and Nyquist plots, the GM and PM, andthe Bode magnitude plot of input disturbance attenuation (from the transfer from betweendi and y).

2. Nov. 29th: Submit a preliminary report on the loop shaping design.

The format of preliminary report is informal.

Formal Final Report:

Write the report in the form of a technical paper, using the IEEE template. It shouldinclude an abstract that summarizes your work; an introduction that provides thebackground, motivation, and the formulation of the control problem (you may also want toinclude some references here on motion control and its applications). Then comes the mainsection of the paper, where you explain the modeling and model verification, the designprocess, reasoning, and the solutions you obtained, using the simulation results as proof. Inthe next section, discuss observations you made, unresolved problems, questions forfurther investigation, etc, and summarize what you have learnt in the entire processworking on this problem during the semester. You may want to move some tediousmathematical derivations, simulation programs, m-files, and some graphical results to anappendix.
http://cact.csuohio.edu/index.php?option=com_content&view=article&id=63&Itemid=78http://cact.csuohio.edu/index.php?option=com_content&view=article&id=63&Itemid=78http://cact.csuohio.edu/index.php?option=com_content&view=article&id=63&Itemid=78http://cact.csuohio.edu/index.php?option=com_docman&task=doc_download&gid=3&Itemid=54http://cact.csuohio.edu/index.php?option=com_docman&task=doc_download&gid=3&Itemid=54http://cact.csuohio.edu/index.php?option=com_content&view=article&id=63&Itemid=78http://cact.csuohio.edu/index.php?option=com_content&view=article&id=63&Itemid=78http://cact.csuohio.edu/index.php?option=com_docman&task=doc_download&gid=3&Itemid=54http://cact.csuohio.edu/index.php?option=com_docman&task=doc_download&gid=3&Itemid=54

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