Robust Current-Mode DC Drive

Aisha Akbar Awan,Mohammad Bilal Malik

Department of Electrical Engineering, College of Electrical and Mechanical Engineering Rawalpindi

National University of Sciences and Technology(Pakistan)

aishamaryum@hotmail.com, mbmalik@ceme.edu.pk

Abstract— In this paper, we propose a robust controller that

converts a conventional voltage-mode H-bridge into a current-

mode drive. The design has also been physically implemented.

This technique results into low-cost, high performance machine drive.

Keywords-component; current mode drives, dc machine, output regulation, disturbance rejection, observer design.

I. INTRODUCTION

PWM based machine drives with current control loops have gained popularity. Although mainly work done on current mode control technique encompasses around inverters and ac drives. The current source controlled is particularly suited for drive systems working in high dynamic conditions such as servo drives for machine tools and robotics[1]. For current-mode controlled drives researchers have introduced various techniques which include hysteresis control, predictive control, adaptive control, ramp compensation, vector-based control techniques. A part from these techniques sliding mode control was being adopted by researchers to deduce current control scheme for dc motor drives[2-3].This technique required extensive calculations to calculate load parameters. Auto tuning technique was proposed in [3] which allows the algorithm to be applied without load information but this has made its implementation bit difficult.

Among these technique hysteresis mode control has gained lot of popularity because of good transient response and ease in implementation requiring minimum hardware [4-8].The main discrepancies of this method is wide variations in frequency, produces current ripples in steady state and is sensitive to phase commutation which subsequently results in generating PWM noise. For reducing current ripples and better steady state response vector-Control and predictive control method were used but their accurate and extensive calculations of parameters to assure good response made them quite complicated[9-11].Ramp compensation technique operates at fixed frequency and inductor current which directly controls the duty cycle of the switch. But these are prone to sub harmonic oscillations when dutycycle approach 50%. In our approach we have used regulator theory and observer design to control current drive. This method has eliminated lengthy calculations of load parameters[12-14].

Section –II will introduce the concept of current drives, role of conventional switches in h-bridge which drives the dc-machine. Section-III will describe interfacing of h-bridge and

dc machine. Section-IV will introduce the robust current mode output feedback regulation controller with its simulation results. Conclusion is presented in Section-V.

II. CURRENT MODE DC-DRIVE:

This section encompasses around the main idea of current mode controlled dc drive scheme. Current drive is preferred over conventional voltage-mode drives because it can directly control the torque of a dc-machine. The operation of current- controlled dc machine can be comprehended by figure-1.Here Q1, Q2, Q3 and Q4 are n-channel MOSFETs. „M‟ is the dc machine whose output current is being monitored by the current sensor continuously. On the basis of output current and reference current error is being calculated. This error signal controls the PWM of the four MOSFETs.

Figure.1 Schematic Diagram of Current Driven DC-Machines

A. Conventional H-bridge and its modes of operation

H-bridge is used for controlling direction, speed and operating modes of dc-machine. For simplification of model we have taken ideal switches having zero rise and fall time to avoid

2011 IEEE Applied Power Electronics Colloquium (IAPEC)

978-1-4577-0008-8/11/$26.00 ©2011 IEEE 28

shorting at one side of bridge. In addition to switches diodes play an important role by connecting in anti-parallel direction to the switches. Whenever DC-Machine has been controlled with H-bridge it can operate in many different modes.

B. Mode-1

In this mode switch 1 and switch 4 are ON for ton. Left Side of the bridge gets connected to voltage source and other side gets connected to the ground. Energy will be flowing from source to the dc machine. During this time, current will increase from 0 to maximum; dc machine is absorbing electrical energy from supply and converting it into mechanical energy so it is working as motor in this mode. Average applied

voltage is given by: ( )s eD v v

Here D is duty cycle vs is applied voltage and ve is the back EMF generated.

C. Mode-2

For current controlled machine devices, we have a choice of the recirculation path the current flows in “off-time”.

In our model for “off-time” duration machine will send back the energy to power supply. Inductor has stored current in ton time and it will act as current source during off duration.

Inductor discharges the current depending on the time constant and current will flow through the anti-parallel diodes now. Here machine is sending back energy to power supply. The motor is forcing current right through its armature, through Q2‟S diode then back to supply.

In this mode mechanical energy is being converted to electrical energy so it is acting as generator. H-bridge applies average applied voltage during “off time” will be given as:

(1 )( )s eD v v

Average applied voltage to the dc machine is:

( ) (1 )( )ap s e s ev D v v D v v

Switch 1 and 4 are turned on for 30% of the time period and for rest of the time period all switches are turned off. Current will initially flow through MOSFET 1 and 4 forcing the machine to work as motor in “ON” duration. For rest of the time inductor will discharge its current through diode and back to the battery. Here in this duration it will work as generator. The net armature current has been shown in figure:2 for 30% on time.

Figure2: Armature Current of DC-Machine

III. MACHINE MODEL:

In dc machines armature current varies depending on the load conditions and applied voltage. We represent variations of the armature current by the following first order differential equation.

aap a a a

div R i L

dt

(1)

This equation represents dc-machine where Ra, ia, La represents armature resistance, armature current, armature inductance.

The average voltage seen by the machine will depend on duty cycle.

+

-

+

29

( ) (1 )( )ap s e s ev D v v D v v

(2)

Whenever motor starts spinning because of change of flux it induces EMF which varies linearly with speed. This back-EMF has been taken as disturbance in the average applied voltage.

e ev k

(3)

Let armature current be the state of the system.

1x i

(4)

11 ap av R xdx

dt L

(5)

11

evdxax bu

dt L

(6)

Now here ;

;R

aL

1

bL

(2 1) su D v

IV. OUTPUT TRACKING CONTROL:

Traditional control theories don‟t model disturbances and reference signals. Utilizing the generalized output regulation technique mentioned in [15] improves the overall performance of current drive. The system is discretized through zero order hold equivalence. Our discrete system is represented by

[ 1] [ ] [ ] [ ]x k ax k bu k Pw k

(7)

Here, x[k] represents the armature current, u[k] is average applied voltage seen by the dc machine. System is subjected to disturbance represented by Pw[k].

Where;

P= [0 b];

In our system we can model class of disturbance and reference signals by;

[ 1] [ ]w k Sw k

(8)

Where;

1 0;

0 1S

1

2

[ ][ ]

[ ]

w kw k

w k

1[ ]w k is the reference signal to be tracked and2[ ]w k is the

disturbance to be rejected.

2[ ]ev w k disturbance

Now the output of our system will be represented by this:

[ ] [ ];y k Cx k

(9)

1;C

Tracking error has been given as;

[ ] [ ]e k Cx k Qw

(10)

Where,

1 0Q

1. When Eigen values of S are outside the unit circle.

2. The pair(A,B) is stabilizable

If these two assumptions hold. Then the output regulation problem via full information feedback is solvable if and only if there exist matrices and which solve linear matrix equations.[15] We can then design a suitable tracking controller which makes the system stable.

1 2 2 2 1 1 1 2 1 1 1 2 1 2S A B P

1 1 1 2 1 20 C Q

(11)

Where;

1 2 1 0 ;

1 2

11

a

b

and solved linear matrix equations so suitable feedback tracking control can be achieved which is given by;

( )u K x w w

(12)

where K is an arbitrary feedback such that (A+BK) should be

stable.

The input for suitable tracking controller which makes the

system stable is given by:

[ ] [ ] [ ] [ ]u k Kx k Nr k d k

(13)

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A. Observer Design

Using output feedback the objectives for closed loop state equation are that output signal should track any constant reference input. The basic idea behind this problem is to use observer so that it can generate asymptotic estimates of both the plant state and the disturbance.

The plant has been represented as :

[ 1] [ ][ ]

[ 1] 0 1 [ ] 0

x k a b x k bu k

d k d k

[ ]

[ ] 1 0[ ]

x ky k

d k

(14)

Observer design has been represented as

[ 1] [ ] [ ]B [ ] ( C )

[ 1] [ ] [ ]

x k x k x kA u k H y

d k d k d k

(15)

Output feedback tracking control has been continuously rejecting the disturbance at the input. Our suitable output feedback tracking control has been given as:

[ ] [ ] [ ] [ ]u k k x k Nr k d k

(16)

Figure 3: Output Feed Back Tracking Control

0 100 200 300 400 500 600-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

time (sec)

Curr

ent(

A)

output armature current

Error between output andreference current

Figure 4:Simulated Results of Regulated Output Current and Error

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We can see error of the system is going to be zero in a finite time. So system is asymptotically stable. System is achieving desired current in finite time by utilizing low cost sensor.

V. EXPERIMENTAL RESULTS:

The current-mode drive has been physically implemented. We have monitored output current of the dc- machine through current sensor.

For experimental verification of results we have used dc machine which has armature resistance and inductance given by these parameters. Ra = 1 Ω, La =2.1mH, Iref =1A . The duty cycle has been calculated which controlled the PWM of the H-bridge as per figure 5. On the basis of output current and reference current duty cycle has been established which ultimately reduces the error of the system to zero as per figure 7and achieves perfect tracking shown in figure.6

0 100 200 300 400 500 600 700 8000.4

0.5

0.6

0.7

0.8

0.9

1

tme(sec)

pw

m

PWM

Figure 5:PWM of the Current Drive

0 100 200 300 400 500 600 700 8000.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

time(sec)

outp

ut

curr

ent

Output Current

0 100 200 300 400 500 600 700 800-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

time(sec)

err

or

Figure 6: Output Current of Practical Systems

Figure 7: Error of the System

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VI. CONCLUSION:

A robust current-mode control scheme for dc drives is presented in this paper. It has been shown that the proposed algorithm achieves asymptotic stability in a finite time. This scheme has utilized Generalized Output Regulation which modeled disturbances and references signals improved overall transient and steady state response of current drive. The disturbances are being continuously rejected which is improving the performance of the system. The experimental results depict the effectiveness of proposed scheme.

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