Speed Control of Buck-Converter Driven DC Motor based on Smooth Trajectory Tracking

Speed Control of Buck-Converter Driven DC Motor based on Smooth Trajectory Tracking

Rajendra Kumar Prajapati1 Department of Electrical Engineering, YMCAUST Faridabad , India

Lakhan Singp

Department of Electrical Engineering, JB Institute of Technology Dehradun , India

Ravi Shankar Bahuguna3

Department of Electrical Engineering, JB Institute of Technology Dehradun , India

Abstract:- Speed control is a common requirement in the industrial drives in the presence of varying operating conditions ie. load disturbance, parameter uncertainties . Conventional controllers with fixed parameters are not successful in the real time applications because of the drift in the plants operating conditions This paper presents the detailed account on the control design of a buck converter driven dc motor Proportional-Integral (PI) and Proportional-Integral-type Fuzzy Logic controller (PI-type FLC) are the Techniques proposed in this investigation to control the speed of a dc motor. The dynamic system composed from converter/motor is considered in this investigation and derived in the state-space and transfer function forms. Complete analyses of simulation results for PI and PI-type FLC technique are presented in frequency domain and time domain, respectively. Performances of the controller are examined in terms of duty cycle input energy, armature current and angular velocity. Finally, a comparative assessment of the impact of each controller on the system.

1. INTRODUCTION

   A common actuator in control systems is a dc motor and is obvious choice for implementation of advanced control algorithms in electric drives, due to the stable and linear characteristics associated with it. It is also ideally suited for tracking control. From a control system point of view, the dc motor can be considered as a SISO plant eliminating the complexity associated with multi-input drive systems. The speed of a driven load often needs to run at a speed that varies according to the operation it is required to perform. The speed in some cases (such as fluctuating loads like rolling mills) may need to change dynamically to suit the conditions, and in other cases may only change with a change in process.

   This paper describes the rejection of deviation in speed caused by load disturbance for a separately excited dc motor under various load-disturbing situations, parameter uncertainties and measurement noise with an adaptive control approach resulting in an improved performance. Dc motors are most commonly driven by PWM signals with respect to the motor input voltage. However, the underlying hard switching strategy causes unsatisfactory dynamic behavior. The resulting trajectories exhibit a very noisy shape. This causes large forces acting on the motor mechanics and also large currents which detrimentally

   stress the electronic components of the motor as well as of the power supply [1]. Since it is usually necessary to add a power supply component, anyway, this contribution shall Present a control for the entire system of buck-converter/dc motor. The combination of dc to dc power converters with dc motors has been reported in [2]. In particular, the composition of a buck converter with a dc motor has been proposed in [3, 4]. The buck type switched dc to dc converter is well known in power- electronics. Due to the fact that the converter contains two energy storing elements, a coil and a capacitor, smooth dc output voltages and currents with very small current ripple can be generated [5]. In this respect, an important issue is the circuit design of the converter in order to obtain, at any time, a high power conversion rate when tracking smooth reference trajectories of the angular velocity. Therefore, this stage is

2. DESIGN OF DC MOTOR

Resistance of the coil windings Ra =Armature winding resistance [ohms];

La =Armature winding inductance [Henry];

ia = Armature current [amps];

if =Field current [amps]=a constant; Va =Applied armature voltage [volts]; Eb = Back emf [volts];

m = Angular velocity of the motor [rad/sec];

Tm = Torque developed by the motor [Newton-m];

Jm =Moment of inertia of the motor rotor [kg-m2 or Newton-m/(rad/sec2];

Bm =Viscous friction coefficient of the motor [Newton- m/(rad/sec)];

Tw =Disturbance load torque [Newton-m];

The input voltage Va is applied to the armature which has a resistance of Ra and inductance of La .The field current

supplied if supplied to the field winding is kept constant

the output variable. Therefore the following state space model can represent the dynamics of dc motor.

and thus the armature voltage controls the motor shaft

output. The moment of inertia and the coefficient of

di R K V

viscous friction at the motor shaft being Jm and fm

a a .ia b .m a

dt L L L

(3.1)

respectively .The speed of the motor is being m radian

a a a

per second. The related dynamics equati

dm KT Bm Tw

V R i

• L dia E

(2.1)

dt J

.ia J

.m J

(3.2)

a a a a dt b

m m m

.

Eb Kb.m

(2.2)

X Ax Bu Fw

(3.3)

V R i L dia K

(2.3)

a a a a dt b m

y Cx

Where

x x x

state

T K i (2.4) 1 2

m T a

vector

T J . dm B .

(2.5)

m m dt m m

B K

Taking the Laplace transform of equation (3.1)-(3.5),

m T

0 1

assuming zero initial conditions, we get

A Jm Jm ; B 1 ; F J

K R

m

b a

L 0

Tm (s) KT Ia (s)

(2.6)

L L a

Eb Kb(s)

(2.7)

a a

C 1 0

Ea (s) Eb (s) (La .s Ra )Ia

(Jm.s B) TM (s) TL (s)

(s)

(2.8)

(2.9)

For the design of MRAC controller the triple (A, B, C) are assumed to be completely controllable and observable. The load changes are considered as changes in motor rotor inertia and viscous-friction coefficient as practically seen in most control applications. Hence plant parameter changes in the simulation studies reflect abrupt load changes of the

Equation (2.6)-(.9) gives the transfer function between the

system.

1. MODEL OF BUCK CONVERTER

   motor velocity given as below.

   m (s)

   and the input voltage

   Ea (s) is

   (s) KT

   Ea (s) (Las Ra )(Jms Bm ) KT Kb

   (2.10)

   Figure 1 Block diagram of a DC motor (armature

   Figure 2: Basic structure of BUCK CONERTE scheme

2. REFERENCE MODEL

   The objective of control system is to find a direct controller that is differentiator free and the output of the plant should follow the output of the pre-specified reference model. The

   controlled) system

   model is chosen in the form of W

   (s) k

   Zm (s)

   (5.1)

   III. STATE SPACE REPRESENTATION

   Let the armature current ( ia x1 ) and angular velocity

   m m

   R

   R

   m

   (s)

   Where Zm (s), Rm (s) monic polynomials and km are is

   ( m x2 ) be the state variable and the angular velocity be

   constant gain and r is the reference input assumed to be a uniformly bounded and piecewise continuous function of

   time. The following assumptions regarding reference model are assumed to hold:

   M1. Zm(s), Rm(s) are monic Hurwitz polynomials of degree qm, pm respectively, where pm<=n.

   M2.The relative degree n p q of W (s) is

   time system,the reference model can be selected as the ideal second order system transfer function.

   (s) 2

   m n

   m m m m

   R(s) s2 2 s 2

   n n

   same as that of G (s), i.e., n n .

   p

   (5.2)

   m

   • T

   u T

   In this case, speed desired is 57.6 rad/s (550rpm). The damping coefficient ( ) is taken as one in order to

   represent critical damping. The above design procedure ensures that the reference model is compatible with the

   is available from the adaptive law, the control law

   given by the above equation can be implemented without the use of differentiators.

   Considering the Lyapunov like function as in the previous case for generating adaptive law

   actual motor dynamics..

   Figure 5. Desired trajectory described by reference model

   VII. SIMULATION RESULTS

   A separately excited dc motor with nameplate ratings of 1

   • T

   ~ e P e

   ~ T ~

   1

   hp, 220 V, 550 rpm is used in all simulations. Following parameter values are associated with it. [6]

   2 2

   2 2

   V ( , e) c

   (5.3)

   J =0.068 kg-m2 or Nm/(rad/sec2).

   m

   Bm=0.03475 Nm-sec or Nm/ (rad/sec).

   where Pc Pc 0 satisfies the MKY Lemma.

   e1 sgn(kp / km )

   The signal vector is expressed as

   (5.4)

   600

   500

   Desired trajectory with no overshoot & settling

   1

   (sI F )1.g.u

   p

   p

   p

   p

   (sI F )1.g.y

   (5.5)

   speed (rpm)

   speed (rpm)

   400

   time of 1.8 sec

   s p0 yp

   300

   r

   ~

   200

   Which implies that e, , e1 L and e, e1 L2 .

3. SELECTION OF REFERENCE MODEL

The first step in controller design is to select a suitable reference model for the motor to follow. Let us assume that the dc motor is to behave as a second order system whose input is r(t) and the output is m (t) . For a continuous-

100

0

0 1 2 3 4 5 6

time (seconds)

Ra=7.56 ohms. La=0.055 Henry. KT=3.475Nm-A-1.

Kb=3.475 V/rad/sec.

In this work the adaptive control scheme (MRAC) is simulated for various loading conditions, parameter uncertainties and measurement noise. The performance of the dc motor is studied from no load to full load and open loop to adaptive closed loop. To test the system performance the data of the dc motor are taken from [6].In Figure 2. Tracking performance at full load (12.95 Nm) applied at t=3 sec.

the design maximum control input limit is kept 250 volts and the maximum motor current is 1.5 times of full load current. The adaptation gain of 0.0008 is selected after number of trials, which suits to the rating of the dc motor.

Enlarged view

555

reference

actual

speed (rpm)

speed (rpm)

550

545

540

3 3.5 4 4.5 5 5.5 6

time(seconds)

Figure 4. Tracking performance at 125% of full load applied at t=3 sec.

Enlarged view

555

550

speed (rpm)

speed (rpm)

reference

actual

545

540

3 3.5 4 4.5 5 5.5 6

time (seconds)

Figure 3. Tracking performance at 75% of full load applied at t=3 sec.

VIII. DISCUSSIONS AND CONCLUSION From the simulation results it is inferred that for the limiting value of the control input, the value of adaptation gain can be varied up to certain maximum value. If it is further increased controller parameter does not converge to some constant value. Although as the adaptation gain is increased (within that max value) the adaptation becomes faster on account of becoming control input violently high this may not be compatible to the system. It is also inferred that with the increase in adaptation gain the error becomes

smaller .All the results are found for the adaptation gain of 0.0008. All the results show the values of control input (armature voltage), input current (armature current) and speed as per the motor ratings (plots are not shown due to space constraints).

REFERENCES

1. Siri weerasooriya &Sharkawi,Identification and control of a DC motor using BP neural networks, IEEE transactions on Energy conversion, DEC, 1991

2. El-Sharakawi and Huang, Variable structure tracking of dc motor for high performance applications,IEEE Transactions on Energy Conversions,Vol.4, No.4, December 1989.

3. Siri Weerasooriya & M.A. EI-Sharkawi, Adaptive Tracking Control High Performance DC DrivesIEEE Transactions on Energy Conversion, Vol.4, No.3, September 1989.

4. M.A. EI-Sharkawi & Siri Weerasooriya, Development and Implementation of Self-Tuning Controller for DC Motor IEEE Transactions on Energy Conversion, Vol.5, No.1, March 1990.

5. Jiangno Zhou and Wang, Global speed control of separately excited dc motor,IEEE proceedings, 0-7803-6672-7/01/2001.

6. Dressler M. Robert, An approach to Model Reference adaptive control systems, IEEE Transactions on Automatic Control, vol.12, No.1, pp.75-79, 1967.