Title of the Paper (18Pt Times New Roman, Bold) s8

Fuzzy Logic Controller Design Applied to Servo-Drive Systems

ALDO PARDO GARCIA1, JORGE LUIS DÍAZ RODRÍGUEZ2 Universidad de Pamplona Ciudadela Universitaria, Pamplona, Norte de Santander COLOMBIA

http://www.unipamplona.edu.co

Abstract: - This paper presents a Fuzzy Logic Controller (FLC) design procedure for a DC motor servo-drive system. The fuzzy controller is synthesized using information from a previous modeling and simulation for the servo-drive system. A conventional speed control scheme with a PI controller was achieved, taking into account optimality criteria and anti-windup action. Both, conventional and fuzzy control schemes were analyzed and compared via computer simulations. Key-Words: - Motor Control, PI Controllers, Windup, Fuzzy Logic Controllers, Servo-Drive Systems Simulation

1 Introduction Direct Current (DC) motors have been the most used option, when electrical drives that operate in a wide Field Circuit Armature Circuit rank of speed, are needed. This is due to its Re operational properties and their control characteristics. The only essential disadvantage is the Ra La Ia mechanical commutator, which restricts the power Ue e and the motor speed, increases inertia and the axial Ea length and make the motor needs periodic maintenance. Alternating Current (AC) motors are fed with static (a) (b) frequency converters; the commutator is eliminated, Ua but associated costs and complexity are considerable. There exist many schemes of DC motor control. One Fig. 1 DC motor equivalent circuit of them, which is described in this work, is the armature control of a independent field DC motor The electrical and mechanical relationships can be using a controlled rectifier, with speed control using obtained from the equations that rule the dynamic current subordination and limit in a cascade scheme behavior [3]: (multi-loop control) [4], which has relative d ia complexity and a wide speed rank. In this work a Ra ia  La   Ea  Ua fuzzy logic controller (FLC) design procedure for a dt (1) DC motor is presented. FLC is synthesized using Ea  k1  e  wr (2) information from previous modeling and simulation. d wr The efficiency of the proposed scheme is illustrated J   M e  M c with computer simulations and it is compared with a dt (3) conventional control scheme using a PI controller. M e  k  e ia (4) d  e Re ie  N e   ue dt (5) 2 DC motor modeling  e  f ie  The figure 1 shows a DC motor equivalent circuit, (6) where it is possible to distinguish its two main parts, M c  k  e ic (7) the stator, the field circuit in charge of providing the excitation flux (which usually remains as constant Where: and equal to its rated value) and the rotor, the Ra , Re Armature and field resistances. armature circuit, which is responsible for torque L generation which allows load movement and make a Armature Inductance. the rotor turn. ua , ue Armature and field voltages. Grafico de la Corriente e Electromotive Force (Emf). 120  e Field flux. 100 ] ia ic ie p , , Armature, load and field current. m A

w  r , Shaft speed and position. u d a m M M r 60

e c A , Motor and load torque. e d

e e i 40 Field winding turn ratio. r r o k Emf and torque constant. C J Motor and load inertia. 20

0 0 0.2 0.4 0.6 0.8 1 A block diagram for the DC motor is presented in TimeTiempo (Sec)

Figure 2 Grafico(a) de Velocidad 140

I c 120 I c R a 1 / R a W r e I a k f i * T m . s 100 V a E a T a . s + 1 S p e e d

M e c h a n i c s P a r t ] E l e c t r i c P a r t s /

I a d a 80 r [

k f i C u r r e n t a d W r i c

o 60 l e Fig. 2 DC Motor Block Diagram V 40

Where: 20 L R a T  J a Ta  m 2 0 R k  e  0 0.2 0.4 0.6 0.8 1 a (8) TimeTiempo (Sec) [Seg] are the electrical and mechanical time constants, (b) respectively. Fig. 4 Open loop Responses. (a) Current Response and (b) Speed Response. 3 Open Loop Control Simulations for open loop armature voltage control A set-point change, equal to the rated voltage divided scheme were achieved, placing a voltage converter by the converter gain, was applied with zero load (controlled rectifier) in cascade with the motor. current. At time instant t = 0.6 sec. was applied a step Figure 3 and Figure 4 illustrate the time evolution of load change to the rated current. current and speed with this open loop scheme 4 Conventional Closed Loop

I c Control K c R s y s 1 / R s y s W r T c . s + 1 V a e I a k f i * T m s . s The armature closed loop control is implemented V r e f E a T a s . s + 1 C o n v e r t e r M e c h a n i c P a r t S p e e d E l e c t r i c P a r t with the aim of static voltage converters (controlled rectifier). These converters may work in the fourth k f i C u r r e n t quadrant, where they can invert the terminals Fig. 3 Open loop model for DC motor and converter. potential difference, allowing the fourth quadrants control corresponding to mechanical characteristics. Where: In the whole control scheme, the armature control Tc , Kc Time constant and converter gain. loop was achieved using conventional current and speed cascade control. For values lower then the rated Rc , Lc Equivalent converter resistance and speed, the field works with maximum and constant inductance. flux, therefore, the controllers design was achieved R  R  R L  L  L sys a c , sys a c Total motor - converter for the armature circuit. There are two classic PI resistance and inductance. controllers, tuned by optimal methods, using for the L Rsys current controller the optimal module method and for T  sys T  J as ms T 2 the speed controller the symmetrical optimum Rsys k   , e Time constants. method [3, 4]. Figure 5 illustrate the closed loop control scheme.

A set-point change, equal to the rated voltage divided by the converter gain, was applied with zero load current. At time instant t = 0.3 sec., the load current was increased with a step change to the rated current. This simulation results illustrate the efficiency of the conventional closed loop scheme, to regulate the Fig. 5 Conventional Closed Loop Control Scheme system when load changes are applied. Nevertheless, this design does not have too many practical Where: application because the starting current demand is too  The anti-ripple block is a pre-filter to high (approximately 750 A), which could probably smooth effects due to set-point changes, cause damage to the motor. Hence, the need to limit allowing to reduce the maximum over-shoot the starting current; this may be obtained limiting the from 43.4% to 8.1 %, and also to reduce the speed controller output to an established value (in this setting time. case the twice of the nominal current). This is known  The current controller was tuning using as current limit, doing this, it is not necessary the Optimal Module Method. anti-ripple block. In order to obtain a better response  The speed controller was tuning using applying the saturation strategy, windup effect should Symmetrical Optimum. be also considered; to avoid a system undesired  Kcc and Ksv are the current and speed behaviour. feedback sensors gains. 4.1 Saturation and the windup effect Figures 6 illustrate simulation results for the The method is based on saturating the speed conventional closed loop scheme. controller output, which does not allow the armature

G r a f i c o d e l a C o r r i e n t e current exceeds the permissible maximum limit 8 0 0 associated to the motor specifications. This, however, 7 0 0 brings undesirable effects due to the PI controller 6 0 0 integral component. ] p m When the controller is saturated, practically there is A 5 0 0 [ a r u no feedback because although the process output d

a 4 0 0 m r changes, the actuator (converter) remains saturated. A

e 3 0 0 d

e In the meantime, the controller continues integrating t n e i 2 0 0 r r the error. Nevertheless, if the controller is well tuned, o C 1 0 0 it produces an output, although constant, in the

0 correct polarity. When the error is reduced, the value of the integral can be high and a large time is required - 1 0 0 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 in order to the integrator get back a normal value. T i e m p o Time [ S e g ] (Sec) This effect considerably increases the setting time Grafico de Velocidad(a) 140 and may produce oscillations before reaching the

120 stable state. This situation is well-known as “windup effect". A solution based on stopping the integration 100 when the controller is saturated, may reduce the ] s / 80 undesired effects [3]. See figures 7 and 8. d a r [ d

a 60 d S a t u r a t e d c o n t r o l i c o l P e 40 V P r o p o r t i o n a l 1 1 20 1 I s O u t S u m S a t u r a t i o n I n I n t e g r a l I n t e g r a t o r 0

U n s a t u r a t e d c o n t r o l -20 0 0.1 0.2 0.3 0.4 0.5 S u m 2 Tiempo [Seg]Time (Sec) M e m o r y R a t e E r r o r (b) E r r o r Fig 6. (a) Close Loop Current Response (b) Closed Fig. 7 PI Controller with Current Limit and Anti- Loop Speed Response. Windup Action. control, medical instrumentation, decision-support systems and servomechanism applications. [6]

In this section it is presented a procedure for fuzzy logic controller design for a servo drive system using The Matlab® Fuzzy Logic Toolbox, which is an effective tool for the conception and design of fuzzy systems. Fig 8. Closed Loop Control Sheme with Current Limit and Anti-Windup Action. There exists several ways for fuzzy logic controller design [1, 5]. In this section is presented a very A set-point step change, equal to the rated voltage simple step by step design procedure, based on was applied with zero load current. At time instant t = Mamdani linguistic models [7] 0.6 sec. the load current was increased with a step change to the rated value. See figure 9 5.1 Fuzzy Logic Controller for a DC Motor. G r a f i c o d e l a C o r r i e n t e Design Procedure 4 0 5.1.1 Discourse Universe Definition: 3 0 In this step the fuzzy logic controller inputs and ] p outputs are defined. For this application the m

A 2 0 [

r conventional speed PI controller with anti windup u d a and saturation strategies, is substituted by the fuzzy m

r 1 0 A

e controller in the closed loop scheme. According to d

n the before mentioned, the input variables to the fuzzy e

i 0 r r o

C system are the speed error, speed error derivative and

- 1 0 the output is the current set point for the slave current PI controller.

- 2 0 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 TimeT i e(Sec) m p o Inputs: Error [-300,300], G r a f i c o(a) d e V e l o c i d a d Error Derivative [-300, 300] 1 4 0

1 2 0 Output: Output (Current Set Point) [-175,175]

1 0 0 5.1.2 Inputs/Outputs Fuzzy Characterization: ] s /

d According to the servo drive simulation, appropriate

a 8 0 r [

d membership functions for input and output variables a d i

c 6 0 o l were defined. Figures 10, 11 and 12 illustrate the e V fuzzy characterization. 4 0

2 0 b n m n s n 0 s p m p b p 1

0 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 0 . 8 TimeT i e m p(Sec) o [ S e g ] p i h s

(b) r e

b 0 . 6

Fig 9. Closed Loop Responses with Current Limit m e m

f and Anti-Windup action. (a) Current Response, (b) o

e 0 . 4 e r

Speed Response g e D

5 Fuzzy Logic Controller Design 0 During the past few years there have had a rapid - 3 0 0 - 2 0 0 - 1 0 0 0 1 0 0 2 0 0 3 0 0 growth in the number and variety of fuzzy logic e r r o r applications. The applications range from consumer Fig. 10. Error Membership Functions (Input 1) products such as cameras, camcorders, washing machines, and microwave ovens to industrial process Plotting the previous table, using the error as x axis, b n m n s n 0 s p m p b p 1 the error derivative as y axis, and the output, the control signal, as z axis, is obtained the Control 0 . 8 Surface illustrated in figure 14. p i h s r e

b 0 . 6 m e m

e 0 . 4 e r g e

D 1 0 0 0 . 2 5 0 t u

0 p 0 t u O - 3 0 0 - 2 0 0 - 1 0 0 0 1 0 0 2 0 0 3 0 0 - 5 0 d e r r o r Fig. 11 Error Derivative Membership Functions - 1 0 0 (Input 2) 2 0 0 3 0 0 2 0 0 0 1 0 0 b n m n s n 0 s p m p b p 0 1 - 1 0 0 - 2 0 0 - 2 0 0 - 3 0 0 d e r r o r e r r o r 0 . 8 p i

h Fig. 13 Control Surface. s r e

b 0 . 6 m e m

o 5.1.4 Computer Simulations

e 0 . 4 e r g e D

0 . 2 For the computer simulation, the speed PI with anti- windup and saturation strategies was replaced by a 0 Fuzzy Logic Controller (FLC). Aditionally, some

- 1 5 0 - 1 0 0 - 5 0 0 5 0 1 0 0 1 5 0 gains were added to the input and output for a fine O u t p u t adjustment [5]. See figures 14 and 15. Fig. 12 Current Membership Functions (Output 1) E r r o r G a i n

1 G e 1 M u x G y 1 Where the fuzzy sets linguistic labels are: I n O u t P I F u z z y O u t p u t bn Big negative. sp Small positive. G e 2 G a i n mn Middle negative 0 Zero mp Middle positive S u m M e m o r y d e r r o r sn Small negative bp Big positive. G a i n Fig. 14 FLC Computer Simulation Scheme 5.1.3 Rules Base Definition The rules base was obtained from the previous simulation with the conventional PI controller, taking into account the relationship between the error, error derivative and the control signal (current set point). Additionally, the rules were defined trying to improve the behavior obtained with the conventional scheme. Table 1 illustrates the selected rules base for the fuzzy controller. Fig. 15 Closed Loop Block Diagram using the FLC. Table 1: Rules Base for the Speed Controller error Figure 16 illustrate the FLC efficiency, it may be

bn mn sn 0 sp mp bp observed the improvements in the current and speed

responses if they are compared with conventional PI bn bn bn bn bn 0 0 0

d mn bn bn mn mn 0 0 0 controller in figure 9.

r pn bn bn sn sm sp sp mp

r 0 bn mn sn 0 sp mp bp A set-point change, equal to the rated voltage, was sp mn sn sn sp sp bp bp applied with zero load current. At time instant t = 0.6 mp 0 0 0 mp mp bp bp sec. the load current was increased with a step change bp 0 0 0 bp bp bp bp to the rated value. G r a f i c o d e l a C o r r i e n t e 3 5 References: 3 0 [1]. Cox, E. The Fuzzy System Handbook.

2 5 AP, 1994. ] p m A

[ [2]. Dewan, S. B., G. R. Slemon and A.

a 2 0 r u

d Straughen, Power Semiconductor Drives, Wiley, a m

A 1984.

n [3]. Leonhard, W, Control of Electrical e i r r o Drives. Springer – Verlag, 3rd ed., 2001. C 5 [4]. Pardo G., A. and Díaz R., J. L. 0 Fundamentos en Sistemas de Control - 5 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 Automático. Ed. Universidad de Pamplona, TimeT i e m p o(Sec) [ S e g ] Colombia, 2004. G r a f i c o(a) d e V e l o c i d a d 1 4 0 [5]. Passino, M. K. and Yurkovich, S. Fuzzy Control. Addison – Wesley, 1998. 1 2 0 [6]. Zadeh, L.A. Fuzzy Logic, Computer, 1 0 0 Vol. 1, No. 4, pp. 83-93, 1988. ] s /

d [7]. R. R. Yager and D. P. Filev, Essential

a 8 0 r [

d of Fuzzy Modelling and Control John Wiley a d i

c 6 0 o

l and Sons, USA, 1994 e V

0 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 TimeT i e m p(Sec) o [ S e g ] (b)

Fig. 16 Close Loop Responses with the FLC. (a) Current Response, (b) Speed Response

5 Conclusions

A fuzzy logic controller for a DC servo drive system was presented. The fuzzy controller is synthesized using information from a previous modeling and simulation for the servo-drive system. The efficiency of the proposed fuzzy scheme was analyzed and compared with a conventional scheme using a PI controller tuned using symmetrical optimum and optimal module methods [3, 4], with saturation and anti-windup strategies.

The fuzzy control scheme provided better current and speed responses without overshoot, when load changes are applied. Additionally, with FLC, the current never take negative values, which would produce braking torques in the motor.