Pid And Fuzzy Logic Controllers

Performance Evaluation of Digital Control Algorithms for A DC Motor System Heng-Ming Tai Department of Electrical Engineering University of Tulsa

DC Motor Control Objectives • Achieve fast and smooth speed response • Robustness to load variations

• However, due to saturation nonlinearity in the speed control loop, windup effect degrades the performance of the PID controller. • Input command to the motor is saturated because of the magnetic saturation and motor overheating protection.

• Both anti-windup PID and fuzzy logic controllers achieve similar control performance. • Improved performance includes small overshoot, short settling time, and robustness.

Control Block Diagram r

+

e

Fuzzy Logic, PID,

u

umax

uc

or Anti-Windup PID Control

yP Motor

umax

(Speed)

e(k) = r(k) - yp(k) ∆e(k) = e(k) - e(k-1) uc(k) = Nu F[Ne e(k), N∆e ∆e(k)] • • •

Ne, N∆e, and Nu are scaling factors e(k) and ∆e(k): the error and change of error of dc motor speed F represents the FLC operation

◆ Scaling factors are tuned according to hardware specification and system response

Experimental Setup IBM 486 Brake TMS320C30 EVM ADC

DAC

Amplifier Circuitry

Attenuator

DC motor

Tachometer

Fuzzy Logic Control Scheme Fuzzy IF-THEN Rules & Membership Functions Ne N∆e Crisp inputs e(k), ∆e(k)

Nu Fuzzification

Inferencing

Defizzification

Crisp output uc(k)

Membership Functions µ NB

NS 1 ZE PS

NM

-1 -0.8

-0.4

-0.15

0 0.15

PM

0.4

PB

0.8

1

e(k), ∆e(k)

µ NB

NM

-1

-0.66

NS

-0.33

ZE

1

0

uc(k)

PS

PM

PB

0.33

0.66

1

Fuzzy Logic Rules Fuzzy IF-THEN rules are derived from heuristics and knowledge of the system response. IF e(k) is L1 AND ∆e(k) is L2 , THEN u is U1 e(k) ∆e(k)

NB

NM

NS

NB

ZE

PS

NB

NB

PM

PB

NM

NB

NB

NB

NS

NB

NM

NM

NM

PM

ZE

NB

NS

ZE

PS

PM

PB

PS

NM

PS

PS

PM

PM

PB

PM

PB

NM

PM PB

PM

PB

PID Control Continuous-time:

u (t ) = K p e(t ) + K i ∫ e(τ ) dτ + K d

de(t ) dt

Discrete-time:

u ( k ) =+u((0k.5−K1)i T+ −( KKpp +−02.5KKd i/TT+)eK(kd −/ T1))e+((kK) d / T )e(k − 2) K p = 50, K i = 0.2, and K d = 0.05

Discrete-Time PID Control

Kd (1 − z −1 ) T

r

+

e

Kp

u

umax

uc umax

K i T (1 + z −1 ) 2(1 − z −1 )

yP Motor

Discrete-Time Anti-Windup Control Ka was chosen large enough so that the anti-windup compensation is capable of following e to keep the output from saturating

Kd (1 − z − 1 ) T +

e Kp

umax

u

+

uc -umax

e1

−1

KiT (1 + z ) 2(1 − z −1 ) 2 z −1 K i T (1 + z −1 )

+

+

rpm

Step response with load

PID Control

PID AntiWindup Control

Fuzzy Logic Control

rpm

Speed response without load

PID Control

PID AntiWindup Control

Fuzzy Logic Control

rpm

Speed response with load

PID Control

PID AntiWindup Control

Fuzzy Logic Control