A First Course in FUZZY and NEURAL CONTROL

2.7. PROPORTIONAL-INTEGRAL-DERIVATIVE CONTROL 69

Figure 2.35. Step response withKp= 500andKd=10

Figure 2.36. Step response withKp= 500andKd= 100

There is no question that the response is critically damped. However, the
steady-state error is not within the acceptable tolerance of being less than 2%.
The answer lies in providing an appropriate amount of integral control that will
bring the error to within the acceptable tolerance. We can implement integral
control action as illustrated in the followingMatlabcode:

kp=500; %Proportional gain

ki=1; %Integral gain

kd=100; %Derivative gain

numc=[kd kp ki] %Define numerator polynomial of PID controller

denc=[1 0] %Define denominator polynomial of PID controller

den=conv(denc,densys);

%Convolve the denominator polynomials of system and controller

sysopenloop=tf(numc,den); %Obtain open-loop TF

sysfeedback=[1]; %Feedback TF