A First Course in FUZZY and NEURAL CONTROL

2.7. PROPORTIONAL-INTEGRAL-DERIVATIVE CONTROL 67

Figure 2.32. Step response of the open-loop transfer function

As outlined previously, thefirststepistoimprovetherisetimesuchthatthe
plant response is at or near the desired level. So, we proceed tofirst implement
proportional control. In the followingMatlabcode, we start by inputting
alowvalueofKdas a start to examine the effect of proportional gain rise
time and subsequently on the error. The followingMatlabcode implements
proportional control:

kp=10; %Proportional gain

sysopenloop=tf(kp*numsys,densys); %Open-loop transfer function

sysfeedback=[1]; %Unity feedback

sysclosedloop=feedback(sysopenloop,sysfeedback);%Closed-loop TF

step(sysclosedloop,0:0.001:2.0); %Step input response

Figure 2.33. Step response withKd=10

Figure 2.33 illustrates the step response of the system with proportional
gain control. Certainly, there is marked improvement in the rise time and also
in thefinal value. The steady-state error has been considerably reduced, but not
enough. The main observation is that the rise time is considerably faster than