A First Course in FUZZY and NEURAL CONTROL

70 CHAPTER 2. MATHEMATICAL MODELS IN CONTROL

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

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

Figure 2.37. Step response withKp= 500,Ki=1. 0 ,andKd= 100

As you can see in Figure 2.37, the addition of a small integral gain, in this
caseKi =1. 0 , has practically no effect in improving the steady-state error.
Note that it would be wise to create a bit of an overshoot and then adjust the
steady-state error. This is where one needs to perform some trial and error, with
some practical knowledge of the limitations of components that will be involved.
Saturation and other limiting factors dictate how these parameter variations can
be made to obtain satisfactory control performance. In this example, however,
we illustrate the systematic nature of the design and the criteria that have to
be met in order to build successful controllers.
Proceeding further, we increase the proportional gain and decrease the deriv-
ative gain to obtain an overshoot within desirable criteria. We also increase the

Figure 2.38. Step response withKp= 1400,Ki= 1000,andKd=75