A First Course in FUZZY and NEURAL CONTROL

76 CHAPTER 2. MATHEMATICAL MODELS IN CONTROL

Figure 2.44. System response

Figure 2.44, where the system response is examined for different values of the
proportional gain. From the response shown in Figure 2.44, we observe that
KP =30provides sufficiently good rate of rise so that an appropriate choice
of derivative gain may be chosen to reduce the overshoot and thereby improve
the settling time. We now examine the system behavior for various values of

Figure 2.45. System response

derivative gainKD,withKP=30. It is clear that forKD=0. 35 the overshoot
is negligible, and the settling time is well within the desired specification of 40
milliseconds. Also, the steady-state error is nearly zero. Hence, a PD controller
would work well for this example.
Note in Figure 2.45 that forKP=30andKD=0. 25 , the overshoot is within
the 5% tolerance. Suppose we decide to choose these parameters and include
integral control to ensure near-zero steady-state error. We could chooseKIin
the range of 1 − 100 and still be within the design specifications. AMatlab
simulation of thefinal PID controlled system response is illustrated in Figure
2.46.
In summary, the design of a PID controller is iterative in nature. There is
no unique solution for the PID parameters. The selection of parameters may
however be governed by hardware limitations. A systematic approach can yield