A First Course in FUZZY and NEURAL CONTROL

60 CHAPTER 2. MATHEMATICAL MODELS IN CONTROL

Figure 2.23. Simulation diagram

The closed-loop transfer function therefore is given by

Y(s)

F(s)

=

G(s)

1+G(s)

=

0. 8

s

1+^0 s.^8

=

0. 8

s+0. 8

Figure 2.24. Large steady-state error

From this, we compute

Y(s)=

0. 8

s+0. 8

F(s)=

μ

0. 8

s+0. 8

∂

10

s

=

10

s

−

10

s+0. 8

The time-domain solution is

y(t)=10u(t)− 10 e−^0.^8 tu(t)

as shown in Figure 2.25. From the above example, we have seen the trial and
error nature of designing a PID controller. It should become clear that if the
model parameters change, so will the parameters of the PID controller. As such,
there is significant redesign effort needed to obtain satisfactory performance
from the controller.