A First Course in FUZZY and NEURAL CONTROL

(singke) #1
26 CHAPTER 2. MATHEMATICAL MODELS IN CONTROL

C=[1000;

0010]

D = [0;

0]

The output gives the following state-space model




x ̇ 1 (t)
x ̇ 2 (t)
φ ̇ 1 (t)
φ ̇ 2 (t)




=





01 00

0 − 0 .1818 2.6727 0

00 01

0 − 0 .4545 31.1818 0









x 1 (t)
x 2 (t)
φ 1 (t)
φ 2 (t)




+





0

1. 8182

0

4. 5455




u(t)


y 1 (t)
y 2 (t)


=


1000

0010






x 1 (t)
x 2 (t)
φ 1 (t)
φ 2 (t)




+


0

0


u(t)

Figure 2.6. Time simulation for a unit step

Figure 2.7. Original control structure

Figure 2.6 shows the response of the open-loop system where the system
is unstable and Figure 2.7 illustrates the closed-loop control structure for this
problem. Note that the control objective is to bring the pendulum to the upright
position. As such, the output of the plant is tracking a zero reference with the

Free download pdf