A First Course in FUZZY and NEURAL CONTROL

4.5. EXERCISES AND PROJECTS 157

five for each of the input variables and the output variable, then we have a total
of 25 fuzzy rules that provide a smoothertransition from one state to another.
We leave this as an example for the student to develop.

4.5 Exercisesandprojects ........................

1. A position control system that positions a massmhas the following open-
   loop transfer function

Y(s)

U(s)

=

40

ms^2 +10s+20

Using theMatlabSimulink capabilities, address the following:

(a) For a unit step input, simulate the open-loop response of the system

form=1kg.

(b) Based on the open-loop response, it is desired to obtain a system

response with settling time of less than 0. 5 seconds and overshoot of

less than5%.Usingamassm=1kg, design a PID controller for

the system.

(c) Using the PID parameters obtained above, simulate the performance

of the system for the conditions when the mass of 1 kg is replaced by

a new massm=0. 2 kg and subsequently form=5kg. Discuss the

results in terms of control performance.

(d) Develop a fuzzy controller to control the position. Simulate the sys-

tem behavior for various masses listed above.

(e) Compare the results from the PID controller and the fuzzy controller.

What can you say about the advantages and disadvantages of using

either PID or fuzzy control.

2. The open-loop transfer function of an antenna positioning system is given
   by
   Y(s)
   U(s)

=

5

s^3 +6s^2 +5s

where the output is measured inradians, and the input is the applied

torque inNewton-metersproduced by the drive mechanism to rotate the

antenna to the desired position.

Using theMatlabSimulink capabilities, address the following:

(a) For a unit-step input, simulate the open-loop response of the system.

(b) For any desired positioning of the antenna, it is desired that a con-

troller produce a near critically damped system response. Design a

PID controller for the system.

(c) Develop a fuzzy controller to control the antenna position.