4.5. EXERCISES AND PROJECTS 161
(b) Develop a fuzzy controller that can magnetically levitate the steel
ball for various positions within the range indicated. Simulate the
system behavior for various disturbances that can act on the steel
ball.
(c) Discuss the results from the PID controller and the fuzzy controller.
- The longitudinal motion of an aircraft is represented by a set of linear
differential equations as
x ̇ 1
x ̇ 2
x ̇ 3
=
− 0 .09 1. 0 − 0. 02
− 8. 0 − 0. 06 − 6. 0
00 − 10
x 1
x 2
x 3
+
0
0
10
δE
where,
x 1 = angle of attack
x 2 = rate of change of pitch angle
x 3 = incremental elevator angle
δE= control input into the elevator actuator
It can be observed from the state equations that changing the elevator
angle affects rate of change of pitch angle and the angle of attack.
(a) Perform open-loop simulations on the system for various inputs, namely,
step, ramp, and sinusoidal inputs. What can you say about the per-
formance of the system to such inputs?
(b) Based on the knowledge gained from open-loop simulations, develop
a fuzzy controller that will maintain stable aircraft performance in
the presence of unexpected disturbances.
- A liquid level system is illustrated in the followingfigure. The objective
in this system is to control the inputflow such that desired heights of the
fluid in both tanks can be maintained.
In thefigure,qi,q 1 ,q 2 = the rates of liquidflow,h 1 ,h 2 = the heights of
fluid level,R 1 ,R 2 =theflow resistance, andA 1 ,A 2 = the cross-sectional
tank areas.
