6.6. EXERCISES AND PROJECTS 227
Assume that the ball position is measured using an optical sensor. Use
the following set of parameters in your model setup.
M Mass of steel ball 20 milligrams (mg)
km Magnetic constant 2. 058 ◊ 10 −^4 N(m/A)^2
R Coil resistance 0. 92 Ohms (Ω)
L Coil inductance 0. 01 millihenry (mH)
i Coil current [0,3]Amps (A)
V Coil voltage [0,5]Volts (V)
g Gravitational constant 9 .80665 m/s^2
z Ball position [min, max] [3,7] cm
(a) Through simulation, obtain a suitable set of training parameters to
train a backpropagation neural network. Use the specified range of
parameters for the currenti, the voltageV, and the distancezover
which the ball is allowed to move in the vertical direction.
(b) Test the neural network performance for various disturbances that
affect the ball position.
(c) Compare your results with the fuzzy controller developed in Chap-
ter 4. Does neural control offer any advantages over fuzzy control?
Explain why, or why not.
- For the liquid level control problem in Chapter 4, we wish to replace the
fuzzy controller with a neural controller.
(a) Develop a suitable set of neural network training parameters using the
same set of system parameters used for the fuzzy controller design.
(b) Compare the neural network performance with the fuzzy control per-
formance.
- A neural controller is desired to control the ball position in the ball and
beam problem of Chapter 4. For convenience, the nonlinear equations are
specified here again along with the system parameters:
∑
J
r^2
+M
∏
R®+Mgsinα−mR(α ̇)^2 =0
The beam angleαmay be approximated by a linear relationshipα=DLθ.
These equations form the set of coupled equations for the system. Using
the following system parameters
Mmass of the ball 0 .2kg
Rradius of the ball 0 .02 m
Dlever arm offset 0 .03 m
ggravitational acceleration 9 .8m/s^2
Llength of the beam 1 .5m
Jthe moment of inertia of the ball 2. 0 e−^6 kg m^2
