Solutions # 1
1 Structure of Control Systems
Shown below is a block diagram for the temperature control system in a refrigerator. A relay is
an on-off switch, and is often the most elementary actuation in control systems. Not shown are
Homework # 6
Issued: Friday March 13, 2015
Due: Friday March 20, 2015
1 PID Controller Design
A process, with input u, disturbance d, and output y is governed by
= y(t) + u(t) + d(t)
where u(t) is the input, d(t) is the disturbance, and y(t)
Homework # 5
Issued: March 4, 2015
Due: March 13, 2015
Note:The last two problems in this assignment require that you use matlab commands.
1 Proportional Control, Routh-Hurwitz Test
Is it possible to design a proportional controller
u = K1 r + K2 (
Homework # 4
Issued: Monday Feb 23, 2015
Due: Wednesday March 04, 2015
1 Finding Transfer functions
(a) Find the transfer function from u to y of the following cascade connection.
y (2) + 3y (1) + 10y = v (1) 5v
100v (1) + v = u
To find the
Solutions # 2
1 Model Properties
Many of you had difficulty with this problem, particularly part (c).
(a) This model is memoryless, nonlinear, time-invariant, causal.
(b) This model is memoryless, nonlinear (because of the affine term b), time-inva
Homework # 8
Issued: Wednesday April 15, 2015
Due: Wednesday April 22, 2015
1 Equilibrium points, Linearization
Consider the nonlinear system
+ y2 = u
(a) Obtain a state-variable description of this system. (Hint: Let x1 = y, x2 = y)
Homework # 7
Issued: Wednesday April 8, 2015
Due: Wednesday April 15, 2015
1 Consider the block diagram shown below.
The numerical values of the parameters are K = 51 , a = 100, and b = 98.
(a) Find the closed-loop transfer functions GRY (s) and GD