In order to control the output of a system accurately and reliably, a control system is required. Without a controller, the system may drift or become unstable. Take the example of a car, where your foot is on the

In order to control the output of a system accurately and reliably, a control system is required. Without a
controller, the system may drift or become unstable. Take the example of a car, where your foot is on the
pedal and not making adjustments. If you enter a downward slope, the car may speed up; that could be
dangerous! Closing the loop with a controller on the car, exactly what a cruise control does, will help keep
the speed steady. This is an example where closed-loop control can help get rid of disturbances due to
unmodeled dynamics.
In another example, consider a pendulum with one end attached to a motor. In order to keep the
pendulum upright many fast and accurate adjustments must be made. If a human operator attempts to do
this and the pendulum rod is too short, the pendulum will fall from its upright position. A closed-loop
controller with fast dynamics can however be able to stabilize the pendulum in the upright position. This is
an example where an “unstable” plant is stabilized via closed loop control. What about disturbances? If
you tap the pendulum gently it may even reject that disturbance and manage to stay upright!
The above two examples serve as a brief introduction to the world of closed-loop control and why it is
necessary in automation. You should get familiar with the basic concepts of linear feedback control
systems from lectures, and this manual will not focus on teaching, rather on assignments. Any MATLAB
command you may not have been introduced to in the previous labs will be provided. You are to complete
all exercises and produce their results as asked in your reports. EEE304 Lab 3 Answer Sheet
Name: Date: Lab Description Write a paragraph explaining what you have learned from this lab exercise. Task 1 For the control system shown in Fig. 1,
d
r + e C(s) u + P(s) y – where 1.
2. Figure 1. A closed loop control system with disturbance
P(s) is the transfer function of the plant
C(s) is the transfer function of the controller
r is the reference signal
e is the error signal
u is the output signal from the controller
d is the disturbance signal
y is the output signal Find the transfer function Tdy from the disturbance d to the output y (assume r = 0). Find the transfer
function Try from the reference r to the output y (assume d = 0).
If the transfer functions of the plant and controller are given as Plant: P ( s )= 1
, (e.g., a normalized description of car velocity with force as the input; this
s can represent a cruise control system.) a) Controller: C ( s )=K s+z

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