Final Exam Revision
Name: ___________________________________________________________
Course Name: Control System
Duration: 3 hours
Prepare by: Wee Cheng
Question
Q1(a)
(b)
(c)
Q2(a)
(b)
(c)
Q3(a)
(b)
Q4(a)
(b)
Q5(a)
(b)
Total
Obtain
Marks
8
6
6
10
5
5
10
10
3
17
10
10
100
Q1(a) Use your knowledge of motorcycle and and/or riding motorcycle and relate it to
feedback control system to design the block diagram of the speed control system of a
motorcycle with a human driver.
(8 marks)
(b)
A level control system shown in Figure Q1(b). Use your control system knowledge to
identify all important parts of the control system, then distinguish briefly when the
system be an open-loop and closed-loop systems, respectively.
(6 marks)
(c)
Suppose that you are a control engineer and required to design the control system for
an elevator of a five-level building. With the air of flow chart, discuss the control system
design process to be done.
(6 marks)
Q2(a) Consider two carts system as shown in Figure Q2. The input force to the system is u,
and the output displacement from the system is x1. m1 and m2 are mass of the cart,
respectively. k1, k2 and k3 are spring stiffness attached to the cart, b is velocity
coefficient for the port, x1 and x2 are the displacement of the cart after input force
applied to cart 1.
(i)
(ii)
(b)
Draw the free body diagram for each cart and derive the force equation for every
cart.
(4 marks)
Determine the overall transfer function, xi/u of the system using Laplace Transform.
(6 marks)
Evaluate the transfer function, G(s)=Vo(s)/Vi(s) for the network shown in Figure
Q2(b).
(5 marks)
Figure Q2(b)
(c)
Evaluate the state space representation for the system shown in Figure Q2(c).
(5 marks)
Figure Q2(c)
Q3(a) The model for a position control system using a DC motor is shown in Figure Q3(a).
Calculate the value K1 and K2 so that the response peak time is 0.2 second and the
overshoot for a unit step input us less than 4%.
(10 marks)
Figure Q3(a)
(b)
For a system shown in Figure Q3(b)
(i)
Determine Kp, Kv, and Ka
(ii)
evaluate steady state error, ess, for an input of 50u(t), 50tu(t), and
50t2u(t).
(iii)
state the system type
Figure Q3(b)
(10 marks)
Q4(a) Differentiate the characteristics of natural response when time approaches infinity for
three different conditions of a system.
(i)
stable
(ii)
unstable
(iii)
marginally stable
(3 marks)
(b)
The transfer functions of the individual block are as follows:
1
G1(s)=2s, G2(s)=3, G3(s)=5K, H1(s)=10 and H2(s)=𝑠+2
(i)
Write the characteristic equation for the system.
(5 marks)
(ii)
Using the Routh-Hurwitz stability criterion, calculate the range of K for which the
system shown in Figure Q4(b) is stable.
Figure Q4(b)
(12 marks)
Q5
A unity feedback control system has a plant transfer function:
𝐺(𝑠) =
(a)
(b)
1
𝑠+3
Show that a PI controller can be used to achieve zero steady state error for a step
input.
(10 marks)
Design a PI controller so that the response to a step input has 5% overshoot and
settling time approximately 1 second.
(10 marks)