Tutorial 1

Control ENGD3113 2022/2023
Tutorial 1
Dr. Yunda Yan
Objectives
The objective of this tutorial is to learn:
• how to represent an engineering system as an input output model,
• the purpose of control systems and their role in different applications,
• how to draw a block diagram of a closed-loop control system for a particular

application,
• the structure of a computer control system including sensors and actuators.
Problem 1
Consider a home heating system
1. Identify components of the system and represent each of them by an input-output

model.
2. Sketch the block diagram of the home temperature control system and describe
how the temperature control is achieved.
3. Sketch an approximate graph of the temperature if the heating system is switched

on for the first time in the morning and the outside temperature is 5◦ C and the
set point is 20◦ C.
Problem 2
Figure 1 below depicts a refrigeration cycle (a heat pump).
1. Look at the figure and describe in words the working principle of the above heat
pump.
2. Sketch a block diagram of the temperature control system for the fridge. Rep-
resent the heat pump described in a) as a single functional block. Describe the
diagram including all input and output signals.
Page 1
Figure 1: A refrigeration cycle
3. Assume that the fridge is switched ON for the first time in a kitchen with a
temperature of 20◦ and that the fridge thermostat was set up to maintain a tem-
perature of 5◦ . Sketch an approximate graph of the temperature inside the fridge
over the first few hours.
Problem 3
Figure 2 below depicts a tank system. The inlet flow i n is uncontrolled and the
objective is to keep the tank level x constant by operating the valve opening u. The
valve is fully open for u=1 and is fully closed for u = 0.
Figure 2: A tank system
1. Represent the tank as an input-output model, i.e. identify the input, output and
the disturbance.
Page 2
2. Propose and sketch a structure of a closed-loop control system which would

achieve the control objective. Propose a control algorithm which would maintain
the tank level constant at 10 m.
3. The outflow qout in l/s depends on the water level x in m and valve opening u
√
and can be calculated from the equation qout = 0.8u 2gx , where g is the gravity
acceleration g = 9.81 m/s2 . Calculate the valve openings to keep the water level
constant x = 10 m for:
• the minimum inflow qin,min = 5 l/s and

• the maximum inflow qin,min = 10 l/s
Problem 4
A schematic representation of one degree of freedom rectilinear mechanical sys-
tem is shown in Figure 3 below, where a trolley of mass m experiences elastic force
produced by attached coil spring with stiffness coefficient k and linear viscous friction
produced by attached dashpot or damper with coefficient c.
Figure 3: Left: One DOF Mass-Spring-Damper System. Right: The Experimental

Control System ECP M210
1. Represent the 1DoF apparatus as an input output model if the objective is to

control position of the mass m.
2. Explain the physical meaning of the variables F and x and the parameters k, m
and c shown in Figure 1a. Write down a mathematical model of the system.
Problem 5
The rectilinear apparatus is controlled by a computer as shown in Figure 4. A
generic block diagram of a closed loop system with negative feedback, known as a
Page 3
Figure 4: Computer (Digital) control of the rectilinear apparatus
servo system, which controls mechanical single degree-of-freedom mass-spring damper

system is shown in Figure 5.
Figure 5: Block diagram of a servo system
A detailed block diagram of the computer control system is depicted in Figure 6.
1. Describe the function of each block.
2. Describe working principle of the BLDC motor. Calculate the torque developed
by the motor for the input current equal to 4.81 A.
3. Sketch a rack and pinion mechanism and explain its working principle. Calculate
the radius of the wheel from the given gain kmp = 26.25 m−1 .
4. Sketch the pulley mechanism and explain its working principle. Calculate the
radius of the wheel from the given gain kep = 89 m−1 .
Page 4
Figure 6: Block diagram of the digital closed-loop control system for 1DOF rectilinear
system
5. Describe the working principle of a basic incremental encoder as depicted in

Figure 7, below.
Figure 7: Basic incremental encoder
Problem 6
A schematic representation of one degree of freedom torsional mechanical system
is shown in Figure 8 below.
1. Explain the physical meaning of the variables T and θ and the parameters J and
c shown in Figure 8. Write down a mathematical model of the system.
2. The torsional apparatus is controlled by a computer as depicted in Figure 9. Draw

a block diagram of the closed-loop control system similar to that in Figure 6.
Page 5
Figure 8: One DOF Torsional System
Problem 7
The pitch angle of an aircraft is controlled by changing the angle of elevators shown
in Figure 10.
1. Explain what is meant by the term “fly by wire”.
2. Represent the aircraft as an input-output model for the purpose of pitch control,
identify the input, output and disturbances.
3. Draw a block diagram of the feedback system to control the aircraft pitch angle
including sensors and actuators and explain the role of the pilot in the pitch
control system.
Page 6
Figure 9: Computer (Digital) control of the torsional apparatus
Figure 10: An aircraft
Page 7

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Control ENGD3113 2022/2023

• how to represent an engineering system as an input output model,

• the purpose of control systems and their role in different applications,

• how to draw a block diagram of a closed-loop control system for a particular

• the structure of a computer control system including sensors and actuators.

1. Identify components of the system and represent each of them by an input-output

3. Sketch an approximate graph of the temperature if the heating system is switched

Figure 1: A refrigeration cycle

Figure 2: A tank system

2. Propose and sketch a structure of a closed-loop control system which would

• the minimum inflow qin,min = 5 l/s and

Figure 3: Left: One DOF Mass-Spring-Damper System. Right: The Experimental

1. Represent the 1DoF apparatus as an input output model if the objective is to

Figure 4: Computer (Digital) control of the rectilinear apparatus

servo system, which controls mechanical single degree-of-freedom mass-spring damper

Figure 5: Block diagram of a servo system

A detailed block diagram of the computer control system is depicted in Figure 6.

1. Describe the function of each block.

5. Describe the working principle of a basic incremental encoder as depicted in

Figure 7: Basic incremental encoder

2. The torsional apparatus is controlled by a computer as depicted in Figure 9. Draw

Figure 8: One DOF Torsional System

1. Explain what is meant by the term “fly by wire”.

Figure 9: Computer (Digital) control of the torsional apparatus

Figure 10: An aircraft

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