Chapter1
1.1
Introduction to Control Systems
Introduction
Automatic control has become an important and integral part of the modern life. It has been applied
in all most every engineering field, such as mechanical, metallurgical, petrolic, chemical, electronic,
electrical, aeronautic, astronautic, marine, and nuclear industries. In recent years, automatic control
has been extended into transportation, biomedicine, environment, economy management, social
science and other fields. It facilitates the development and the interaction of different scientific
disciplines. The automatic control theory and practice provide the means for the industrial process
to operate automatically, improving productivity and product quality, cutting cost, and relieving the
drudgery of many routine and repetitive manual operations. It plays an important role in helping
people conquer the nature, explore new energy sources, develop space technologies, and propel the
evolution of civilization.
The theory of automatic control studies the integration, analysis and design of control systems.
It reveals the general rules of automatic control. Its task is to understand and alter the dynamics of a
system to improve its performance. Since the theory of automatic control provides the guidelines
for establishing high performance control systems, most engineers and scientists must now have a
good understanding of this field.
1.2
A Brief History
The theory of automatic control is generated in the course of human practice of conquering the
nature. It develops with the evolution of productivity and technologies.
In ancient time, with the idea of feedback, people had created pieces of excellent work
sparking the idea of the control theory. The Water-Powered Armillary Sphere created by Su Song
and Han Gongqian in Northern Song Dynasty (1086～1089 D.C.) is a closed-loop nonlinear
automatic control system based on the negative feedback idea; In 1681, Dennis Papin invented
steam pressure regulator for boilers; in 1765, I. Polzunov invented water level regulator for boilers.
James Watt adapted the fly-ball governor (also called a centrifugal governor) to his steam
engine for controlling the rotating speed in 1788. However, the attempts later to improve the
accuracy of the system lead to oscillation or instability.
To resolve the problem, scientists have been carrying on theoretical studies. Until 1868,
British scientist J.C. Maxwell developed the differential equation model of the governor and gave
out the conditions for stability. The mathematical theory was then adapted to the study of control
systems. British scientist E.J. Routh and German scientist A. Hurwitz independently presented their
algebraic criterions for stability in 1877 and 1895 respectively. The criterions stated the conditions
on the coefficients of a polynomial that would hold if the system was stable. These methods have
been the foundation of the time-domain analysis and design of control systems.
In 1932, by analyzing the distortion of the long distance telephone signal, American scientist
H. Nyquist developed the stability criterion in frequency domain using Laplace transform. By the
end of 1930s and the early 1940s, the frequency-response has been developed fully especially due
to the work of H.W. Bode and N.B. Nichols. The frequency-response methods provided an efficient
way for engineers to design feedback control systems.
During World War II, the feedback control approach was applied necessarily to design and
construct airplane autopilots, gun-positioning systems, radar antenna control systems, and other
military systems. The complexity and expected performance of rapidness and accuracy of these
military systems necessitated an extension of the existing control techniques and fostered interest in
control systems and the development of new insight and methods.
In 1948, American scientist W.R. Evans introduced the root locus method to control systems
design. It allowed one to follow graphically the paths of the roots of the characteristic equation as a
parameter was changed. This method remains an important technique today.
The time-response, root locus and frequency-response methods based on the mathematical
model in the transfer function formulation underlie the classical control theory. By 1950s, the
classical control had been playing an important role in control engineering.
The classical control theory deals only with the linear time-invariant,
single-input-single-output (SISO) systems. It is incapable of solving more complex problems such
as time-varying, multi-variables, and highly coupled systems.
With the advent of Sputnik and the space age, another new impetus was imparted to control
engineering. It became necessary to solve the optimal control problem for multi-variable nonlinear
systems, such as the accurate and low power consuming control for guidance, tracking and landing
of missiles. The ubiquitous use of computers stimulated the development of the control theory in
the way of carrying out complex calculations. The state-space representation then became the main
stream of the control theory research because of its merits on describing the motion of space
vehicles and fitting for computer calculation. The stability theory proposed by Russian scientist
A.M. Lyapunov in 1892 was translated into the language of control at about this time. In 1956, L.S.
Pontryagin in the U.S.S.R proposed his maximum principle. In the same year, the dynamic
programming was presented by R. Bellman. The maximum principle and the dynamic
programming supported the optimal control theory to find the best possible control or decision for a
dynamic system. In the early 1960s, modern control theories came into bloom, which involved the
optimal control and Kalman filtering based the state space equations.
The modern control theory copes with multi-variable, nonlinear and time-varying systems. It
uses computers for modeling, analysis, design and control. It has been used to achieve the stringent
requirements on accuracy, weight, and cost in military, space, and industrial applications.
For more complicated problems, recent developments in control theory are in the field of
adaptive control, fuzzy control, predictive control, robust control, nonlinear control and large scale
systems control etc..
Control theories continue developing today. Leaps on theoretical study and practical
engineering are observed often. They have been contributing to the advance of productivity,
improving the level of people’s life, propelling the progress of human society.
1.3 Basic Concepts of Automatic Control and Automatic Control
Systems
1.3.1
Automatic Control
In modern manufacturing and industrial process, the value of some variables such as temperature,
pressure, flow, liquid level, voltage, etc. needs to remain a constant or vary in a prescribed way.
The adjustment to the process for this end is called control, including manual control and automatic
control.
Figure 1-1 (a) shows a manual system for water level control. The water level in the tank is
the controlled variable. The tank is the plant. When the water level is at the desired position, and
the input flow is equal to the output, the system is at its equilibrium. When the output flow varies
or the desired position is changed, the input flow has to be adjusted for the water level staying with
the desired position. In the manual control case, the eye sees the actual water level, and the brain
compares the actual level to the desired one to determine the adjustment of the valve. The hand
operates on the valve until the actual level meets the desired one. When the actual level leaves the
desired level, the process is repeated.
Figure 1-1(b) shows an automatic replacement for the system shown in Figure 1-1(a), where
the float measures the actual level instead of the eye. A lever is acting as the brain and the hand to
compare the levels, calculate the error and control the valve. An end of the lever is driven by the
float and the other acts on the valve. When the output flow increases, the water level falls, so does
the float. The lever then controls the valve to allow the flow into the tank to increase so that the
level will return to the desired position. On the contrary, when the output flow decreases, the water
level and the float rises. The flow is reduced and, if necessary, cut off. The process is accomplished
automatically involving no human actions.
Although the system shown in Figure 1-1(b) is an automatic control system, it can not keep
the water level at an exact position due to its simple structure. The steady-state level varies with the
output flow. When the output flow increases, the valve is supposed to open wider to allow more
water intake. However, the way to open the valve wider is for the float or the water level to fall
more, which means the discrepancy between the actual water level and the desired water level has
to increase. Thus, a new equilibrium is set up at a lower water level. The more output flow
increases, the more the steady-state water level falls.
To cope with the above problem, Figure 1-2 shows an automatic control system with more
components. The float is still the component for measurement. The lever compares the actual and
desired water level and adjusts the potentiometer according to the error. The output voltage of the
potentiometer indicating the magnitude and the direction of the error is amplified by the amplifier,
which drives the servo motor to control the valve through the reducer.
When the actual water level meets the desired position, the wiper arm is at the middle point of
the potentiometer, therefore, u e  0 . When the output flow increases, the falling float shifts the
wiper arm up by the lever. The error voltage u e  0 is amplified to u a to control the motor
rotating in the positive direction. The valve is open wider to allow more water intake so that the
water level will return to the desired position. The system returns to the equilibrium when the water
level meets the desired position and the voltage u e  0 .
This system is able to remain the water level at the desired position by eliminating the error
caused by disturbances. The control accuracy is thus improved much.
The automatic control system and the manual control system are alike in the sense of the same
mechanism. The automatic control system replaces human in the loop by integrating some
components. In Figure 1-2, the float acts as the eye measuring the actual water level. The lever and
the potentiometer are the substitute of the brain determining the magnitude and direction of the
error. The motor is like the hand operating on the valve to control the water level. The mechanism
performing the control function is called the controller. All control systems are consists of the
controller and the plant.
1.3.2
Open-Loop Control Systems
Usually, there are three kinds of control systems: open-loop control systems, closed-loop
control systems and composite control systems. How to choose the control method depends on the
purpose and the requirements of the system.
Systems in which the output has no effect on the control action are called open-loop control
systems. In an open-loop control system, there is no feedback path but only forward path between
the input and the output.
The speed control system of a DC motor shown in Figure 1-3(a) is an open-loop control
system. It controls the DC motor to rotate at a given desired speed with the load.
In this system, the DC motor is the plant. The speed  is the controlled variable, also the
output signal. The reference voltage u r is called the input.
Figure 1-3(a) shows that the output  has no effect on the input u r , so the system is called
open-loop control system.
The component block diagram of the speed control system for the DC motor is shown in
Figure 1-3(b), where the component is represented by the box and the signal with direction is
indicated by the arrow head. The variation of the load M c will make the speed  leave the
desired value, so it is regarded as the disturbance or perturbation, which is indicated by an arrow
head on the shaft in Figure 1-3(b).
1.3.3
Closed-Loop Control System
What is missing in the open-loop control system for more accurate and more adaptive control is a
link or feedback from the output to the input of the system. To obtain more accurate control, the
controlled signal should be fed back and compared with the reference input, and an actuating signal
proportional to the difference of the input and the output must be sent through the system to correct
the error. The control system in which the output has an effect on the control action is called as
closed-loop control system.
By adding a tachometer, the open-loop control system shown in Figure 1-3(a) becomes a
closed-loop control system shown in Figure 1-4(a).
Figure 1-4(a) shows that the tachometer is driven by the motor through a shaft. It converts the
actual speed  (the output) to a voltage u f , which is fed back to the input end and compared
with the input by the amplifier. The error voltage u e  u r  u f indicating the magnitude and the
direction of the difference between the actual and desired speed is amplified to u a to control the
speed  .
The component block diagram of the closed-loop control system is shown in Figure 1-4(b).
The path from the input signal to the output signal is called forward path. The path from the output
signal to the feedback signal is called feedback path. “○” is called summing point, whose output is
the sum of its inputs marked with the positive or negative sign. It can be seen that the system has a
closed loop, by which the output has an effect on the control action. A system that compares the
output and the reference input and uses the difference as a means of control is called a closed-loop
control system or feedback control system.
Note that, only the negative feedback in the main feedback path can reduce the error to obtain
the desired control objective. The positive feedback will bring response diverge by aggravating the
error
The mechanism of the closed-loop feedback control system is to compare the output and the
input and use the difference to adjust the system to reduce the error. This is the negative control
theory, the core of the closed-loop control system.
The closed-loop control method is the common control approach. A control system is usually
referred a closed-loop control system.
1.3.4 Open-Loop control versus Closed-Loop control
An advantage of the closed-loop control system lies on the fact that the structure is simpler
than that of a corresponding closed-loop system. Thus the open-loop system is easier to build and
lower in cost. However, due to its sensitivity to external disturbances and internal variations in
system parameters, the open-loop control system can only be used when the requirement for
accuracy is low and the disturbance can be neglected, such as the control of washing machines,
stepper motors.
By the use of feedback, the closed-loop control system is relatively insensitive to external
disturbances and internal variations in system parameters. It is thus possible to use relatively
inaccurate and inexpensive components to obtain the accurate control of a given plant. However,
the number of components used in a closed-loop control system is more than that for a
corresponding open-loop control system. Thus, the closed-loop control system is generally high in
cost and complexity. If the system parameters are not configured properly, the output may oscillate
or even diverge. Therefore, the control theory is to answer the question that how to analyze the
system and choose the system parameters to achieve satisfactory performances.
1.3.5 Composite Control System
The feedback control acts when it “sees” the effect of the input or disturbance. For systems with
large time delay, the feedback control can not adjust the system instantly after the input or
disturbance is imposed, but does it only after the effect on the output appears. This usually results
in oscillations in the output. The feedforward measures the input or disturbance itself rather than
the response to the disturbance, then takes a corrective action to counter the error. The composite
control which can improve the accuracy of the control system is the composition of the feedback
control and the feedforward control. The structure and design of composite control systems are
covered in Chapter 3.
1.4
Control System Composition
All automatic control system consists of the plant and the controller, although their structure may
be different for different plants or control objectives. Figure 1-5 shows the component block
diagram of a typical automatic control system, where the box represents a component. Besides the
plant, there are the measurement component, comparison component, amplifying component,
actuating component, compensation component, and reference component in the system.
Plants. Any physical object to be controlled (such as a mechanical device or a production operation)
is called plant. The variable to be controlled is called the controlled variable.
Reference Components. A reference component generates the reference signal or the input signal.
The potentiometer in the speed control system shown in Figure 1-4(a) is a reference component.
Measurement Components. A measurement component measures the output or the controlled
variable and generates the feedback signal. It usually converts a non-electric signal to an electric
signal. The tachometer in Figure 1-4(a) is a measurement component.
Comparison Components. A comparison component compares the feedback signal and the input
signal to generate the error signal.
Amplifying Components. An amplifying component amplifies the error signal to control the plant,
such as the amplifier and electro-hydraulic servo valve.
Actuators. An actuator acts on the plant directly to adjust the controlled variable, such as a valve
or a servo motor.
Compensation Components. A compensation component improves the performance of the system.
It is usually cascaded in the system, such as an RC network or a tachometer.
1.5
Examples of Control Systems
EXAMPLE 1
Voltage control system
A voltage control system is shown in Figure 1-6. The system is to maintain the output voltage of
the generator a constant given by the potentiometer in spite of any changes of the load. At the
equilibrium state, the load is not changing and the output of the generator agrees with the desired
voltage. The motor stays static due to the zero output of the amplifier. The wiper arm of the
potentiometer stays at the origin position. When the load increases, the output voltage of the
generator drops below the desired value. The error voltage u  u r  u  0 that appears at the
reference potentiometer terminal is amplified by the amplifier. The output voltage u1 of this
amplifier is applied to the motor and the motor rotates the wiper arm of the excitation
potentiometer clockwise. Thus, the excitation current increases, so does the output voltage of the
generator. When the output voltage u agrees with the reference voltage u r , the motor stops. The
generator is then working at the new equilibrium and the output voltage meets the requirement.
In this system, the generator is the plant, whose output voltage is the controlled variable. The
reference is the voltage u r given by the reference potentiometer. The component block diagram is
shown in Figure 1-7.
EXAMPLE 2
Plotter
A plotter (e.g. the Calcomp 565 of 1959) worked by placing the paper over a roller which moved
the paper back and forth for X motion, while the pen moved back and forth on a single arm for Y
motion to provides the plot of some variable with time.
The schematic of a plotter is shown in Figure 1-8. It consists of the measurement component,
amplifying component, servomotor-tachometer set, gear train and rope sheave. The input (the
reference) of the system is the voltage to be recorded. The plant is the pen and the shift of the pen is
the controlled variable. This system controls the shift of the pen to plot the variation of the input
voltage with time.
Figure1-8
The schematic of a plotter
The mearsurement curcuit consists of the potentiometers RQ and RM . The pen is fixed on
the wiper arm of RM . The voltage u p is proportional to the shift of the pen. When the input
voltage u r changes slowly, the error votage u  u r  u p appears on the input terminals of the
applifier. The output voltage of the amplifier is applied to the DC motor, which drives the gear train
and the rope sheave moving the wipe arm of RM (and the pen) to reduce the error. When the
error voltage u  0 , indicating u p  u r , the motor stops, so does the pen. Thus, the pen plots
the curve of the voltage variation with time.
The component block diagram is shown in Figure 1-9, where the tachometer is the
compensation component. It generates the feedback signal of the speed of the motor. The
tachometer feedback improves the system performance in that it increases the system damping
ratio.
Figure1-9
EXAMPLE 3
The block diagram of a plotter
Pointing Angle control system
Figure 1-10 shows a pointing angle control system for self-propelled guns. A selsyn system
working in the transformer state acts as an error-measuring device. The input shaft of the synchro
transmitter is connected to the input device. The output shaft of the synchro receiver is connected
with the shaft of the gun.
Figure1-10
pointing angle control system for self-propelled guns
When the input shaft is rotated to the angular position
 i such that the output angular
 o   i , the difference between the input angular position and the output angular
position is the error signal  e . The voltage u e that appears on the receiver rotor terminals is the
error voltage, which is proportional to  e . The polarity of  e determines the phase of u e , a
positive value of  e for a positive phase of u e and vice versa. The error voltage u e is
converted to a dc voltage, which is amplified by the amplifier. The output voltage u a of the
position
amplifier is applied to the armature circuit of a dc motor. The motor then develops a torque to
rotate the gun in such a way as to reduce the error to zero. Thus the gun is rotated to the same
angular position given by the input device.
Figure 1-11 shows the component block diagram of the pointing angle control system, where
the gun is the plant, whose angular position
the angular position
EXAMPLE 4
 o is the controlled variable. The reference signal is
 i given by the input device.
Aircraft-Autopilot System
Autopilot is an equipment to control the aircraft in flight automatically. It can stabilize the altitude
and control the maneuvers of the aircraft. A system consisting of the aircraft and autopilot is an
aircraft-autopilot system.
The autopilot controls the aircraft by acting on three control surfaces (elevator, rudder, and
aileron). The torque developed by the control surfaces changes the aircraft altitude. Figure 1-12
shows an aircraft-autopilot system stabilizing the pitch angle of the aircraft.
Figure1-12
aircraft-autopilot system stablizing the pitch angle of the aircraft
The vertical gyroscope is the measuring component for the pitch angle. When the actual pitch
angle agrees with the reference, the output voltage of the potentiometer is zero. If a disturbance
causes an error between the actual and reference pitch angle, a proportional voltage will appears on
the terminals of the potentiometer. The error voltage is amplified and applied to the actuator to
push the elevator deflecting upward. A torque is developed by the deflection to make the airplane
nose up. Therefore, the error is reduced. The wiper arm of the feedback potentiometer is turned by
the actuator simultaneously. Thus the output voltage of the feedback potentiometer is proportional
to the deflecting angle of the elevator. The output voltage of the gyroscope decreases until the pitch
angle meets the desired value and the error is reduced to zero.
Figure 1-13 shows the component block diagram of the aircraft-autopilot system, where the
aircraft is the plant, whose pitch angle is the controlled variable. The control device, or the
autopilot, consists of the amplifier, actuator, gyroscope and feedback potentiometer. The reference
signal is the given pitch angle. The control system is to remain the pitch angle in spite of any
disturbance in the flight.
1.6
Classification of Automatic Control Systems
There are different classifications for automatic control systems. The following are some typical
classifications.
1.6.1
Regulator systems,
servo systems and programmed control system
By the different forms of input signals, control systems can be classified as regulator systems and
servo systems.
1．Regulator systems
A regulator system is to maintain the system output at a prescribed level with respect to the
constant input, such as the water lever control system and the speed control system. The input of
the regulator system does not vary.
2．Servo system
If the reference signal is not known ahead of time, and the output follows the input with a limited
error, then the system is called as servo system. The pointing angle control system of self-propelled
guns, and the aircraft-autopilot system are examples.
3. Programmed control system
If the reference signal is known in advance and expressed analytically or by curves, and the output
follows the input, then the system is called as programmed control system. such as the numerically
controlled (NC) machine tools.
1.6.2
Time-invariant versus Time-varying control systems
A time-invariant control system is one whose parameters do not vary with time.
If the parameters of a control system do not vary with time during the course of its operation,
the system is a time-invariant control system (constant coefficient control system). Otherwise, it is
a time-varying control system. In practice, there are actually no time-invariant systems due to
amplifier drift, temperature variation and component aging. A system can be regarded as a
time-invariant system when the parameter varies much slower than the system dynamics do.
1.6.3 Linear Systems versus Nonlinear Systems
By the principle of superposition, systems can be classified into linear systems and nonlinear
systems.
The system is called as linear system if it is constituted by the linear components. The
dynamical equation of the system can be expressed by the linear differential equations. The main
characteristic of the linear is homogeneity andsuperposition. The response is independent of initial
state and stability is independent of the input.
The system is called as the nonlinear system is it has one or more nonlinear component. The
nonlinear doesn’t satisfy the superposition principle. The response is dependent of the initial state
and the input. We will introduce the nonlinear system in chapter 7.
Strictly speaking, most physical systems are nonlinear to some extents. However, some of
them can be accurately described by linear system through some reasonable simplification. In this
book, we mainly focus on the linear time invariant system.
1.6.4
Continuous-time versus Discrete-time control system
In a continuous-time control system, all the variables are in the form of continuous function.
The system mentioned in section 1.5 are the continuous system.
A discrete-time control system involves one or more variables that are known only at discrete
instants of time. The computer control system is the example. We shall introduce the discrete
system analysis and design in Chapter 6.
1.6.5 Single Variable Systems versus Multivariable Systems
By the number of the inputs and outputs, systems can be classified into
single-input-single-output (SISO) systems and multi-input-multi-output (MIMO) systems
A SISO system is also called a single variable system, which has an input (except the
disturbance) and an output. A MIMO system is also called multi-variable system, which has multi
inputs or multi outputs. A SISO system can be regarded as a special MIMO system.
1.7
General Requirements for Control Systems
Since inertia, mass, and inductance are inherent in physical systems, the response of a typical
control system cannot follow sudden changes in the input instantaneously, and transients are often
observed. Therefore, the time response of a control system consists of two parts: the transient
response and the steady-state response. By transient response, we mean the process in which the
controlled variable goes from the initial state to the final state. By steady-state response, we mean
the manner which the system output behaves as t approaches infinity.
For different plants and different objectives, the performance requirements for control systems
are different. Nevertheless, they are of stability, accuracy and swiftness.
Stability. Stability indicates the ability of a system to return to its equilibrium. It is the primary
requirement of a control system, since any working system must be a stable system.
The feedback of the closed-loop system may cause the response to oscillate or diverge. For
example, the system shown in Figure 1-10 stays at the equilibrium state when the pointing angle of
   i . When the input shaft is rotated to a different angle suddenly
the gun is equal to the input, o
(which can be represented by a step
function signal), the error voltage
u e will appear on the receiver rotor
u
terminals. The output voltage a of
the amplifier is then applied to the
motor. The motor drives the gun in
the way to reduce the error. When
 o   i again, the output shaft can
not stop rotating immediately due to
the inertia of the motor and the gun,
which results in the overshoot,
 o   i . The sign of the error signal
is now changed due to the overshoot.
A torque in the opposite direction
will be developed by the motor. The output shaft will stop rotating and rotate in the other direction.

Thus the gun will be oscillating around the expected position i . If the damp of the system is
   i . The system
sufficient, the oscillation will converge and the gun will stop at the position o
is stable. The tracking process is presented by the curve 1 in Figure 1-14.
Not all negative feedback systems work properly. The system may oscillate or diverge due to
unreasonable system structures or parameters. Curves 3, 4 and 5 in Figure 1-14 show these cases.
In these cases, the system is not stable.
Unstable system is useless. Constant and drastic oscillation will overload the amplifying
components and ruin the system. This is not permitted in practice.
Accuracy: Accuracy is a requirement for the steady (static) state of the system. For a stable
system, steady state error is the difference between the steady state parts of the actual and the
expected output after the transient response ends. The steady state error is an important criteria for
control accuracy. Smaller steady state error indicates higher accuracy of the control system.
Swiftness: Swiftness is a requirement for the transient (dynamic) response. The performance
of the transient response can be evaluated by smoothness and swiftness. Smoothness requires
smaller overshoot and less oscillation during the transient of the system from the initial state to a
new equilibrium state. Swiftness requires less settling time of the transient process. Transient
response performance is an important aspect of the system performance.
Different system has different requirement for the above three criterions. Regulator systems
require better performance of the steady state response while servo systems require better
performance of the transient response.
The three criterions of a system usually conflict with each other. Higher swiftness may induce
stronger oscillation; Better smoothness may result in a sluggish process or worse accuracy.
Analyzing and resolving these conflicts are important tasks of this course.
1.8
Contents of This Book
“Principles of Automatic Control” studies common rules of automatic control. It is the theoretical
foundation for the automatic control technology. In this course, we will study the analysis and
design of control systems.
1．System Analysis
System analysis determines system stability, obtains transient and steady-state response
specifications, and analyzes the relationship between the performance and the structure and
parameters of a system.
2．System Design
System design is to obtain a control system for a given plant to satisfy given performance
specifications. Usually, to obtain satisfactory performance, one needs to alter the system parameters
or even the structure, choose proper components and determine their parameters. This process is
called alteration.
System design is more complex than system analysis in that,
1）e answer for a design problem is not unique. Different design solutions may satisfy a same
set of requirements;
2）Different performance requirements usually conflicts each other. Compromises must be
considered. The solution must be realizable in practice.
In addition, issues such as cost, reliability, assembling techniques are also needed to be
considered in the design process.
System analysis and design are two reverse subjects. System analysis is to understand a given
system. It is more important for an engineer to design a control system to achieve expected
specifications.
Summary
Starting from comparison between manual control systems and automatic control systems, we have
introduced basic concepts and integration of control systems.
Control systems can be classified into open-loop systems and closed-loop systems by the
presence of feedbacks. Closed-loop control system is also called feedback control system. The
output of closed-loop systems is measured and fed back to compare with the input signal. The
difference of the comparison controls the system in the way to reduce the error.
EXERCISES
E1.1 A speed control system of electromotor is shown in Figure 1-15.
(1)Connect a, b to c, d so that the system becomes negative feedback system.
(2)Sketch a block diagram of the system.
Figure 1-15
Speed control system
E1.2 Figure 1-16 shows an automatic control system of a warehouse gate. Identify the principle of the automatic
open/close control system of the gate, and sketch a block diagram for the control system.
Figure 1-16 Automatic open/close control system of the warehouse gate
E1.3 Figures 1-17 shows a schematic diagram of temperature control of an industrial stove. Analyze the principle
of the system, dentifying the plant, controlled variables and references. Draw a block diagram for the control
system.
Figure 1-17
Stove temperature control system
E1.4 A potentiometer servo system for missile launcher is shown in Figure 1-18 . In which, the paralleled
potentiometers
and P2 are then connected to the power source E0 .The slide-arm is connected with the
input axis and the output axis respectively to constitute the given elements and the measure feedback
P1
elements of Azimuth. The input axis is operated by hand wheel, while the output axis is driven by the
decelerated DC motor with armature control.
Analyse the work principle of system, identify the plant, controlled variables and references, and draw
the block diagram of system.
Figure 1-18
E1.5
A potentiometer servo system for missile launcher
A steam engine rotational speed control system, which adapts centrifugal governor, is shown in Figure 1-19.
The principle is: When the steam engine drives load rotating, it will drive a pair of flying hammers to rotate
horizontally through bevel gear. The Fflying hammer will drive the sleeve to slide up and down by gemel.
There is a balance spring in the sleeve which can drive the lever. The other end of lever can adjust the open
degree of steam valve. When the engine works regularly, centrifugal force of flying hammer is balanced
with the rebound force of spring, and the sleeve will be kept at a certain height to hold the valve at a
balanced position. However, if the load is too large and make the engine rotate speed  decrease, flying
hammer will drive the sleeve to slide down due to the reduced centrifugal force. This will increase the valve
open degree through lever, which will speed up engine. With the same principle, if the load becomes less
and the engine speed increases, the sleeve will be driven up due to increased centrifugal force of flying
hammer couple. This will make the engine slow down through the lever and valve open degree controlled by
the lever. Consequently, Centrifugal Governor can balance the effect that load variation imposes to the
engine speed and keep the steam engine working around an expected speed.
Identify the plant, controlled variables and references, and sketch the system block diagram.
Figure 1-19
E1.6
Steam engine rotational speed control system
An angle position auto tracking system of camera is shown in Figure 1-20. When the spot displayer aims at a
certain direction, camera will automatically track to this direction. Please analyze its principle and identify
the plant, controlled variables and references. Draw a block diagram for the control system.
Figure 1-20
Angle position auto tracking system of camera
E1.7 Figure 1-21(a), (b) show the voltage control system. If the unloaded voltages of electricity generators of the
two systems are both 110V, which system will keep this voltage and which one will be lower than 110V
when loaded? why?
Figure 1-21
Voltage control system
E1.8 Figure 1-22 shows the water temperature control system. Cold water will be heated by vapor in heat
exchanger to a certain temperature. The variation of cold water flow is measured by flow meter. Draw the
system block diagram and describe how this system works to keep the water temperature. Identify the plant
and control device.
Figure 1-22 Water temperature control system
E1.9 Many machines, such as lathe, milling machine and grinding machine, have followers with them to replicate
the contour of model. Figure 1-23 shows one kind of servo system. In this system, cutter can replicate the
contour of model on the raw material. Please analyse its principle and draw a system block diagram.
Figure 1-23
Servo system
E1.10
Figure 1-24(a), (b) both show speed regulating system.
(1) Draw the system block diagrams responding to figure 1-24(a), (b) respectively. And give the correct
feedback connecting method.
(2) With the constant input, which system has steady error and which one does not? Please prove it.
Figure 1-24 speed regulating system
E1.11
Figure 1-25 shows the grain humidity control system. There is an optimal grinding humidity on which
we can acquire the most flour. So, we need to add some water to grain to achieve the optimal grain humidity.
As shown in the Figure 1-25, grain is conveyed with a constant flow under an auto valve which controls the
water quantity. In this process, grain flow, initial grain humidity and water pressure consist of the
disturbance of the grain humidity control system. In order to get better precision, feed forward control is
adapted. Please draw the block diagram of the system.
Figure 1-25 Grain humidity control system