This document provides an introduction to control systems. It defines a control system as a system used to achieve a desired output. The basic components of a control system are identified as a plant, controller, actuator, sensor, and disturbance. Control systems are classified as open-loop or closed-loop based on whether feedback is used. A brief history of control is provided, highlighting early examples and the development of modern control theory. Requirements for control systems like stability, quickness, and accuracy are also discussed.

1. Clase 01
Introducción a los Sistemas de
Control
Luis Sánchez

2. Contenido
• What is a control system?
• A brief history of control
• Basic components of a control system
• Classification of control systems
• Open-loop control vs. closed-loop control
• Basic requirements of control systems

3. Introduction to Control Systems:
What is “a Control system”?
What is “a system”?
Es la acción o el efecto de poder decidir sobre el
desarrollo de un proceso o sistema. También se puede
entender como la forma de manipular ciertas variables
para conseguir que ellas u otras variables actúen en la
forma deseada.
System is composed of a set of interacting components
(elements) stimulated or excited by an external input to
produce an external output.
What is “ control”?

4. What is a control system?
• Generally speaking, a control system is a system
that is used to realize a desired output or objective.
• Control systems are everywhere
– They appear in our homes, in cars, in industry, in
scientific labs, and in hospital…
– Principles of control have an impact on diverse fields as
engineering, aeronautics ,economics, biology and
medicine…
– Wide applicability of control has many advantages (e.g.,
it is a good vehicle for technology transfer)

5. Simplified description of a control system
diagrama de bloque

6. A brief history of control
• Two of the earliest examples
– Water clock (270 BC)
– Self-leveling wine vessel (100BC)
The idea is
still used
today, i.e.
flush toilet

7. A brief history of control
• the first modern controller
• regulated speed of steam engine
• reduced effects of variances in load
• propelled Industrial Revolution
Regulador Centrifugo (James Watt,1769)

8. A brief history of control
• Birth of mathematical control theory
– G. B. Airy (1840)
• the first one to discuss instability in a feedback control system
• the first to analyze such a system using differential equations
– J. C. Maxwell (1868)
• the first systematic study of the stability of feedback control
– E. J. Routh (1877)
• deriving stability criterion for linear systems
– A. M. Lyapunov (1892)
• deriving stability criterion that can be applied to both linear and
nonlinear differential equations
• results not introduced in control literature until about 1958

9. A brief history of control
• Birth of classical control design method
–H. Nyquist (1932)
• developed a relatively simple procedure to determine
stability from a graphical plot of the loop-frequency
response.
–H. W. Bode (1945)
• frequency-response method
–W. R. Evans (1948)
• root-locus method
With the above methods, we can design control
systems that are stable, acceptable but not optimal in
any meaningful sense.
core of classical
control design

10. A brief history of control
• Development of modern control design
–Late 1950s: designing optimal systems in some
meaningful sense
–1960s: digital computers help time-domain analysis
of complex systems, modern control theory has
been developed to cope with the increased
complexity of modern plants
–1960s~1980s: optimal control of both deterministic
and stochastic systems; adaptive control and
learning control

11. Basic components of a control system
Plant
Controlled Variable
Expected Value
Controller
Actuator
Sensor
Disturbance

12. Basic concepts of a control system
Plant
1.Plant: a physical object to be controlled
such as a mechanical device, a heating furnace,
a chemical reactor or a spacecraft.
Controlled
variable
2.Controlled variable: the variable
controlled by Automatic Control System ,
generally refers to the system output.
Expected
value
3.Expected value : the desired value of
controlled variable based on requirement,
often it is used as the reference input

13. Disturbance
7.Disturbance: the unexpected factors
disturbing the normal functional relationship
between the controlling and controlled parameter
variations.
Controller
4.Controller: an agent that can calculate
the required control signal.
Actuator
5.Actuator: a mechanical device that takes
energy, usually created by air, electricity, or
liquid, and converts that into some kind of
motion.
Sensor
6.Sensor : a device that measures a physical
quantity and converts it into a signal which
can be read by an observer or by an
instrument.

14. Block diagram of a control system
Controller Actuator Plant
Sensor
-
r
Expected
value
e
Error
Disturbance
Controlled
variable
n
y
comparison component
(comparison point) :
its output equals the
algebraic sum of all input
signals.
“+”: plus; “-”: minus
lead-out point:
Here, the signal is
transferred along
two separate routes.
The Block represents
the function and name of its
corresponding mode, we don’t
need to draw detailed structure,
and the line guides for the transfer route.
u

15. Classification of control systems
1. According to
structure
Open-loop control Closed-loop control Composition
control

16. Open-loop control systems
• Open-loop control systems: those systems in which
the output has no effect on the control action.
• The output is neither measured nor fed back for
comparison with the input.
• For each reference input, there corresponds a fixed
operating conditions; the accuracy of the system depends
on calibration.
• In the presence of disturbances, an open-loop system will
not perform the desired task.
CONTROLLER PLANT
Control
signal
System
output
System
input

17. Open-loop control systems
• Examples
–Washing machine
–Traffic signals
Note that any control systems that
operates on a time basis are open-
loop.

18. Open-loop control systems
• Some comments on open-loop control
systems
–Simple construction and ease of
maintenance.
–Less expensive than a closed-loop system.
–No stability problem.
–Recalibration is necessary from
time to time.
–Sensitive to disturbances, so less accurate.
Good
Bad

19. Open-loop control systems
• When should we apply open-loop control?
–The relationship between the input and output
is exactly known.
–There are neither internal nor external
disturbances.
–Measuring the output precisely is very hard
or economically infeasible.

20. Closed-loop control systems
• Closed-loop control systems are often referred to as
feedback control systems.
• The idea of feedback:
– Compare the actual output with the expected value.
– Take actions based on the difference (error).
– This seemingly simple idea is tremendously powerful.
– Feedback is a key idea in the discipline of control.
CONTROLLER PLANT
Control
signal
System
output
Expected
value Error

21. Closed-loop control systems
• In practice, feedback control system and
closed-loop control system are used
interchangeably
• Closed-loop control always implies the use of
feedback control action in order to reduce
system error

22. Example 1 : Control de Nivel de agua
(flush toilet)
threshold
piston
float
water
h(t)
q1(t)
q2(t)
Lever
Water
Tank
Float
Piston
0h ( )h t1( )q t
lever
Plant:
Controlled Variable:
Output:
Expected value:
Sensor:
Controller:
Actuator:
0h
( )h t
0h
PlantController Actuator
Sensor
water tank
water flow
water level
float
lever
piston

23. Example 2: Cruise control
Calculation
element
Engine Auto
Speedometer
Desired
velocity
Measured
velocity
Actual
velocity
ActuatorController Plant
Sensor
Controlled
variable
Reference
input
Disturbance
engu
desv v
Control
signal
Error

24. Car driving system
 Objective: To control direction of a car
 Outputs: Actual direction of car
 Control inputs: Road markings.
 Disturbances: Road surface and grade, wind, obstacles
Example 3: Car Control direction

25.  Functional block diagram:
 Time response:
Measurement, visual
Steering
Mechanism
AutomobileDriver
Desired
course of
travel
Actual
course of
travelError+
-
Example 3: Car Control direction

26. Position Control
 Specification:
Speed of disk:
1800 rpm to 7200 rpm
Distance head-disk:
Less than 100nm
Position accuracy:
1 µm
Move the head from
track ‘a’ to track ‘b’
within 50ms

27. Comments on feedback control
• Main advantages of feedback:
–reduce disturbance effects
–make system insensitive to variations
–stabilize an unstable system
–create well-defined relationship between
output and reference

28. Comments on feedback control
• Potential drawbacks of feedback:
–cause instability if not used properly
–couple noise from sensors into the dynamics
of a system
–increase the overall complexity of a system

29.  Application: CD player, computer disk drive
 Requirement: Constant speed of rotation
 Open loop control system:
 Block diagram representation:
Open -Loop Control (FeedForward) To Close -
Loop Control

30. Closed Loop (Feedback Control)
 Closed-loop control system:
 Block diagram representation:

31. Other examples of feedback
Feedback systems are not limited to engineering
but can be found in various non-engineering fields
as well.
The human body is highly advanced feedback
control system.
Body temperature and blood pressure are kept
constant by means of physiological feedback.
Feedback makes the human body relatively
insensitive to external disturbance. Thus we can
survive in a changing environment.

32. Human Body
Temperature
 Regulated temperature around 37°C
Eyes
 Follow moving objects
Hands
 Pick up an object and place it at a
predetermined location
Pancreas
 Regulates glucose level in the blood

33. Open-loop vs. closed-loop
• Open-loop control • Closed-loop control
Simple structure,
low cost
Low accuracy and
resistance to disturbance
Easy to regulate
Ability to correct error
Complex structure,
high cost
High accuracy and
resistance of disturbance
Selecting parameter is critical
(may cause stability problem)
Open-loop＋Closed-loop＝Composite control system

34. 2. According to
reference input
Constant-value
control
Servo/tracking
control
Programming
control
Classification of control systems
• the reference input (expected
value) is a constant value
• the controller works to keep the
output around the constant value
e.g. constant-temperature
control, liquid level control and
constant-pressure control.
• the reference input may be
unknown or varying
• the controller works to
make the output track the
varying reference
e.g. automatic navigation
systems on boats and planes,
satellite-tracking antennas
• the input changes
according to a program
• the controller works
according to predefined
command
e.g. numerical control
machine

35. Classification of control systems
3. According to
system
characteristics
Linear control
system
Nonlinear
control
system
• superposition principle applies
• described by linear differential
equation
• described by nonlinear differential
equation
1 1 2 2( ) ( )f x y f x y 
1 2 1 2 1 2( ) ( ) ( )f x x f x f x y y    
superposition principle

36. Remark on nonlinear systems
• Quite often, nonlinear characteristics are
intentionally introduced in a control system to
improve its performance or provide more effective
control.
For instance, to achieve a temperature control, an on-
off (bang-bang or relay) type controller is used
• There are no general methods for solving a wide
class of nonlinear systems.

37. Classification of control systems
4. According to
signal form
Continuous
control system
Discrete
control system
All the signals are functions of
continuous time variable t
Signals are in the form of either a
pulse train or a digital code
e.g. digital control system

38. Classification of control systems
5. According to
parameters
Time-invariant
system
Time-varying
system
The parameters of a control
system are stationary with respect
to time
System contain elements that drift
or vary with time
e.g. Guided-missile control system, time-
varying mass results in time-varying
parameters of the control system

39. Basic requirements for control systems
Elevator input and output

40. Basic requirements for control systems
• Stability: refer to the ability of a system to
recover equilibrium
• Quickness: refer to the duration of transient
process before the control system to reach its
equilibrium
• Accuracy: refer to the size of steady-state error
when the transient process ends
(Steady-state error=desired output – actual
output)

41. Note
• For a control system, the above three
performance indices (stability, quickness,
accuracy) are sometimes contradictory.
• In design of a practical control system, we
always need to make compromise.