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7/25/2019 Control System MEC709 Notes Week 1
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MEC709 Winter 2016 Instructor Siyuan He
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Week 1 (Jan. 11~Jan. 15 2016)
Chapter 1 Concepts of Control Systems
What is a control system?
Basic components of a control system
Open-loop and closed-loop control systems
Examples of control systems
Steps of designing a control systems
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1.1 What is a control system?
1. 1. 1 Definition
A process (or a plant) under consideration is forced to behave in a
desired way.
Or, the variable of a process (or a plant) is kept to adhere to a desired
reference value, which could be either fixed or changing with time.
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1. 1. 2 Example 1: Water lever control system
Fig. 1.1 Water level control system.
The system is composed of a tank, an inlet valve Vc and an outlet
valveV0.
The tank water levelccan be controlledto the desired water level r
by adjusting the inlet valve Vc.
Fig. 1.2 Descriptive block diagram of the water level control system.
Block diagram: used to graphically describe the control systems to
shown the composition and the interconnection of a system, as well as
the flow of information.
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1. 1. 3 Example 2: House temperature control system
Fig. 1.3 House temperature control system.
The thermostat measures the temperature in the house and controls
the gas valve to turn on (Tin
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1. 2 Basic components in a control system
Fig. 1.5 Basic components in a tank water level control system.
Fig. 1.6 Basic components in a house temperature control system.Process: its output is to be controlled, e.g., tankor house.
Output: controlled variable, e.g., water level or house temperature.
Reference (or input): desired value of the controlled variable, e.g.,
desired water level or desired house temperature.
Actuator:the deviceable to influence the controlled variable, e.g.,
inlet adjustable valve or the furnace (the furnace also includes the gas
valve and a fan).
Controller: the component computing the control signal, e.g., the
thermostat.
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Sensor:the component used to measure the controlled variable.
Plant:the combination of the process and the actuator.
Control signal (actuating signal): it is computed by the controller
and is sent to the actuatorto influence the controlled variable.
Error signal: the difference between the input and the output. It is
sent to the controller to compute the control signal.
Comparator: computing the difference between the reference signal
and the sensor output.
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1. 3 Open-loop and closed-loop control systems
1. 3. 1 Definition
Open-loopcontrol systems do not measurethe outputand there is no
correctionof the actuating signal to make the output conform to the
reference signal.
In closed-loop control systems (or feedback control systems), the
outputis measuredand comparedwith the input. The error signal is
sent to the controller to influence the output.
In a feedback system, corrective actions are taken to correct the
output whenever a difference between the output and the input is
detected by the sensor, regardless of whatever reasonsthe difference
is caused by.
1. 3. 2 Structure of a closed-loop control system
Fig. 1.7 General structure of a closed-loop control system.
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1. 3. 3 Motivations of using closed-loop control systems
Motivation 1):Reducing the effect of parameters variations.
Motivation 2):Reducing the effects of disturbances.
Motivation 3): Improving transient response characteristics. (will be
discussed in later chapters)
Motivation 4): Improving steady-state response (reducing steady-
steady errors). (will be discussed in later chapters)
In the open-loop water level control example: 1) pressurevariations upstream of Vc and downstream of Vo can be important
disturbances affecting inflow and outflow; 2) a sudden or gradual
change of flow resistanceof the valves due to foreign matter or valve
deposits is a system parameter variation.
Fig. 1.9 Closed-loop control of the tank water-level.
If a closed-loop is applied to the water level control system as
shown in Fig. 1.9: 1) the output water level is measured
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continuously and is compared with the desired water level; 2) the
error signal r c is used through the controller to adjust the inlet
valve to keep the tank water level cequal to the desired water level r.
In closed-loop water level control system, the feedback loop causes
the system to take corrective action if the output c (actual level)
deviates from input r(desired level), whatever the reason.
Hence, the closed-loop water level control systems is not sensitiveto
either the disturbancesor parameters variations.
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1. 4 Examples of control systems
1. 4. 1 Cruise control
Fig. 1.10 Cruise control (Ref 1)
The goal is to keep the car at a constant speed.
Process:the car, Output(controlled variable): speed of the car,
Actuator: the throttle and the engine, Disturbance: grade changes
Fig. 1.11 Open loop cruise control.
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Open-loop cruise control: the position of the throttle is locked the
moment the driver engages cruise control.
The open-loop control works well if the vehicle is driving on
perfectly flat terrain. On hilly terrain, the vehicle will slow down
when going uphill and accelerate when going downhill. Therefore the
speed is not well controlled.
In this open-loop cruise control, the output (real car speed) is not
measured to be compared with the input (desired car speed) to
influence the output. In another word, no corrective actions are
taken based on the difference between the output and the input to
correct the output. Thus the system is sensitive to both disturbances
(grade changes) and parameter variations(e.g., tire pressure change
leads to friction change, and then speed change).
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Closed-loop cruise control: is the actual way implemented in car cruise
control, whereby the speed is monitored and the amount of throttle is
increased if the car is driving slower than the intended speed and decreased
if the car is driving faster.
Fig. 1.12 Closed-loop cruise control.
In the closed-loopcruise control, the output (real car speed) is measured
and comparedwith the input (desired speed). The speed difference between
the output and the input is sent to the controller, which computes control
signal to adjustthe throttle and then the engine to influence the car speed.
The above three steps of measuring-comparing-adjusting are done in
an automaticand continuousway.
In the closed-loop cruise control system, corrective actions are taken to
influence the car speed, as long asa difference between the car speed and
the desired speed is detected by the sensor, regardlessof whatever reasons
the speed difference is caused by.
Hence, in the closed-loop cruise control, the system is less sensitive to
disturbancesand parameter variationsthan the open-loop cruise control.
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1. 4. 2 Open-loop examples
Open-loop control is useful for well defined systems where the
relationship between input and the resultant state can be modeled by a
mathematical formula.
An open-loop controller is often used in simple processesbecause of
its simplicity and low-cost, especially in systems where feedback is
not critical.
Examples of open-loop systems are washing machine, hair dryerand
trafficsignal controlwhere the systems work on a preprogrammed
mannerand there is no feedback.
In a traffic signalsystem, the light is turned on for a given period of
time. A timer counts the time and sends a signal to turn on the light.
The system doesnt checkwhether the light has been really turned on
or not.
In a conventional washing machinethe washing cycle is broken into
several fixed steps, such as washing, rinsing and drying. Each step
takes a certain fixed period of time.
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1. 4. 3 Servo examples (self-study)
A regulating control or a regulator: the reference value is fixed. A
system is designed to maintain an output fixed regardless of
disturbances. For example, house temperature control, water level
control, cruise control and son on.
Tracking control or a servo:A systems is designed to follow a
changing reference. For example, robotics, auto manufacturing
machinery, car steering control system and so on.
Automobile steering control system (tracking control)
Fig. 1.13 Automobile steering control system.(Ref2)
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Fig. 1.14 Block diagram of automobile steering control system.
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1. 5 Steps of designing a control system
Steps of designing a control system for a given process and required
performance:
Modeling:Obtain mathematical descriptionof the systems.
Analysis:Analyze performanceof a given process in response
to inputs and disturbances, as well as in response to changes of
inputs and disturbances.
Design: If the performance of the process is not satisfactory,
how can the performance be improved without changing the
process, actuator and power amplifier blocks? (Instead, an
appropriate controller is to be designed.)
Ref 1:Gene F. Franklin,Feedback Control of Dynamic Systems, 4thedition, Prentice Hall, 2002
Ref 2: I. J. Nagrath, Control Systems Engineering,New Age International (P) Limited, 2006
http://www.amazon.com/s/ref=cm_cr_pr_pdt_bl_sr?ie=UTF8&field-keywords=Gene+F.+Franklinhttp://www.amazon.com/s/ref=cm_cr_pr_pdt_bl_sr?ie=UTF8&field-keywords=Gene+F.+Franklinhttp://www.amazon.com/s/ref=cm_cr_pr_pdt_bl_sr?ie=UTF8&field-keywords=Gene+F.+Franklinhttp://www.amazon.com/Feedback-Control-Dynamic-Systems-Edition/dp/0130323934/ref=cm_cr_pr_product_top?ie=UTF8http://www.amazon.com/Feedback-Control-Dynamic-Systems-Edition/dp/0130323934/ref=cm_cr_pr_product_top?ie=UTF8http://www.amazon.com/Feedback-Control-Dynamic-Systems-Edition/dp/0130323934/ref=cm_cr_pr_product_top?ie=UTF8http://www.amazon.com/Feedback-Control-Dynamic-Systems-Edition/dp/0130323934/ref=cm_cr_pr_product_top?ie=UTF8http://www.amazon.com/s/ref=cm_cr_pr_pdt_bl_sr?ie=UTF8&field-keywords=Gene+F.+Franklin7/25/2019 Control System MEC709 Notes Week 1
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Chapter 2 Modeling Physical Systems
Contents
2.1 Differential equations of physical systems
2.1.1 Mechanical systems
2.1.2 Electric circuits
2.1.3 Electromechanical systems (DC motor)
2.2 Laplace transform
2.3 Transfer function
2.4 Block diagram, signal-flow graph and system modeling
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2. 1 Differential equations of physical systems
2. 1. 1 Mechanical systems
2. 1. 1. 1 Translation motion
dampDirection opposite to velocit
spring
Direction opposite to displacement
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Rule:
1)Assign variables such as x to represent the position of massw. r. t.
the reference line. The acceleration x is also indicated.
2)Draw free-body diagram for mass Indicate all forces (magnitude and
direction) by letting a small displacement of mass along its positive
direction.
3)
Apply Newtons Law of Motion to obtain a differential equation for
each rigid body.
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Assume both m and m1 move a smal l displacement along their posit ive dir ections
< Streched
k1(x1-x) k1(x1-x)
+k1(x1-x)
-k1(x1-x)
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That means only one possible condition is needed to be assumed to
determine the forces, and then to derive the differential equations.
Summary on modeling translation mechanical systems
1) Assign variablessuch as x to represent the position of each rigid body
w. r. t. the reference line. Indicate the positive direction of x. The
acceleration x is also indicated.
2) Draw free-body diagram for each rigid body. Indicate all forces acting
on each mass and their reference directions by assuming a small
displacement of each mass along its positive direction. The acceleration of
each mass is also indicated.
3) If there are forces whose directions are determined by the displacement
or velocityof more than one rigid body, e.g.,xandx1 or x and 1x , assume
one possible conditionsuch as x>x1 and x > 1x to determine the directions
of the forces. Newtons 3rd Law of Motion (action and reaction forces)
should be used in determining action and reaction forces.
4) Apply Newtons Law of Motion to obtain a differential equation for each
rigid body.
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2. 1. 1. 2 Rotational motion
Modeling rotational motion systems follows the same rules for modeling
translational motion systems.
spring
damp
Direction: opposite to angulardisplacement
Direction: opposite to angularvelocity
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2. 1. 2 Electric circuits
Electric circuits consist of interconnections of sourcesof electric voltage
and current, resistors, capacitors, inductors and other electronic
elements.
Kirchhoffs current law: The algebraic sum of currents leaving a node
equals the algebraic sum of currents enteringthat node.
Kirchhoffs voltage law: The algebraic sum of all voltagestaken around a
closed pathin a circuit is zero.
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For simpleelectric circuits, Kirchhoffs current and voltage laws can be
directly used.
For complicated circuits, a methodof node analysiscan be used. i)One
node (common, ground or terminal) is chosen as a referenceand assume
the voltages of all other nodes to be unknowns; ii) Apply Kirchhoffs
current law at each node by representing currents in terms of the
unknown voltages.
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( in/out current)
2
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2. 1. 3 Electromechanical systems (DC motor) (self-study)
DC motor structure (Ref 1)
DC motors are widely used in control systems. A DC motor is device
converting electric energy into kinetic energy and is a typical
electromechanicalsystem.
A typical DC motor consists of a stator(magnet), a rotor(armature) and acommutator.
When a voltage is applied to the armature through the commutator, a
torqueis produced to rotate the rotor.
Various DC motors are developed. More details can be found in text 4.6.
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An armature-controlled DC motor can be modeled as follows.
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