control system mec709 notes week 1

7/25/2019 Control System MEC709 Notes Week 1

1/33

MEC709 Winter 2016 Instructor Siyuan He

1

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


2/33


2

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.


3/33


3

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.


4/33


4

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


5/33


5

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.


6/33


6

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.


7/33


7

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.


8/33


8

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


9/33


9

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.


10/33


10

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.


11/33


11

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).


12/33


12

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.


13/33


13

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.


14/33


14

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)


15/33


15

Fig. 1.14 Block diagram of automobile steering control system.


16/33


16

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.+Franklin


17/33


17

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


18/33


18

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


19/33


19


20/33


20


21/33


21

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.


22/33


22

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)


23/33


24/33


24

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.


25/33


25

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


26/33


26

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.


27/33


27

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.


28/33


28

( in/out current)

2


29/33


29


30/33


30

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.


31/33


31

An armature-controlled DC motor can be modeled as follows.


32/33


32


33/33


control system mec709 notes week 1

Documents