1 / 28

Introduction to Control Systems

G(s)

_

Course Objectives

- To provide a general understanding of the

characteristics of dynamic systems and feedback

control. - To teach classical methods for analysing control

system accuracy, stability and dynamic

performance. - To teach classical control system design methods.

Course Contents

- Introduction to control systems
- Modelling of the physical systems
- Time domain analysis, Laplace transforms,

Transfer functions, System Responses - Closed loop control systems
- Classical design in the s-domain
- Classical design in the frequency domain
- Digital control systems
- Nonlineer control systems, on/off control
- Design examples

Course Book

- Advanced Control Engineering
- Roland S. Burns
- Butterworth-Heineman
- Paperback, 464 pages, publication date

OCT-2001ISBN-13 978-0-7506-5100-4ISBN-10

0-7506-5100-8

http//www.elsevier.com/wps/find/bookdescription.c

ws_home/677158/descriptiondescription

Introduction to Control Systems

Control System Concepts

- A system is a collection of components which are

co-ordinated together to perform a function. - Systems interact with their environment across a

separating boundary. - The interaction is defined in terms of variables.
- system inputs
- system outputs
- environmental disturbances

Systems

Disturbance Inputs

System Outputs

System

Engineering systems Biological systems Information

systems

Environment

Control Inputs

System Variables

- The systems boundary depends upon the defined

objective function of the system. - The systems function is expressed in terms of

measured output variables. - The systems operation is manipulated through the

control input variables. - The systems operation is also affected in an

uncontrolled manner through the disturbance input

variables.

Car and Driver Example

- Objective function to control the direction and

speed of the car. - Outputs actual direction and speed of the car
- Control inputs road markings and speed signs
- Disturbances road surface and grade, wind,

obstacles. - Possible subsystems the car alone, power

steering system, braking system, . . .

Antenna Positioning Control System

- Original system the antenna withelectric motor

drive systems. - Control objective to point theantenna in a

desired reference direction. - Control inputs drive motor voltages.
- Outputs the elevation and azimuth of the

antenna. - Disturbances wind, rain, snow.

Antenna Control SystemFunctional Block Diagram

Wind force

Antenna System

Angular position

volts

torque

volts

power

Ref. input

_

Antenna

Motor

Power amp

Diff. amp

Error

volts

Angle sensor

Feedback Path

Physical Variables

Information Variables

Control System Components

- System or process (to be controlled)
- Actuators (converts the control signal to a power

signal) - Sensors (provides measurement of the system

output) - Reference input (represents the desired output)
- Error detection (forms the control error)
- Controller (operates on the control error to form

the control signal, sometimes called

compensators)

Feedback System Characteristics

- Consider the following speed control system

Open Loop System Characteristics

- The accuracy of the open loop system depends upon

the calibration of the gains and prior knowledge

of the disturbance (choose the control u to give

the desired wo ). - Problems
- nonlinear or time varying gains
- unknown and varying disturbances

Closed Loop Characteristics

- Now consider the case with feedback

Closed Loop Characteristics

- If Ka is very large such that,
- then,
- Ks is the sensor gain in units of volts per

rad/s. - The input/output relationship is not very

sensitive to disturbances or changes in the

system gains

Closed Loop Characteristics System Error

- The control error is
- Again, if the loop gain, Ka Km Kl Ks is large,

then the error is small.

Note Gain Definitions

- forward gain Ka Km Kl
- feedback gain Ks
- loop gain Ka Km Kl Ks
- closed loop gain forward gain
- 1 loop gain

System Dynamics

- Consider a sudden change in the speed reference,

?r . - The output speed, ?o will not respond

instantaneously due to the inertial

characteristics of the motor and load, i.e. their

dynamic characteristics. - The motor and load need to be represented by

dynamic equations rather than simple gains. - The output response will generally lag the input

and may be oscillatory.

System Dynamics Step Responses

Ka 20

Ka 2

?o

?r

?o

?r

Tm

Tm

Assume Ks 1.0

Control System Design Objectives

- Primary Objectives
- 1. Dynamic stability
- 2. Accuracy
- 3. Speed of response
- Addition Considerations
- 4. Robustness (insensitivity to parameter

variation) - 5. Cost of control
- 6. System reliability

Control System Design Steps

- Define the control system objectives.
- Identify the system boundaries.
- define the input, output and disturbance

variables - Determine a mathematical model for the components

and subsystems. - Combine the subsystems to form a model for the

whole system.

Control System Design Steps

- Apply analysis and design techniques to determine

the control system structure and parameter values

of the control components, to meet the design

objectives. - Test the control design on a computer simulation

of the system. - Implement and test the design on the actual

process or plant.

Control System Design Steps

Examples of Control SystemsRoom Temperature

Control System

- Proportional mode Better accuracy, complex
- On/Off control mode Thermostatic control,

simple, low accuracy

Examples of Control SystemsAircraft Elevator

Control System

- Hydraulic servomechanisms have a good

power/weight ratio, and are ideal for

applications that require large forces to be

produced by small and light devices.

Examples of Control SystemsComputer Numerically

Controlled (CNC) Machine

- The purpose of this latter device, which produces

an analog signal proportional to velocity, is to

form an inner, or minor control loop in order to

dampen, or stabilize the response of the system.

Examples of Control SystemsShip Autopilot

Control System

- Actual heading is measured by a gyro-compass (or

magnetic compass), compared with desired value.

Error are send to autopilot (Course-keeping

system) - Actual rudder angle is sensed, and autopilot

controls the ship course by steering-gear.