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Chapter 1Introduction

Prof. Ju-Jang Lee

Control System Eng. 2

Chapter Objectives

Control System ApplicationsHistory of Control SystemsHow to benefit from studying control systemsBasic features and configurationsAnalysis and Design ObjectivesDesign Process


1.1 Introduction

Control system definitionSubsystem(controller) + Processes(Plants)The outputs of the processes is controlled by the subsystemE.g.: Fuel valve(fuel valve actuator) + Furnace


Advantages of control systemsPower amplificationRemote control

− In remote and dangerous location

Convenience of input form− Input form can be changedfor convenience.

Compensation for disturbances− Measure the disturbance and compensate controller inputs accordingly.


1.2 History of Control Systems

Liquid-level controlA water clock around 300 B.C. in GreeceAn oil lamp

Steam pressure and temperature controlSteam pressure regulation Temperature control system in the 17th century

Speed controlA windmill blade area controlSpeed control of steam engines in the 18th century


Stability, stabilization, and steeringThe stability criterion for a 3rd order system

− by J.C.Maxwell in 1868Extended to 5th order systems

− by E. J. Routh in 1874‘The Criterion of Dynamical Stability’

− awarded The Adams Prize in 1877The Routh-Hurwitz criterion

− First contained in Routh’s ‘A treatise on the Stability of a Given State of Motion

Lyapunov Stability Theory− Extension of Routh’s theory to nonlinear systems in

1892


Twentieth-century developmentsPID control based on the theory of Nicholas Minorsky in early 20th centuryAnalysis of a feedback amp

− H.W.Bode and H. Nyquist at Bell lab in 1920s and 1930s

− Evolved into sinusoidal frequency analysis and design techniques

The root locus− To map the roots of the characteristic equation of a

feedback system developed by W.R. Evans in 1948.


Contemporary applicationsWidespread application in

− The control of missiles, spacecraft, planes and ships and− Process control, etc.

Digital computers as part of control systemsHome application, entertainment systems


1.3 The Control Systems EngineerControl systems engineering

Concerns designing systems to meet overall system requirementsRequires knowledge of numerous branches of engineering and sciences

Bottom-up design− In typical engineering curricula

Top-down design− Formulate system requirements first− Define functions and hardware to implement

Students are encouraged to take a top-down design as a result of the course


1.4 Response Characteristics and System Configurations

Input and output(Reference) Input

− Desired response of the plantOutput

− Actual response of the plant


1.4 Response Characteristics and System Configurations

Transient response− Gradual change of the response from its initial state

Steady-state response− Approximation to the desired response− Steady-state error

− ess = Desired response – Steady-state response


Open-loop SystemsController + Process (plant) in cascade form

− A transducer may be required to change the input form to the controller

− Disturbances may existCannot compensate the disturbance signals

E.g.: toasters, mechanical systems, etc.


Closed-loop (feedback control) systemsThe plant output is incorporated:

Plant Input = Reference Input - Plant Output− Plant input and output transducers may be required.− More complex than open loop system, but− Transient response and steady-state error can be

controlled more efficiently.


Computer-controlled systemsDigital computers

− Server as the controller in modern control systems− Perform supervisory functions− Control algorithms and gains are implemented in

software.


1.5 Analysis and Design Objectives

Major objectives of system analysis and designProducing the desired transient responseReducing steady-state errorAchieving stability


1.5 Analysis and Design Objectives

Transient responseThe response is related to

− User patience− Physical damage

Tuning parameters to have desired transient response is done through system analysis.

Steady-state responseAnalyzing the steady-state error and Reducing the error through analysis


StabilityMost important issue in control theorySystem response = Forced response + Natural responseNatural response, for stability, must

− Eventually approach to zero or− Oscillate.

Unstability could lead to self-destruction of the system


Other considerationsSize, power of actuators,Sensor accuracy,Finances,Robustness, etc.


1.6 The Design Process

Control system design steps


1.6 The Design Process

Step1: Transform requirements into a physical systemPower, weight, physical dimension, sensor accuracy must be determined considering transient response and steady-state error

Step2: Draw a functional block diagramBlock diagram representation and interconnection of the subsystemsFunctions and hardware descriptions should be described.


Step 3: Create a schematicDerive a schematic from the block diagram by

− making approximations, assumptions of the system.

The schematic should be compact and simple, but must be able to account for observed behavior of the system.


Step 4: Develop a mathematic modelUsing physical laws such as Kirchhoff’s laws and Newton’s laws model the system mathematicallyThe system is often represented by

− Differential equations,− Transfer functions, or− State-space representation

Parameters needed in the model are provided from the vendors or must be obtained through experiments.

Step 5: Reduce the block diagramSeveral blocks (subsystems) can be reduced into a single block so that analysis can be more easily done.


Step 6: Analyze and designThe engineers check if

− the response specification and− performance requirements can be met by adjustments of

system parameters.Typical test signals


− Impulse input:− the response is only the transient response− a mathematical model of the system can be derived

− Step input:− both the transient and the steady-state response are

clearly visible− Ramp or parabolic input:

− additional information about steady-state error− Sinusoidal input:

− Test a physical system to arrive at a mathematical model


Through all the steps the design requirements must be satisfied

StabilityTransient responseSteady-state response


1.7 Computer-Aided Design

Use of computer in designing and analyzing control systems is strongly encouraged

MATLABMost popular and strong computer tool.Most algorithms in control systems, neural networks, fuzzy logic, signal processing, etc. are available in MATLAB toolbox.Simple C-style code is required to run MATLAB.


Summary

Control systemscover numerous branches of engineering and sciencesHave widespread applications

Terms in control systemControllerProcess = plant(Reference) Input = desired response of the plantOutput = actual response of the plantOpen-loopClosed-loop


Objectives of design and analysisSystem stabilityTransient responseSteady-state response

Design procedureStep1: Determine a physical system and specificationsStep2: Draw a functional block diagramStep3: Draw a schematicStep4: Obtain a mathematical modelStep5: Reduce the block diagramStep6: Analyze and design to meet the requirements

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Documents

feedback system

plantcontrol system

centurycontrol system

coursecontrol system

process control

control of missiles

system configurations

overall system requirementsz