**LINEAR CONTROL SYSTEM**

Chapter-1 basics of control systems

Background

Definitions

Classification of control systems

Open loop system

Advantages

Disadvantages

Real time applications of an open loop system

Sprinkler used to water a lawn

Stepper motor positioning system

Automatic toaster system

Traffic light controller

Automatic door opening and closing system

Closed loop system

Advantages

Disadvantages

Real time applications of closed loop system

Human being

Home heating system

Ship stabilization system

Manual speed control system

D.C motor speed control

Temperature control system

Missile launching system

Voltage stabilizer

Comparison of open loop and closed loop control system

Digital and sampled data control systems

Advantages of digital control

Limitations of digital control

Applications

Sampled data systems

Servomechanisms

Regulating systems

Feedback and feed forward system

Real time application of feed forward system

Requirements of an ideal control system

Review questions

Chapter-2 Basics of Laplace transform

Background

Definition of Laplace transform

Properties of Laplace transform

Linearity

Scaling theorem

Real differentiation

Real integration

Differentiation by s

Complex translation

Real translation

Initial value theorem

Final value theorem

Inverse Laplace transform

Simple and real roots

Multiple roots

Complex conjugate roots

Use of laplace transform in control system

Special case of inverse laplace transform

University examples with solutions

Review questions

Chapter-3 transfer function and impulse response

Background

Concept of transfer function

Transfer function

Definition

Advantages and features of transfer function

Disadvantages

Procedure to determine the transfer function of a control system

Impulse response and transfer function

Some important terminologies related to the T.F

Poles of a transfer function

Characteristics equation of a transfer function

Zeros of a transfer function

Pole-zero plot

Order of a transfer function

Laplace transform of electrical network

Examples with solutions

Review questions

Chapter-4 Mathematical modeling of control systems

What is mathematical model

Analysis of mechanical systems

Translational motion

Mass

Linear spring

Friction

Rotational motion

Equivalent mechanical system

Remarks on nodal method

Gear trains

Gear train with inertia and friction

Belt or chain drives

Leavers

Electrical systems

Analogous systems

Mechanical system

Force voltage analogy

Force current analogy

Steps to solve problems on analogous systems

Models of thermal systems

Heat transfer system

Thermometer

Actuators

Hydraulic actuator

Pneumatic actuator

Comparison between pneumatic and hydraulic systems

Liquid levels systems

Resistance and capacitance

Transfer function of simple liquid level system

Transfer function of liquid level system with interaction

Analog in various systems

Concept of state variable modeling

Concept of state

Definitions

State model

Examples with solutions

University examples with solutions

Review questions

Chapter-5 Block diagram representation

Background

Elements of block diagram

Illustrating concept of block diagram representation

Advantages of block diagram

Simple or canonical form of closed loop system

Derivation of T.F. of simple closed loop system

Rules for block diagram reduction

Critical rules

Converting nonunity feedback to unity feedback

Procedure to solve block diagram reduction problems

Examples with solutions

Analysis of multiple input multiple output systems

Review questions

Chapter-6 Signal flow graph representation

Background

Properties of signal flow graph

Terminology used in signal flow graph

Methods to obtain signal flow graph

From the system equations

From the given block diagram

Mason’s gain formula

Comparison of block diagram and signal flow graph methods

Application of mason’s gain formula to electrical network

Obtaining block diagram from signal flow graph

Examples with solutions

University examples with solutions

Review questions

Chapter-7 Time domain analysis of control systems

Background

Definition and classification of time response

Standard test inputs

Steady state analysis

Derivation of steady state error

Effect of input on steady state error

Effect of change in G h on steady state error

Analysis of TYPE 0,1 AND 2 systems

Disadvantages of static error coefficient method

Generalized error coefficient method

Transient response analysis

Method to determine total output

Analysis of first order system

Unit step response of first order system

Closed loop poles of first order system

Analysis of second order system

Effect of on second order system performance

Derivation of unit step response of a second order system

Transient response specifications

Derivations of time domain specifications

Derivation of peak time T p

Derivation of Mp

Derivation of T,

Derivation of Ts

Examples with solutions

University examples with solutions

Review questions

Chapter-8 Concepts of stability

Background

Concept of stability

Stability of control systems

Zero input and asymptotic stability

Remarks about asymptotic stability

Relative stability

Routh-hurwitz criterion

Necessary conditions

Hurwitz ‘s criterion

Disadvantages of Hurwitz’s method

Routh’s stability criterion

Routh’s criterion

Special cases of routh’s criterion

Special case 1

Special case 2

Procedure to eliminate this difficulty

Importance of an auxiliary equation

Change in criterion of stability in special case 2

Applications of routh’s criterion

Relative stability analysis

Determining range of values of K

Advantages of routh’s criterion

Limitations of routh’s criterion

Marginal k and frequency of sustained oscillations

Examples with solutions

Review questions

Chapter-9 Root locus

Background

Basic concept of root locus

Angle and magnitude condition

Angle condition

Use of angle condition

Magnitude condition

Use of magnitude condition

Graphical method of determining ‘k’

Construction of root locus

Rules for construction of root locus

Graphical determination of ‘k’ for specified damping ratio

General steps to solve the problem on root locus

Effect of addition of open loop poles and zero

Addition of pole

Addition of zeros

Advantages of root locus method

Obtaining G H from characteristics equation

University examples with solutions

Review questions

Chapter -10 Basic of frequency domain analysis

Background

Advantages of frequency domain approach

Limitation of frequency response methods

Conceptual approach to frequency response

Steady state response sinusoidal input

Frequency domain methods

Co-relation between time domain and frequency domain for second

Order system

Derivations of M,and

Comments on co-relations between time domain and frequency domain

B.W

Examples with solutions

Review questions

Chapter-11 Stability analysis using bode plots

Introduction to bode plot

Magnitude plot

The phase angle plot

Logarithmic scales

Standard form of open loop T.F

Bode plots of standard factors of G

Factor 1 system gain ‘k’

Factor 2 poles or zeros at the origin

Factor 3 simple poles or zeros

Factor-4 quadratic factors

Steps to sketch the bode plot

Frequency response specifications

Calculation of G.M. and P.M.from bode plot

What should be values of G.M.and.P.M of a good system

How to improve the G.M.and.P.M

Determination of wgc and P.M.for standard second order system

Calculation of transfer function from magnitude plot

Advantages of bode plots

Examples with solutions

University examples with solutions

Review questions

Chapter -12 Polar and nyquist plots

Background

Polar plot

Wgc and wpc in polar plot

Determination of G.M and P.M. from polar plot

Determining wpc mathematically

Stability determination from polar plot

Nyquist plot analysis

Pole-zero configuration

Encirclement

Counting number of encirclements

Analytic function and singularities

Mapping theorem or principles of argument

Nyquist stability criterion

Generalized nyquist path and its mapping

Steps to solve problems by nyquist criterion

Behavior of right half pole

Advantages of nyquist plot

Magnitude-phase plots

Stability analysis using magnitude-phase plot

Closed loop frequency response

Circles (constant magnitude loci)

Circles (constant phase loci)

Use of M circles

Use of N circles

Nichol ‘s chart

Frequency specifications from the nichol’s chart

Examples with solutions

University examples with solutions

Review questions

Chapter-13 Compensation techniques

Introduction

Types of compensation

Series compensation

Parallel compensation

Series-parallel compensation

Compensating networks

Lead compensator

Maximum lead angle m and

Polar plot of lead compensator

Bode plot of lead compensator

Steps to design lead compensator

Effects of lead compensation

Limitations of lead compensation

Lag compensator

Maximum lag angle and b

Polar plot of lag compensator

Bode plot of lag compensator

Steps to design lag compensator

Effects and limitations of lag compensator

Lag –lead compensator

Polar plot of lag-lead compensator

Effects of lag-lead compensator

Effects of lag-lead compensator

Compensation using root locus

Designing lead compensator using root locus

Designing lag compensator using root locus

Designing lag-lead compensator using root locus

Examples with solutions

Review questions

Chapter-14 control system components

Potentiometer

Potentiometer as an error detector

Types of potentiometers

Characteristics of precision potentiometer

Loading in potentiometers

Synchros

Synchro transmitter

Synchro control transformer

Synchros as an error detector

Tachogenerators

D.C tachometer

Advantages

A.C.tachometer

Advantages

Servomotors

Requirements of good servomotor

Types of servomotors

D.C. servomotor

Field controlled D.C servomotor

Features of field controlled D.C servomotor

Armature controlled D.C servomotor

Features of armature controlled D.C servomotor

Characteristics of D.C servomotors

Applications of D.C servomotor

Transfer function of field controlled D.C motor

Transfer function of armature controlled D.C motor

A.C servomotor

Construction

Rotor

Torque-speed characteristics

Features of A.C servomotor

Applications

Transfer function of A.C servomotor

Comparison of servomotors

Comparison between A.C D.C servomotors

Comparison between armature controlled and field controlled D.C servomotors

Magnetic amplifier

Various control systems used in industry

Generators

Generator driving motor

Position control system

Position control with field controlled motor

Speed control system

Speed control using generator driving motor

Typical position control system used in industry

Examples with solutions

Review with solutions

Review questions

Appendix A controllers

Introduction to P-I-D controllers

PD type of controller

PI type of controller

PID type of controller

Rate feedback compensation

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