Syllabus For The Subject Linear Control System



Chapter-1 basics of control systems



Classification of control systems

Open loop system



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



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


Sampled data systems


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


Definition of Laplace transform

Properties of Laplace transform


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


Concept of transfer function

Transfer function


Advantages and features of transfer function


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


Linear spring


Rotational motion

Equivalent mechanical system

Remarks on nodal method

Gear trains

Gear train with inertia and friction

Belt or chain drives


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



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


State model

Examples with solutions

University examples with solutions

Review questions


Chapter-5 Block diagram representation


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


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


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


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


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


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


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


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


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


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 as an error detector

Types of potentiometers

Characteristics of precision potentiometer

Loading in potentiometers


Synchro transmitter

Synchro control transformer

Synchros as an error detector


D.C tachometer





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



Torque-speed characteristics

Features of A.C servomotor


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


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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