## Description

This book is written covering theory of control systems having the following important features.

Chapter 1: Introduces open loop and closed – loop control systems.

Chapter 2: Deals with mathematical modeling of mechanical systems and electrical systems, analogues systems including both force-voltage and force-current analogy is covered.

Chapter 3: Explains transfer function approach using Block Diagram Algebra.

Chapter 4: Explains signal flow graphs and using them how to determine input-output relationship.

Chapter 5: Deals with time response of second order systems including steady state error.

Chapter 6: Explains Routh-Hurwitz Criterion and analyze stability of systems based on the Routh-Hurwitz criteria.

Chapter 7: Describes Root locus methods of analysis of stability of control systems when open-loop gain *K* is varied from 0 to ∞.

Chapter 8: Deals frequency response method of stability analysis using Nyquist plot and Bode plots.

Chapter 9: Covers state space analysis of control systems by writing state equations in phase variables, canonical form, from transfer functions. State transition matrix and solution of state equations is covered with number of solved problems.

## Table of Content

**Chapter 1 Introduction to Linear Control Systems **

OpenLoopControlSystem

ClosedLoopControlSystem(FeedbackControlSystem)

*Review Questions *

**Chapter 2 Mathematical Models of Linear Control Systems **

2.1 Introduction

2.2 DifferentialEquations ofPhysicalSystems

2.2.1 MechanicalSystems

2.2.2 MechanicalTranslationalSystem

2.2.3 Fixed-axisRotation

2.3 ElectricalSystems

2.4 Analogous Systems

2.4.1 Force-voltageAnalogy

2.4.2 Force-currentAnalogy

*Solved Problems *

2.5 TransferFunction

2.5.1 Procedure forDerivingTransferFunction

*Solved Problems (2.8 to 2.11) *

2.5.2 ArmatureControl ofDCMotor

2.5.3 FieldControl ofDCMotor

*Review Questions *

**Chapter 3 Block Diagram Algebra **

3.1 Introduction

3.2 BlockDiagramAlgebra

3.2.1 Summing ofSignals

3.2.2 Difference ofSignals

3.2.3 Take ofPoint ofSignals

3.3 BlockDiagramof aClosedLoop (FeedbackControl)System

3.4 BlockDiagramofArmatureControlledDCMotor

3.5 BlockDiagramofFieldControlledDCMotor

3.6 BlockDiagramReductionTechniques

3.6.1 CombiningBlocks inCascade

3.6.2 Moving aSummingPointAfter aBlock

3.6.3 Moving aSummingPointAhead of aBlock

3.6.4 Moving aTake-offPointAfter aBlock

3.6.5 Moving aTake-offPointAhead of aBlock

3.6.6 Eliminating aFeedbackLoop

*Solved Problems (3.1 to 3.7) *

*Review Questions *

**Chapter 4 Signal Flow Graphs **

4.1 Introduction

4.2 Definitions

4.2.1 Input Node (Source)

4.2.2 Output Node (Sink)

4.2.3 Path

4.2.4 ForwardPath

4.2.5 Loop

4.2.6 PathGain

4.2.7 ForwardPathGain

4.2.8 LoopGain

4.3 Mason’sGainFormula

*Solved Problems (4.1 to 4.12) *

*Review Questions *

**Chapter 5 Time Response of Control Systems **

5.1 Introduction

5.2 Typical Test Input Signals

5.2.1 Step Input Function

5.2.2 Ramp Input Function

5.2.3 Parabolic Input Function

5.3 Transient Response of Second Order System

5.4 Time Domain Specifications of aSecondOrderSystem

5.4.1 Delay Time (*td*)

5.4.2 Rise Time (*tr*)

5.4.3 Peak Time (*tp*)

5.4.4 Peak Overshoot (*Mp*)

5.4.5 Settling Time (*ts*)

5.4.6 Steady State Error (*ess*)

5.5 Time Response Specifications of Second Order Systems for a Step Input 5.5.1 Rise Time (*tr*)

5.5.2 Peak Time (*tp*)

5.5.3 Peak Overshoot (*Mp*)

5.5.4 Settling Time (*ts*)

*Solved Problems (5.1 to 5.6) *

5.6 SteadyStateError

5.6.1 Steady State Error Due to a Step Input

5.6.2 Steady State Error for Ramp (Velocity) Input

5.6.3 Steady State Error Due to Parabolic Input or Acceleration Input

*Solved Problems (5.7 to 5.12) *

5.7 ErrorSeries

*Solved Problems (5.13 to 5.14) *

5.7.1 Error Series Using Binomial Theorem (Alternative Method)

*Solved Problems (5.15 to 5.22) *

*Review Questions *

**Chapter 6 R***−***H Criteria **

6.1 Introduction

6.2 Routh*−*HurwitzCriterion

6.2.1 Routh*−*HurwitzArray

6.2.2 Disadvantages of Routh*−*HurwitzCriterion

*Solved Problems (6.1 to 6.16) *

*Review Questions *

**Chapter 7 Root Locus Techniques **

7.1 Introduction

*Solved Problems (7.1 to 7.16) *

*Review Questions *

**Chapter 8 Frequency Response **

8.1 Introduction

8.2 Frequency Response Specifications

8.2.1 To Find Expression for the Resonant Frequency *ωr *

8.2.2 To Find Expression for the Resonant Peak *Mr *

8.2.3 To Find Expression for the Phase Angle *φr *

8.3 Nyquist Plot

8.4 Nyquist Stability Criterion

8.4.1 Nyquist Stability Criterion

*Solved Problems (8.1 to 8.13) *

8.5 BodePlots

8.5.1 GainCrossOverFrequency

8.5.2 PhaseMargin

8.5.3 PhaseCrossoverFrequency

8.5.4 GainMargin

8.5.5 Stability Criteria Using Gain Margin and Phase Margin

8.5.6 GeneralProcedure forConstructingBodePlots

*Solved Problems (8.14 to 8.25) *

*Review Questions *

**Chapter 9 State Space Analysis **

9.1 Introduction

9.2 StateVariables

9.2.1 Definition of State Variables

9.3 StateModel ofLinearSystems

9.3.1 State Model for Single-Input Single-Output Linear Systems

*Solved Problems (9.1 to 9.10) *

9.4 State-SpaceRepresentation

9.4.1 State-SpaceRepresentationUsingPhaseVariables

*Solved Problems (9.11 to 9.18) *

9.5 Development of theStateEquations fromTransferFunctions

*Solved Problems (9.19 to 9.28) *

9.6 State-Space Representation Using Canonical Variables *Solved Problems (9.29 to 9.31) *

9.7 Solution of theStateEquation forLinearTime-InvariantSystems

9.8 Solution by theLaplaceTransformationMethod

9.9 Properties of State Transition Matrix

*Solved Problems (9.32 to 9.42) *

*Review Questions *

*Appendix A *– **Solved Question Papers **

*Appendix B *– **Multiple Choice Questions **

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