Control Engineering


Author: Shivakumar E G

ISBN: 9788195268702

Copy Right Year: 2021

Pages:  532

Binding: Soft Cover

Publisher:  Yes Dee Publishing

SKU: 9788195268702 Category:


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.

Additional information

Weight .33 kg
Dimensions 22 × 15 × 1 cm

Table of Content

Chapter 1 Introduction to Linear Control Systems



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 RH Criteria

6.1 Introduction

6.2 RouthHurwitzCriterion

6.2.1 RouthHurwitzArray

6.2.2 Disadvantages of RouthHurwitzCriterion

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

About The Authors

Dr. E. G. Shivakumar is Professor, Department of Electrical Engineering , University Visvesvaraya College of Engineering, Bangalore University, Bengaluru. He received his B.E. degree (1982) from UVCE, Bangalore University and M. Tech. (Electrical)  degree (1984) from the IITM at Chennai and the Ph. D. degree (2002) from the IISc, Bengaluru. From 1984-89 he worked in HMT R&D as Design Engineer: From 1989-92 he worked in SKF Bearings as Maintenance Engineer: From 1992-95 he worked as Senior Lecturer in DSCE, Bengaluru. Since 1995 he has been with UVCE teaching both undergraduate and postgraduate students. He has published 30 research papers in international conferences and journals. He is a member of the Institution of Engineers (India) and Life member of ISTE.


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