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*Control systems engineering. by i.j. nagrath*

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Control systems engineering. by i.j. nagrath

- 1. FOURTH EDITION Flight path [1 Target pianeLater position of beamr.Ill.1%. . Firing angle 4 t ) i , ' .-5 -r Power amplier. 9nam we d . h n mm a FU m a m L 0 ( PC h j C n _ U V;a LI ugh;

2. Copyright 2006, 1998, 1982, 1975, New Age International (P) Ltd. , Publishers Published by New Age International (P) Ltd. , Publishers First Edition :1975Fourth Edition 2 2006All rights reserved. No part of this book may be reproduced in any form,by photostat,microlm,xerography,or any other means,or incorporated into any information retrieval system,electronic ormechanical,without the written permission of the copyright owner. ISBN :81-224-1775-2 Rs.695.00 C-05-07-261Printed in India at Ajit Printers,Delhi.Typeset at Goswarni Printers,Delhi. PUBLISHING FOR ONE WORLDNEW AGE lNTERNA'I'[0NAL (P) LIMITED.PUBLISHERS (fammj Wilg Earimr bbzikxo 4835/24, Ansari Road,Daryaganj.New Delhi - l l0O02 Visit us at www. newagepubllshers. com 3. $E%TEN? Preface to the Fourth Edition V Preface to the Third Edition viiI ,Iujnagmggngu ' 1-201.1 The Contmlsystem 2 1.2_SenLomenhanisms_61.3 Histog and Develogment of Automatic Control 10 1.4 Digital Comguter Control 141.5 Agglication of Control Theog in Non-engineering Fields 18 2.2 Differential Eguations of Physical Systems 24 2.3 Qgamics of Robotic Mechanisms 42eJ62.5 Block Diagam Algbra 542.6 Signal Flow Graphs 622.7 Illustrative Examples 72 .Lhm3.1 Feedback and Non-feedback Systems 92 3.2 Reduction of Parameter Variations by Use of Feedback 933.3 Control Over System Dmamics by Use of Feedback 973.4 Control of the Effects of Disturbance Signals by Use of Feedback 100 3.5 Linearizing Effect of Feedback 1023.6 Regenerative Feedback 1033.7 Illustrative Examgles 104Bmhlema_119 A Qghmm S131-EMS am:Qgmmmgm-13 .131,102 4.L__InI. rndnctinn__1324.2 Linear Apgmximation of Nonlinear Systems 133 4. 4.3 Controller Components 1344.4 Stepper Motors 154 4.5 Hydraulic Sgtems 1634.6 Pneumatic Systems 177Emhlems_185 5. Time Response Anangs,DESIGN Spscmcanows 193-268mms 5.1__Intmdnctinn_1945.2 Standard Test Sigpals 195 5.3 Time Resmnse of First-order Systems 197 5.4 Time Response of Second-order Sgtems 1995.5 Steady-state Errors and Error Constants 210 5.6 Eect of Adding a Zero to a System 2145.7 Design Specications of Second-order Systems 215 5.8 Desigp Considerations for Higher-order Systems 221 5.9_Bei: fnnnanceJndices_2235.10 Illustrative Examples 2275.11 Robotic Control Systems 237 5.12 State Variable AnalysisLaplace Transform Technique 2455.13 The Approximation of Higher-order Systems by Lower-order 248 6.1 The Concept of Stability 2706.2 Necessgy Conditions for Stability 275 6.3 Hurwitz Stability Criterion 2776.4 Routh Stability Criterion 2786.5 Relative Stability Analysis 2876.6 More on the Routh Stability Criterion 290 6.7 Stability of Systems Modelled in State Variable Form 291Problems 293 7. Tim Roar Locus Tscnmgus 297-3437.1 Introduction 2987.2 The RootLocus Concepts 299 1 3 C I.E II .am17.5 Systems with Transrtation L_ag 332 7.6 Sensitivity of the Roots of the Characteristic Eguation 3347 .7 MATLAB:Tool for Desigp and Analysis of Control S)gtemsApgndix III 340 Ernhlems_340 5. 8. FREQUENCY Response ANALYSIS 345-376s 8.2 Correlation between 131112 and Frequency Response 347 8.3 Polar Plots 3528.4 Bode Plots 3558.5 All-pass and Minimum-phase Systems 3668.6 Experimental Determination of Transfer Functions 3678.7 Log-magnitude versus Phase Plots 3708.8 MATLAB:Tool for Design and Analysis of Control SystemsAppendix III 371Emhlems_3_7_4 9& 9.J__Immdnc1;ion_31s 32] . ]E]. ..m9.3 Nyguist Stability Criterion 3819.4 Assessment of Relative Stability Using Nyguist Criterion 394 9.5 Closed-loop Frequency Response 4099.6 Sensitivity Analysis in Frequency Domain 417 Problems 42010. Iwmonucnon T0 Dssmn 426-51110.1 The Design Problem 42610.2 Preliminary Considerations of Classical Design 428 10.3 Realization of Basic Compensators 43510.4 Cascade Compensation in Time Domain 44010.5 Cascade Compensation in Frequency Domain 459 10.6 Tuning of P11) Controllers 47710.7 Feedback Compensation 48310.8 Robust Control System Design 490IE1:nh1ems_5Di11. DIGITAL CONTROL SYSTEMS 513-568 11.1 Introduction 51411.2 Sgrum Analysis of Sampling Process 51711.3 Signal Reconstruction 51911.4 Diiference Equations 51911.5 The z-transform 52111.6 The z-t: ransf'er Function (Pulse Transfer Function) 53111.7 The Inverse z-transform and Response of Linear Discrete Systems 53511.8 The z-transform Analysis of Sampled-data Control'_Systems 538 11.9 The 2- and s-domain Relationshig 548 6. xii" - comsms11.10 Stability Analysis 54911.11 Comp_ensation Technigues 558 Bmh1ems_55412. Sure Vamasns Ammrsrs AND DESIGN 566-640mLh 12.2 Concepts of State,State Variables and sum Model 57112.3 State Models for Linear Continuous-'lime Systems 57812.4 State Variables and Linear Discrete-Time Systems 59612.5 Diagonalization 59912.6 Solution of State Equations 60412.7 Concepts of Controllsbility and Observability 61712.8 Pole Placement by State Feedback 625 12.9 Observer Systems 632Problems 63418. Lnu= uNovs Srasnm Amnrsxs 641-63213.1 Introduction 64213.2 Liapunov's Stability Criterion 646 ~13.3 The Direct Method of Liapunov and the Linear System 6513.4 Methods of Constructing Lispunov Functions for Nonlinear Systems 652 Bmblems_L YSTEMS 833-712 MJ414.2 Parameter Optimization:Servomechanisms 66514.3 Optimal Control Problems:Transfer Function Approach 67314.4 Optimal Control Problems:State Variable Approach 684 14.5 The State Regulator Problem 68814.6 The Innite-time Regu_lator Problem 697 14.7 The Output Regulator and the Tracking Problems 70214.8 Parameter Optimization:Regators 704 Bmh1ems__'Z0_'Z15. Anvmcss IN CoN'rsoL Srs-rms 713-78315.1 Introduction 71415.2 Adaptive Control 715 15.3 Fuzzy Logic Control 731mLNemProblems 760 7. AEEENDICE8Aggndix-I Fourier and Laglace Transforms and Partial Fractions 766 Agpgndix-II Element of Matrix Analysis 775Appendix-IV MATLAB :Tool for Design and Analysis of Control Systems 784 Amgndix-V Final Value Theorem 796Agp_endix-VI Proof of a Transformation 797Agp3ndixVI!Answers to Problems 803)Bibllgggghx 817-833 h 8. 1INTRODUCTION A 9. 1.1 THE CONTROL SYSTEMThe control system is that means by which any quantity of interest in a machine,mechanism or other equipment is maintained or altered in accordance with a desired manner.Consider,for example,the driving system of an automobile.Speed of the automobile is a function of the position of its accelerator.The desired speed can be maintained (or a desired change in speed can be achieved) by controlling pressure on the accelerator pedal.This automobile driving system (accelerator,carburettor and engine-vehicle) constitutes a control system.Figure 1.1 shows the general diagrammatic representation of a typical control system.For the automobile driving system the input (command) signal is the force on the accelerator pedal which through linkages causes the carburettor valve to open (close) so as to increase or decrease fuel (liquid form) ow to the engine bringing the engine-vehicle speed (controlled variable) to the desired value. Rate of iuelvow Input (command) ; ' " Output (controlled) signal Acfefrator p: :a| ' ._ Enoine- V3"3ll3 ~ ~ ~ . - l aqesa = ~~ *.' ~ A F' carburetter Vemcle 399Fig.1.1. The basic control system. The diagrammatic representation of Fig.1.1 is known as block diagram representation wherein each block represents an element,a plant,mechanism,device etc. , whose inner details are not indicated.Each block has an input and output signal which are linked by a relationship characterizing the block.It may be noted that the signal ow through the block is unidirectional. 10. closed-Loop controlLet us reconsider the automobile driving system.The route,speed and acceleration of the automobile are determined and controlled by the driver by observing traffic and road conditions and by properly manipulating the accelerator,clutch,gear-lever,brakes and steering wheel,etc.Suppose the driver wants to maintain a speed of 50 km per hour (desired output).He accelerates the automobile to this speed with the help of the accelerator and then maintains it by holding the accelerator steady.No error in the speed of the automobile occurs so long as there are no gradients or other disturbances along the road.The actual speed of the automobile is measured by the speedometer and indicated on its dial.The driver reads the speed dial visually and compares the actual speed with the desired one mentally.If there is a deviation of speed from the desired speed,accordingly he takes the decision to increase or decrease the speed.The decision is executed by change in pressure of his foot (through muscular power) on the accelerator pedal. These operations can be represented in a diagrammatic form as shown in Fig.1.2. In contrast to the sequence of events in Fig.1.1, the events in the control sequence of Fig.1.2 follow a closed-loop,i. e.,the information about the instantaneous state of the output is feedback to the input and is used to modify it in such a manner as to achieve the desired output.It is on account of this basic difference that the system of Fig.1.1 is called an open-loop system,while the system of Fig.1.2 is called a closed-loop system. Raleof fut-Maw O Desired UlDU- . ~ 1. .A ': .., -. ' ma.ms : F3'~"3d . _ Drwerseycs Lag . AA'_ CC_r: :a: J;3S Er'7rv. - Wspfji and brain rn'. l:: c>: s _ ' ' v. ~ew, :w * cdrbJ'ene. ' ) Force Spa: -d: 'r-amVisual link trcm speedometerFig.1.2. Schematic diagram of a manually controlled closed-loop system. Let us investigate another control aspect of the above example of an automobile (engine vehicle) say its steering mechanism.A simple block diagram of an automobile steering mechanism is shown in Fig.1.3(a).The driver senses visually and by tactile means (body movement) the error between the actual and desired directions of the automobile as in Fig.1.3(b).Additional information is available to the driver from the feel