Digital Control of Dynamic Systems

by Franklin, Gene F.; Powell, J. David; Workman, Michael L.

• ISBN13: 9780201820546
• ISBN10: 0201820544
• Edition: 3rd
• Format: Hardcover
• Copyright: 1998-01-01
• Publisher: Prentice Hall

Summary

This well-respected, market-leading text discusses the use of digital computers in the real-time control of dynamic systems. The emphasis is on the design of digital controls that achieve good dynamic response and small errors while using signals that are sampled in time and quantized in amplitude. Both classical and modern control methods are described and applied to illustrative examples. The strengths and limitations of each method are explored to help the reader develop solid designs with the least effort. Two new chapters have been added to the third edition offering a review of feedback control systems and an overview of digital control systems. Updated to be fully compatible with MATLAB versions 4 and 5, the text thoroughly integrates MATLAB statements and problems to offer readers a complete design picture. The new edition contains up-to-date material on state-space design and twice as many end- of-chapter problems to give students more opportunities to practice the material.

Table of Contents

Preface	xix
1 Introduction	1	(10)
1.1 Problem Definition	1	(4)
1.2 Overview of Design Approach	5	(2)
1.3 Computer-Aided Design	7	(1)
1.4 Suggestions for Further Reading	7	(1)
1.5 Summary	8	(1)
1.6 Problems	8	(3)
2 Review of Continuous Control	11	(46)
2.1 Dynamic Response	11	(11)
2.1.1 Differential Equations	12	(1)
2.1.2 Laplace Transforms and Transfer Functions	12	(2)
2.1.3 Output Time Histories	14	(1)
2.1.4 The Final Value Theorem	15	(1)
2.1.5 Block Diagrams	15	(1)
2.1.6 Response versus Pole Locations	16	(4)
2.1.7 Time-Domain Specifications	20	(2)
2.2 Basic Properties of Feedback	22	(2)
2.2.1 Stability	22	(1)
2.2.2 Steady-State Errors	23	(1)
2.2.3 PID Control	24	(1)
2.3 Root Locus	24	(7)
2.3.1 Problem Definition	25	(1)
2.3.2 Root Locus Drawing Rules	26	(2)
2.3.3 Computer-Aided Loci	28	(3)
2.4 Frequency Response Design	31	(8)
2.4.1 Specifications	32	(2)
2.4.2 Bode Plot Techniques	34	(1)
2.4.3 Steady-State Errors	35	(1)
2.4.4 Stability Margins	36	(1)
2.4.5 Bode's Gain-Phase Relationship	37	(1)
2.4.6 Design	38	(1)
2.5 Compensation	39	(2)
2.6 State-Space Design	41	(9)
2.6.1 Control Law	42	(4)
2.6.2 Estimator Design	46	(2)
2.6.3 Compensation: Combined Control and Estimation	48	(1)
2.6.4 Reference Input	48	(1)
2.6.5 Integral Control	49	(1)
2.7 Summary	50	(2)
2.8 Problems	52	(5)
3 Introductory Digital Control	57	(16)
3.1 Digitization	58	(5)
3.2 Effect of Sampling	63	(3)
3.3 PID Control	66	(2)
3.4 Summary	68	(1)
3.5 Problems	69	(4)
4 Discrete Systems Analysis	73	(82)
4.1 Linear Difference Equations	73	(5)
4.2 The Discrete Transfer Function	78	(18)
4.2.1 The z-Transform	79	(1)
4.2.2 The Transfer Function	80	(2)
4.2.3 Block Diagrams and State-Variable Descriptions	82	(8)
4.2.4 Relation of Transfer Function to Pulse Response	90	(3)
4.2.5 External Stability	93	(3)
4.3 Discrete Models of Sampled-Data Systems	96	(23)
4.3.1 Using the z-Transform	96	(3)
4.3.2 (*)Continuous Time Delay	99	(2)
4.3.3 State-Space Form	101	(9)
4.3.4 (*)State-Space Models for Systems with Delay	110	(4)
4.3.5 (*)Numerical Considerations in Computing XXX and XXX	114	(3)
4.3.6 (*)Nonlinear Models	117	(2)
4.4 Signal Analysis and Dynamic Response	119	(12)
4.4.1 The Unit Pulse	120	(1)
4.4.2 The Unit Step	120	(1)
4.4.3 Exponential	121	(1)
4.4.4 General Sinusoid	122	(3)
4.4.5 Correspondence with Continuous Signals	125	(3)
4.4.6 Step Response	128	(3)
4.5 Frequency Response	131	(6)
4.5.1 (*)The Discrete Fourier Transform (DFT)	134	(3)
4.6 Properties of the z-Transform	137	(11)
4.6.1 Essential Properties	137	(5)
4.6.2 (*)Convergence of z-Transform	142	(4)
4.6.3 (*)Another Derivation of the Transfer Function	146	(2)
4.7 Summary	148	(1)
4.8 Problems	149	(6)
5 Sampled-Data Systems	155	(32)
5.1 Analysis of the Sample and Hold	156	(4)
5.2 Spectrum of a Sampled Signal	160	(4)
5.3 Data Extrapolation	164	(6)
5.4 Block-Diagram Analysis of Sampled-Data Systems	170	(10)
5.5 Calculating the System Output Between Samples: The Ripple	180	(2)
5.6 Summary	182	(1)
5.7 Problems	183	(3)
5.8 Appendix	186	(1)
6 Discrete Equivalents	187	(24)
6.1 Design of Discrete Equivalents via Numerical Integration	189	(11)
6.2 Zero-Pole Matching Equivalents	200	(2)
6.3 Hold Equivalents	202	(6)
6.3.1 Zero-Order Hold Equivalent	203	(1)
6.3.2 A Non-Causal First-Order-Hold Equivalent: The Triangle-Hold Equivalent	204	(4)
6.4 Summary	208	(1)
6.5 Problems	209	(2)
7 Design Using Transform Techniques	211	(68)
7.1 System Specifications	212	(2)
7.2 Design by Emulation	214	(8)
7.2.1 Discrete Equivalent Controllers	215	(3)
7.2.2 Evaluation of the Design	218	(4)
7.3 Direct Design by Root Locus in the z-Plane	222	(12)
7.3.1 z-Plane Specifications	222	(5)
7.3.2 The Discrete Root Locus	227	(7)
7.4 Frequency Response Methods	234	(30)
7.4.1 Nyquist Stability Criterion	238	(5)
7.4.2 Design Specifications in the Frequency Domain	243	(16)
7.4.3 Low Frequency Gains and Error Coefficients	259	(1)
7.4.4 Compensator Design	260	(4)
7.5 Direct Design Method of Ragazzini	264	(5)
7.6 Summary	269	(1)
7.7 Problems	270	(9)
8 Design Using State-Space Methods	279	(80)
8.1 Control Law Design	280	(9)
8.1.1 Pole Placement	282	(3)
8.1.2 Controllability	285	(1)
8.1.3 Pole Placement Using CACSD	286	(3)
8.2 Estimator Design	289	(13)
8.2.1 Prediction Estimators	290	(3)
8.2.2 Observability	293	(1)
8.2.3 Pole Placement Using CACSD	294	(1)
8.2.4 Current Estimators	295	(4)
8.2.5 Reduced-Order Estimators	299	(3)
8.3 Regulator Design: Combined Control Law and Estimator	302	(8)
8.3.1 The Separation Principle	302	(6)
8.3.2 Guidelines for Pole Placement	308	(2)
8.4 Introduction of the Reference Input	310	(12)
8.4.1 Reference Inputs for Full-State Feedback	310	(4)
8.4.2 Reference Inputs with Estimators: The State-Command Structure	314	(3)
8.4.3 Output Error Command	317	(2)
8.4.4 A Comparison of the Estimator Structure and Classical Methods	319	(3)
8.5 Integral Control and Disturbance Estimation	322	(15)
8.5.1 Integral Control by State Augmentation	323	(5)
8.5.2 Disturbance Estimation	328	(9)
8.6 Effect of Delays	337	(8)
8.6.1 Sensor Delays	338	(3)
8.6.2 Actuator Delays	341	(4)
8.7 (*)Controllability and Observability	345	(6)
8.8 Summary	351	(1)
8.9 Problems	352	(7)
9 Multivariable and Optimal Control	359	(66)
9.1 Decoupling	360	(4)
9.2 Time-Varying Optimal Control	364	(7)
9.3 LQR Steady-State Optimal Control	371	(11)
9.3.1 Reciprocal Root Properties	372	(1)
9.3.2 Symmetric Root Locus	373	(1)
9.3.3 Eigenvector Decomposition	374	(5)
9.3.4 Cost Equivalents	379	(1)
9.3.5 Emulation by Equivalent Cost	380	(2)
9.4 Optimal Estimation	382	(18)
9.4.1 Least-Squares Estimation	383	(6)
9.4.2 The Kalman Filter	389	(5)
9.4.3 Steady-State Optimal Estimation	394	(2)
9.4.4 Noise Matrices and Discrete Equivalents	396	(4)
9.5 Multivariable Control Design	400	(19)
9.5.1 Selection of Weighting Matrices XXX(1) and XXX(2)	400	(1)
9.5.2 Pincer Procedure	401	(2)
9.5.3 Paper-Machine Design Example	403	(4)
9.5.4 Magnetic-Tape-Drive Design Example	407	(12)
9.6 Summary	419	(1)
9.7 Problems	420	(5)
10 Quantization Effects	425	(24)
10.1 Analysis of Round-Off Error	426	(11)
10.2 Effects of Parameter Round-Off	437	(3)
10.3 Limit Cycles and Dither	440	(5)
10.4 Summary	445	(1)
10.5 Problems	445	(4)
11 Sample Rate Selection	449	(30)
11.1 The Sampling Theorem's Limit	450	(1)
11.2 Time Response and Smoothness	451	(3)
11.3 Errors Due to Random Plant Disturbances	454	(7)
11.4 Sensitivity to Parameter Variations	461	(4)
11.5 Measurement Noise and Antialiasing Filters	465	(4)
11.6 Multirate Sampling	469	(5)
11.7 Summary	474	(2)
11.8 Problems	476	(3)
12 System Identification	479	(64)
12.1 Defining the Model Set for Linear Systems	481	(3)
12.2 Identification of Nonparametric Models	484	(11)
12.3 Models and Criteria for Parametric Identification	495	(7)
12.3.1 Parameter Selection	496	(2)
12.3.2 Error Definition	498	(4)
12.4 Deterministic Estimation	502	(8)
12.4.1 Least Squares	503	(3)
12.4.2 Recursive Least Squares	506	(4)
12.5 Stochastic Least Squares	510	(11)
12.6 Maximum Likelihood	521	(5)
12.7 Numerical Search for the Maximum-Likelihood Estimate	526	(9)
12.8 Subspace Identification Methods	535	(3)
12.9 Summary	538	(1)
12.10 Problems	539	(4)
13 Nonlinear Control	543	(106)
13.1 Analysis Techniques	544	(38)
13.1.1 Simulation	545	(5)
13.1.2 Linearization	550	(9)
13.1.3 Describing Functions	559	(14)
13.1.4 Equivalent Gains	573	(4)
13.1.5 Circle Criterion	577	(2)
13.1.6 Lyapunov's Second Method	579	(3)
13.2 Nonlinear Control Structures: Design	582	(53)
13.2.1 Large Signal Linearization: Inverse Nonlinearities	582	(17)
13.2.2 Time-Optimal Servomechanisms	599	(12)
13.2.3 Extended PTOS for Flexible Structures	611	(4)
13.2.4 Introduction to Adaptive Control	615	(20)
13.3 Design with Nonlinear Cost Functions	635	(7)
13.3.1 Random Neighborhood Search	635	(7)
13.4 Summary	642	(1)
13.5 Problems	643	(6)
14 Design of a Disk Drive Servo: A Case Study	649	(40)
14.1 Overview of Disk Drives	650	(5)
14.1.1 High Performance Disk Drive Servo Profile	652	(2)
14.1.2 The Disk-Drive Servo	654	(1)
14.2 Components and Models	655	(11)
14.2.1 Voice Coil Motors	655	(3)
14.2.2 Shorted Turn	658	(1)
14.2.3 Power Amplifier Saturation	659	(1)
14.2.4 Actuator and HDA Dynamics	660	(3)
14.2.5 Position Measurement Sensor	663	(1)
14.2.6 Runout	664	(2)
14.3 Design Specifications	666	(4)
14.3.1 Plant Parameters for Case Study Design	667	(2)
14.3.2 Goals and Objectives	669	(1)
14.4 Disk Servo Design	670	(16)
14.4.1 Design of the Linear Response	671	(3)
14.4.2 Design by Random Numerical Search	674	(4)
14.4.3 Time-Domain Response of XPTOS Structure	678	(5)
14.4.4 Implementation Considerations	683	(3)
14.5 Summary	686	(1)
14.6 Problems	687	(2)
Appendix A Examples	689	(12)
A.1 Single-Axis Satellite Attitude Control	689	(2)
A.2 A Servomechanism for Antenna Azimuth Control	691	(3)
A.3 Temperature Control of Fluid in a Tank	694	(3)
A.4 Control Through a Flexible Structure	697	(2)
A.5 Control of a Pressurized Flow Box	699	(2)
Appendix B Tables	701	(4)
B.1 Properties of z-Transforms	701	(1)
B.2 Table of z-Transforms	702	(3)
Appendix C A Few Results from Matrix Analysis	705	(8)
C.1 Determinants and the Matrix Inverse	705	(2)
C.2 Eigenvalues and Eigenvectors	707	(2)
C.3 Similarity Transformations	709	(2)
C.4 The Cayley-Hamilton Theorem	711	(2)
Appendix D Summary of Facts from the Theory of Probability and Stochastic Processes	713	(12)
D.1 Random Variables	713	(2)
D.2 Expectation	715	(2)
D.3 More Than One Random Variable	717	(2)
D.4 Stochastic Processes	719	(6)
Appendix E MATLAB Functions	725	(2)
Appendix F Differences Between MATLAB v5 and v4	727	(4)
F.1 System Specification	727	(2)
F.2 Continuous to Discrete Conversion	729	(1)
F.3 Optimal Estimation	730	(1)
References	731	(6)
Index	737