Introduction to linear control systems
'Introduction to Linear Control Systems' is designed as a standard introduction to linear control systems for all those who one way or another deal with control systems. It can be used as a comprehensive up-to-date textbook for a one-semester 3-credit undergraduate course on linear control...
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| Main Author | |
|---|---|
| Format | eBook Book |
| Language | English |
| Published |
London
Academic Press
2017
Elsevier Science & Technology |
| Edition | 1 |
| Subjects | |
| Online Access | Get full text |
| ISBN | 0128127481 9780128127483 |
| DOI | 10.1016/C2016-0-03896-2 |
Cover
Table of Contents:
- Front Cover -- Introduction to Linear Control Systems -- Copyright Page -- Dedication -- Contents -- Preface -- Acknowledgments -- I. Foundations -- 1 Introduction -- 1.1 Introduction -- 1.2 Why control? -- 1.3 History of control -- 1.4 Why feedback? -- 1.5 Magic of feedback -- 1.6 Physical elements of a control system -- 1.7 Abstract elements of a control system -- 1.8 Design process -- 1.9 Types of control systems -- 1.10 Open-loop control -- 1.10.1 Stability and performance -- 1.10.2 Sensitivity and robustness -- 1.10.3 Disturbance -- 1.10.4 Failure tolerance, optimality, and linearity -- 1.11 Closed-loop control -- 1.11.1 Stability and performance -- 1.11.2 Sensitivity and robustness -- 1.11.3 Disturbance and noise -- 1.11.4 Failure tolerance, optimality, and linearity -- 1.11.5 A closer look -- 1.12 The 2-DOF control structure -- 1.12.1 Negative feedback or positive feedback? -- 1.13 The Smith predictor -- 1.14 Internal model control structure -- 1.15 Modern representation-Generalized model -- 1.16 Status quo -- 1.16.1 Overview -- 1.16.1.1 Summary -- 1.16.1.2 The forgotten -- 1.16.2 Relation with other disciplines -- 1.16.3 Challenges -- 1.16.4 Outlook -- 1.16.4.1 Kansei engineering -- 1.16.4.2 Overall system engineering -- 1.16.5 Postscript -- 1.17 Summary -- 1.18 Notes and further readings -- 1.19 Worked-out problems -- 1.20 Exercises -- References -- Further Reading -- 2 System representation -- 2.1 Introduction -- 2.2 System modeling -- 2.2.1 State-space -- 2.2.1.1 Linearization -- 2.2.1.2 Number of inputs and outputs -- 2.2.2 Frequency domain -- 2.2.2.1 Finding the output -- 2.2.3 Zero, pole, and minimality -- 2.3 Basic examples of modeling -- 2.3.1 Electrical system as the plant -- 2.3.2 Mechanical system as the plant -- 2.3.3 Liquid system as the plant -- 2.3.4 Thermal system as the plant -- 2.3.5 Hydraulic system as the plant
- 4.9 Effect of addition of pole and zero -- 4.10 Performance region -- 4.11 Inverse response -- 4.12 Analysis of the actual system -- 4.12.1 Sensor dynamics -- 4.12.2 Delay dynamics -- 4.13 Introduction to robust stabilization and performance -- 4.13.1 Open-loop control -- 4.13.2 Closed-loop control -- 4.13.2.1 Disturbance and noise rejection and setpoint tracking -- Design for disturbance and noise rejection -- Design for sinusoidal reference tracking -- 4.14 Summary -- 4.15 Notes and further readings -- 4.16 Worked-out problems -- 4.17 Exercises -- References -- 5 Root locus -- 5.1 Introduction -- 5.2 The root locus method -- 5.3 The root contour -- 5.4 Finding the value of gain from the root locus -- 5.5 Controller design implications -- 5.5.1 Difficult systems -- 5.5.1.1 System without NMP zeros -- 5.5.1.2 Systems with NMP zeros -- 5.5.1.3 Examples of systems without NMP zeros -- 5.5.1.4 Examples of system with NMP zeros -- 5.5.2 Simple systems -- 5.6 Summary -- 5.7 Notes and further readings -- 5.8 Worked-out problems -- 5.9 Exercises -- References -- II. Frequency domain analysis & -- synthesis -- 6 Nyquist plot -- 6.1 Introduction -- 6.2 Nyquist plot -- 6.2.1 Principle of argument -- 6.2.2 Nyquist stability criterion -- 6.2.3 Drawing of the Nyquist plot -- 6.2.4 The high- and low-frequency ends of the plot -- 6.2.5 Cusp points of the plot -- 6.2.6 How to handle the proportional gain/uncertain parameter -- 6.2.7 The case of j-axis zeros and poles -- 6.2.8 Relation with root locus -- 6.3 Gain, phase, and delay margins -- 6.3.1 The GM concept -- 6.3.1.1 Definition of GM in the Nyquist plot context -- 6.3.2 The PM and DM Concepts -- 6.3.3 Stability in terms of the GM and PM signs -- 6.3.4 The high sensitivity region -- 6.4 Summary -- 6.5 Notes and further readings -- 6.6 Worked-out problems -- 6.7 Exercises -- References -- 7 Bode diagram
- 7.1 Introduction -- 7.2 Bode diagram -- 7.2.1 Logarithm -- 7.2.2 Decibel -- 7.2.3 Log magnitude -- 7.2.4 The magnitude diagram -- 7.2.5 Octave and decade -- 7.2.6 Some useful figures to remember -- 7.2.7 Relation between the transfer function and its constituting components -- 7.2.7.1 Gain K -- 7.2.7.2 Zeros at origin (jω)+m -- 7.2.7.3 Poles at origin (jω)−m -- 7.2.7.4 Real zeros not at origin (1+jωT)+m -- 7.2.7.5 Real poles not at origin (1+jωT)−m -- 7.2.7.6 Error in Lm -- 7.2.7.7 Error in ɸ -- 7.2.7.8 Double zeros [1+2ζωnjω+1ωn2(jω)2]+m -- 7.2.7.9 Double poles [1+2ζωnjω+1ωn2(jω)2]−m -- 7.2.8 Manual drawing of the Bode diagram -- 7.3 Bode diagram and the steady-state error -- 7.4 Minimum phase and nonminimum phase systems -- 7.4.1 NMP zero with positive gain: z−s, z> -- 0 -- 7.4.2 NMP pole with positive gain: 1/(p−s), p> -- 0 -- 7.4.3 NMP zero with negative gain: −(z−s)=s−z, z> -- 0 -- 7.4.4 NMP pole with negative gain: −1/(p−s)=1/(s−p), p> -- 0 -- 7.4.5 Determination of NMP systems from the Bode diagram -- 7.5 Gain, phase, and delay margins -- 7.6 Stability in the Bode diagram context -- 7.7 The high sensitivity region -- 7.8 Relation with Nyquist plot and root locus -- 7.9 Standard second-order systems -- 7.10 Bandwidth -- 7.11 Summary -- 7.12 Notes and further readings -- 7.13 Worked-out problems -- 7.14 Exercises -- References -- 8 Nichols-Krohn-Manger-Hall Chart -- 8.1 Introduction -- 8.2 S-Circles -- 8.3 M-Circles -- 8.4 N-circles -- 8.5 M- and N-Contours -- 8.6 NKMH chart -- 8.7 System features: GM, PM, DM, BW, stability -- 8.7.1 Gain, phase, and delay margins -- 8.7.2 Stability -- 8.7.3 Bandwidth -- 8.8 The high sensitivity region -- 8.9 Relation with Bode diagram, Nyquist plot, and root locus -- 8.10 Summary -- 8.11 Notes and further readings -- 8.12 Worked-out problems -- 8.13 Exercises -- References
- 2.3.6 Chemical system as the plant -- 2.3.7 Structural system as the plant -- 2.3.8 Biological system as the plant -- 2.3.9 Economics system as the plant -- 2.3.10 Ecological system as the plant -- 2.3.11 Societal system as the plant -- 2.3.12 Physics system as the plant -- 2.3.13 Delay -- 2.3.13.1 Exact modeling of delay -- 2.3.13.2 Approximate modeling of delay -- 2.3.14 The other constituents -- 2.3.14.1 Sensors -- 2.3.14.2 Amplifiers -- 2.4 Block diagram -- 2.5 Signal flow graph -- 2.5.1 Basic terminology of graph theory -- 2.5.2 Equivalence of BD and SFG methods -- 2.5.3 Computing the transmittance of an SFG -- 2.6 Summary -- 2.7 Notes and further readings -- 2.8 Worked-out problems -- 2.9 Exercises -- References -- 3 Stability analysis -- 3.1 Introduction -- 3.2 Lyapunov and BIBO stability -- 3.3 Stability tests -- 3.4 Routh's test -- 3.4.1 Special cases -- 3.5 Hurwitz' test -- 3.6 Lienard and Chipart test -- 3.7 Relative stability -- 3.8 D-stability -- 3.9 Particular relation with control systems design -- 3.10 The Kharitonov theory -- 3.11 Internal stability -- 3.12 Strong stabilization -- 3.13 Stability of LTV Systems -- 3.14 Summary -- 3.15 Notes and further readings -- 3.16 Worked-out problems -- 3.17 Exercises -- References -- 4 Time response -- 4.1 Introduction -- 4.2 System type and system inputs -- 4.3 Steady-state error -- 4.4 First-order systems -- 4.4.1 Impulse input -- 4.4.2 Step, ramp, and parabolic inputs -- 4.5 Second-order systems -- 4.5.1 System representation -- 4.5.2 Impulse response -- 4.5.3 Step response -- 4.5.3.1 Time response characteristics -- 4.5.4 Ramp and parabola response -- 4.6 Bandwidth of the system -- 4.6.1 First-order systems -- 4.6.2 Second-order systems -- 4.6.3 Alternative derivation -- 4.6.4 Higher-order systems -- 4.6.5 Open-loop and closed-loop systems -- 4.7 Higher-order systems -- 4.8 Model reduction
- 10.12 Minimal closed-loop pole sensitivity
- 9 Frequency domain synthesis and design -- 9.1 Introduction -- 9.2 Basic controllers: proportional, lead, lag, and lead-lag -- 9.3 Controller simplifications: PI, PD, and PID -- 9.4 Controller structures in the Nyquist plot context -- 9.5 Effect of the controllers on the root locus -- 9.6 Design procedure -- 9.7 Specialized design and tuning rules of PID controllers -- 9.7.1 Heuristic rules -- 9.7.2 Analytical rules -- 9.7.2.1 Pole placement method -- 9.7.2.2 Direct synthesis -- 9.7.2.3 Skogestad tuning rules -- 9.7.3 Optimization-based rules -- 9.8 Internal model control -- 9.9 The Smith predictor -- 9.10 Implementation with operational amplifiers -- 9.10.1 Proportional control-P-term -- 9.10.2 Integral control-I-term -- 9.10.3 Proportional-integral-PI-term -- 9.10.4 Proportional-derivative-PD-term -- 9.10.5 Nonideal/actual derivative-D-term -- 9.10.6 Series proportional-integral-derivative-Series PID -- 9.10.7 Lead -- 9.10.8 Lag -- 9.10.9 Lead or lag -- 9.10.10 Lead-lag -- 9.11 Summary -- 9.12 Notes and further readings -- 9.13 Worked-out problems -- 9.14 Exercises -- References -- III. Advanced Issues -- 10 Fundamental limitations -- 10.1 Introduction -- 10.2 Relation between time and frequency domain specifications -- 10.3 The ideal transfer function -- 10.4 Controller design via the TS method -- 10.5 Interpolation conditions -- 10.6 Integral and Poisson integral constraints -- 10.7 Constraints implied by poles and zeros -- 10.7.1 Implications of open-loop integrators -- 10.7.2 MP and NMP poles and zeros -- 10.7.3 Imaginary-axis poles and zeros -- 10.8 Actuator and sensor limitations -- 10.8.1 Maximal actuator movement -- 10.8.2 Minimal actuator movement -- 10.8.3 Sensor precision -- 10.8.4 Sensor speed -- 10.9 Delay -- 10.10 Eigenstructure assignment by output feedback -- 10.10.1 Regulation -- 10.10.2 Tracking -- 10.11 Noninteractive performance