1 Introduction |
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1 | (72) |
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1 | (1) |
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1.2 Notation and Nomenclature |
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1 | (3) |
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1.2.1 Scalars, Vectors and Matrices |
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1 | (1) |
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1.2.2 Subscripts and Superscripts |
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2 | (1) |
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1.2.3 Constants and Variables |
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2 | (1) |
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1.2.4 Nomenclature and Standard Symbols |
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3 | (1) |
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1.2.5 Variables and Their Laplace Transforms |
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4 | (1) |
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1.3 Review of Traditional PID Controllers and Their Variants |
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4 | (39) |
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1.3.1 Traditional Error-Actuated Controllers |
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4 | (15) |
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1.3.2 Zero-Less Versions of the Traditional Controllers |
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19 | (3) |
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1.3.3 Traditional Controller Selection Guidelines |
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22 | (3) |
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1.3.4 Measurement Noise Filtering for Derivative Term |
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25 | (7) |
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1.3.5 Anti-windup Loop for Integral Term |
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32 | (11) |
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1.4 Dominance in the Pole-Zero Distribution |
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43 | (26) |
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43 | (1) |
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1.4.2 Modes of Linear Systems |
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43 | (6) |
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1.4.3 Dominance in Pole Distributions |
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49 | (4) |
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1.4.4 Dominance in Systems with Zeros |
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53 | (16) |
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1.5 The Steps of Control System Design |
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69 | (2) |
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1.6 The Flexibility of Digital Implementation |
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71 | (1) |
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71 | (2) |
2 Plant Modelling |
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73 | (96) |
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73 | (8) |
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73 | (1) |
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2.1.2 Dynamical and Non-Dynamical Systems |
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73 | (3) |
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2.1.3 Linearity and Nonlinearity |
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76 | (4) |
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2.1.4 Modelling Categories and Basic Forms of Model |
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80 | (1) |
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81 | (40) |
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81 | (1) |
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2.2.2 Mechanical Modeling Principles |
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81 | (11) |
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2.2.3 Two Basic Mechanical Components |
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92 | (5) |
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2.2.4 Modelling for Vehicle Attitude and Position Control |
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97 | (7) |
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104 | (5) |
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2.2.6 Vector-Controlled AC Motors as Control Actuators |
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109 | (8) |
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2.2.7 Fluid and Thermal Subsystems |
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117 | (4) |
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2.3 Identification of LTI Plants from Measurements |
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121 | (46) |
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121 | (1) |
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2.3.2 Plant Model Determination from Step Response |
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122 | (5) |
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2.3.3 Plant Model Determination from Frequency Response |
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127 | (24) |
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2.3.4 Recursive Parameter Estimation: An Introduction |
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151 | (16) |
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167 | (2) |
3 Plant Model Manipulation and Analysis |
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169 | (126) |
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169 | (1) |
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3.2 The State Space Model |
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170 | (24) |
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170 | (1) |
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3.2.2 Forming a State-Space Model |
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171 | (1) |
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3.2.3 The General State-Space Model |
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172 | (1) |
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3.2.4 The General LTI State-Space Model |
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173 | (2) |
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3.2.5 Some Preliminary Control Theory |
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175 | (4) |
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3.2.6 Controllability Analysis of Continuous LTI Plant Models |
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179 | (4) |
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3.2.7 Observability Analysis of Continuous LTI Plant Models |
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183 | (4) |
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3.2.8 The State-Variable Block Diagram |
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187 | (3) |
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3.2.9 Transfer Function from Continuous LTI State Space Model |
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190 | (2) |
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192 | (2) |
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194 | (61) |
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194 | (6) |
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3.3.2 LTI SISO State-Space Models from Transfer Functions |
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200 | (11) |
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3.3.3 Transformation Matrices Connecting Linear Models |
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211 | (6) |
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3.3.4 Modal Forms for Multivariable LTI Plants: Transformations |
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217 | (20) |
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3.3.5 SISO Controller and Observer Canonical Forms |
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237 | (8) |
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3.3.6 Multivariable Controller and Observer Canonical Forms |
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245 | (10) |
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3.4 Discrete LTI Plant Models |
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255 | (38) |
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3.4.1 Formation of the Discrete State Space Model |
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255 | (4) |
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3.4.2 State Space Model Derivation from Modal Basis Functions |
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259 | (15) |
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3.4.3 Plant z-Transfer Function Model |
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274 | (8) |
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3.4.4 Change of Sampling Period for z-Transfer Function Models |
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282 | (5) |
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3.4.5 Controllability Analysis of Discrete LTI Plant Models |
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287 | (3) |
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3.4.6 Analysis of Discrete LTI Plant Models |
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290 | (3) |
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293 | (2) |
4 Traditional Controllers: Model Based Design |
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295 | (60) |
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295 | (2) |
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297 | (2) |
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4.3 Definition of Settling Time |
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299 | (1) |
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4.4 PID Controllers and Their Variants |
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300 | (25) |
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4.4.1 First Order Systems |
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300 | (7) |
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4.4.2 Second Order Systems |
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307 | (12) |
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4.4.3 Cascade Control Structure |
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319 | (6) |
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4.5 Systems of Third and Higher Order |
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325 | (12) |
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4.5.1 Attainable Closed Loop Dynamics |
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325 | (2) |
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4.5.2 The Laplace to Time Domain Inverse Scaling Law |
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327 | (2) |
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4.5.3 Step Responses with Coincident Closed Loop Poles |
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329 | (2) |
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4.5.4 Derivation of the Settling Time Formulae |
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331 | (2) |
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4.5.5 Settling Time Formula Error Determination and Correction |
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333 | (2) |
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4.5.6 Closed Loop Poles for Given Overshoot and Settling Time |
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335 | (2) |
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4.6 Performance Specifications in the Frequency Domain |
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337 | (17) |
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337 | (1) |
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4.6.2 Closed Loop System Bandwidth |
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337 | (2) |
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4.6.3 Sensitivity and Robustness |
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339 | (8) |
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4.6.4 Stability Analysis in the Frequency Domain |
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347 | (7) |
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354 | (1) |
5 Linear Controllers for LTI SISO Plants of Arbitrary Order: Model-Based Design |
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355 | (60) |
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355 | (1) |
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5.2 Linear Continuous State Feedback Control |
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356 | (42) |
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356 | (1) |
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5.2.2 Linear State Feedback Control Law |
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357 | (1) |
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5.2.3 Matrix—Vector Formulation |
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358 | (2) |
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5.2.4 Closed-Loop Transfer Function |
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360 | (1) |
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5.2.5 Pole Assignment Using the Matrix—Vector Formulation |
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361 | (3) |
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5.2.6 Pole Assignment Using Mason's Formula |
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364 | (4) |
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5.2.7 Pole Assignment for Plants with Significant Zeros |
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368 | (19) |
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5.2.8 State Feedback Controllers with Additional Integral Terms |
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387 | (11) |
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398 | (16) |
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398 | (1) |
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5.3.2 Formulation of Polynomial Controller Structure |
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399 | (2) |
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5.3.3 Constraints on Controller Polynomial Degrees |
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401 | (2) |
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5.3.4 Determination of the Controller Parameters |
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403 | (4) |
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5.3.5 The Polynomial Integral Controller |
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407 | (7) |
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414 | (1) |
6 Discrete Control of LTI SISO Plants |
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415 | (66) |
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415 | (1) |
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6.2 Real-Time Operation of Digital Controllers |
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416 | (1) |
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6.3 Dynamics of Discrete Linear Systems |
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417 | (18) |
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6.3.1 Stability Analysis in the z-Plane |
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417 | (8) |
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6.3.2 Connection Between Dynamic Behaviour and the z-Plane Pole Locations |
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425 | (7) |
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6.3.3 The Effects of Zeros in the z-Plane |
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432 | (3) |
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6.4 Criterion for Applicability of Continuous LTI System Theory |
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435 | (4) |
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6.5 Discrete Control for Small Iteration Intervals |
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439 | (13) |
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439 | (1) |
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6.5.2 Discrete Equations of the Basic Elements |
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439 | (4) |
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6.5.3 Discrete Controller Block Diagrams for Simulation |
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443 | (4) |
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6.5.4 Control Algorithms and Flow Charts |
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447 | (5) |
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6.6 Discrete Control with Unlimited Iteration Intervals |
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452 | (28) |
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6.6.1 Pole Placement Design with the Settling Time Formulae |
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452 | (4) |
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6.6.2 Pole Placement for Negligible Digital Processing Time |
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456 | (8) |
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6.6.3 Computational Delay Allowance |
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464 | (8) |
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6.6.4 Discrete Integral Polynomial Control |
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472 | (4) |
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6.6.5 Control of Plants Containing Pure Time Delays |
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476 | (4) |
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480 | (1) |
7 Model Based Control of Nonlinear and Linear Plants |
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481 | (80) |
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481 | (1) |
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7.2 Linearisation About an Operating Point |
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482 | (9) |
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482 | (2) |
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7.2.2 Linear State-Space Model |
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484 | (7) |
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491 | (1) |
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7.3 Feedback Linearising and Forced Dynamic Control |
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491 | (69) |
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491 | (4) |
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7.3.2 Feedback Linearising Control of Plants with Full Relative Degree |
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495 | (14) |
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7.3.3 Feedback Linearising Control of Plants Less Than Full Relative Degree |
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509 | (13) |
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7.3.4 Forced Dynamic Control of Continuous LTI Plants |
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522 | (21) |
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7.3.5 FDC and FLC Using Discrete Plant Models |
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543 | (7) |
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7.3.6 Near-Time-Optimal Position Control Through FDC |
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550 | (10) |
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560 | (1) |
8 State Estimation |
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561 | (64) |
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561 | (1) |
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8.2 The Full State Continuous Observer for LTI SISO Plants |
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562 | (25) |
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562 | (3) |
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8.2.2 The Separation Principle and the Transparency Property |
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565 | (2) |
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8.2.3 Design of the Real-Time Model Correction Loop |
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567 | (8) |
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8.2.4 Estimation of Disturbances |
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575 | (12) |
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8.3 The Full State Discrete Observer for LTI SISO Plants |
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587 | (5) |
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587 | (1) |
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8.3.2 Observer Algorithm and Design Procedure |
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587 | (5) |
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8.4 The Full State Observer for Multivariable Plants |
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592 | (4) |
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592 | (1) |
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8.4.2 Matrix—Vector Design Method for SISO LTI Plants |
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592 | (2) |
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8.4.3 Matrix—Vector Design Method for Multivariable LTI Plants |
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594 | (2) |
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8.5 The Noise Filtering Property of the Observer |
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596 | (17) |
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596 | (1) |
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8.5.2 Lumped Plant Noise and Measurement Noise Sources |
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597 | (1) |
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8.5.3 State Estimation Error Variation with Observer Gains |
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598 | (1) |
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8.5.4 State Estimation Error Transfer Function Relationship |
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599 | (3) |
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8.5.5 Considering Noise Levels in Observer Design |
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602 | (11) |
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613 | (11) |
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613 | (1) |
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8.6.2 The Discrete Observer |
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614 | (1) |
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8.6.3 The Kalman Filter: State Difference and Error Equations |
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615 | (2) |
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8.6.4 Derivation of the Discrete Kalman Gain Algorithm |
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617 | (4) |
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8.6.5 The Steady-State Kalman Filter |
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621 | (1) |
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8.6.6 The Kalman—Bucy Filter |
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622 | (2) |
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624 | (1) |
9 Switched and Saturating Control Techniques |
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625 | (80) |
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625 | (3) |
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625 | (2) |
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627 | (1) |
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9.2 Pulse Modulation for Use with Continuous Controllers |
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628 | (10) |
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628 | (1) |
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629 | (9) |
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9.3 Switched State Feedback Control: Basic Concepts |
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638 | (3) |
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9.4 Switching Function Sign Convention |
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641 | (1) |
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9.5 Boundary Layer for Saturating Control Systems |
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642 | (2) |
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644 | (7) |
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644 | (1) |
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9.6.2 Optimal Control Through Pontryagin's Maximum Principle |
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644 | (7) |
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9.7 Feedback Control of First-Order Plants |
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651 | (15) |
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9.7.1 Time-Optimal Feedback Control: Analytical Method |
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651 | (3) |
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9.7.2 Time-Optimal Feedback Control: Graphical Approach |
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654 | (1) |
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9.7.3 Limit Cycling and Its Control |
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655 | (3) |
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9.7.4 Control with Time-Varying Reference Inputs |
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658 | (4) |
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9.7.5 Continuous Control with Saturation |
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662 | (4) |
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9.8 Feedback Control of Second-Order Plants |
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666 | (21) |
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666 | (1) |
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9.8.2 State Trajectories and State Portraits |
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666 | (3) |
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9.8.3 Time-Optimal Feedback Control of the Double Integrator Plant |
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669 | (3) |
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9.8.4 Time-Optimal Control Law Synthesis Using State Portraits |
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672 | (4) |
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9.8.5 Continuous Control with Saturation |
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676 | (11) |
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9.8.6 Limit Cycling Control |
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687 | (1) |
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9.9 Feedback Control of Third and Higher-Order Plants |
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687 | (17) |
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687 | (1) |
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9.9.2 Time-Optimal Control of the Triple Integrator Plant |
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687 | (9) |
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9.9.3 Posicast Control of Fourth-Order Plants with Oscillatory Modes |
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696 | (8) |
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704 | (1) |
10 Sliding Mode Control and Its Relatives |
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705 | (88) |
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705 | (8) |
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10.1.1 Purpose and Origin |
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705 | (1) |
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705 | (2) |
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10.1.3 Implementation for Robustness |
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707 | (6) |
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10.2 Control of SISO Second-Order Plants of Full Relative Degree |
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713 | (17) |
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713 | (1) |
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714 | (2) |
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716 | (2) |
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10.2.4 The Equivalent Control |
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718 | (1) |
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718 | (1) |
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10.2.6 Conditions for the Existence of Sliding Motion |
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719 | (1) |
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10.2.7 Reaching the Sliding Condition |
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720 | (3) |
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10.2.8 Closed-Loop Dynamics in the Sliding Mode |
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723 | (1) |
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10.2.9 Control with Time-Varying Disturbances and Reference Inputs |
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723 | (2) |
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10.2.10 Rate-Limiting Switching Boundary for Zero Overshoot |
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725 | (1) |
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10.2.11 Sub-Time-Optimal Control |
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726 | (4) |
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10.3 Control of SISO Plants of Arbitrary Order |
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730 | (12) |
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10.3.1 Control of Plants Having Full Relative Degree |
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730 | (8) |
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10.3.2 Control of Plants Less Than Full Relative Degree |
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738 | (4) |
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10.4 Methods for Elimination of Control Chatter |
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742 | (24) |
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10.4.1 The Boundary Layer Method |
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742 | (4) |
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10.4.2 The Control Smoothing Integrator Method |
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746 | (10) |
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10.4.3 Higher-Order Sliding Mode Control |
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756 | (10) |
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10.5 Controllers with Robust Pole Placement |
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766 | (7) |
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766 | (1) |
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10.5.2 Output Derivative State Feedback Controller |
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767 | (3) |
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10.5.3 Dynamic Controllers with Robust Pole Placement |
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770 | (3) |
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10.6 Multivariable Sliding Mode Control: An Introduction |
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773 | (19) |
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773 | (1) |
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10.6.2 Simple Approach with Minimum Plant Information |
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774 | (4) |
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10.6.3 Discrete Sliding Mode Control |
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778 | (14) |
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792 | (1) |
11 Motion Control |
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793 | (54) |
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793 | (1) |
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11.2 Controlled Mechanisms |
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793 | (12) |
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11.2.1 The General-Purpose Jointed-Arm Robot |
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793 | (1) |
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794 | (4) |
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11.2.3 Feedback Linearising Control Law |
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798 | (1) |
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11.2.4 Simplified Model for Mechanisms with Geared Actuators |
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799 | (6) |
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11.3 Dynamic Lag Pre-compensation |
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805 | (21) |
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11.3.1 Definition of Dynamic Lag |
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805 | (1) |
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11.3.2 Derivative Feedforward Pre-compensation |
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806 | (16) |
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11.3.3 Implementation with Feedback Linearising Control |
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822 | (4) |
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11.4 Optimal Control for Minimising Frictional Energy Loss |
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826 | (20) |
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826 | (1) |
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11.4.2 Formulation of Optimal Control |
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827 | (3) |
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11.4.3 Minimum Frictional Energy State Feedback Control Law |
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830 | (2) |
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11.4.4 Higher-Order Mechanisms |
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832 | (1) |
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11.4.5 Near-Optimal Control Using a Reference Input Generator |
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832 | (14) |
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846 | (1) |
Erratum |
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E1 | |
Tables |
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847 | (6) |
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Laplace Transforms and z-Transfer Functions |
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847 | (3) |
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Characteristic Polynomial Coefficients of the Settling Time Formulae |
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850 | (3) |
Appendices |
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853 | (150) |
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853 | (47) |
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A2.1 Kinematics of Vehicle Attitude Control |
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853 | (14) |
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A2.2 Plant Model Determination from Frequency Response |
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867 | (14) |
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A2.3 A Case Study of Plant Modelling Undertaken in Industry: Modelling for a Throttle Valve Servomechanism |
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881 | (18) |
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899 | (1) |
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900 | (20) |
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A4.1 Application of Mason's Formula Using Block Diagrams |
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900 | (8) |
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A4.2 Traditional Controller Zero Cancellation by Pole Assignment |
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908 | (7) |
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A4.3 Partial Pole Assignment for Traditional Controllers |
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915 | (4) |
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919 | (1) |
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920 | (20) |
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A5.1 Computer Aided Pole Assignment |
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920 | (7) |
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A5.2 Linear Characteristic Polynomial Interpolation |
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927 | (9) |
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A5.3 Routh Stability Criterion |
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936 | (4) |
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940 | (14) |
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A8.1 An Approach for State Estimation for Nonlinear Plants |
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940 | (14) |
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A8.1.2 Observer Based on Linearised Plant Model |
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941 | (1) |
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A8.1.3 Output Derivative Based State Estimator |
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941 | (13) |
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954 | (17) |
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A9.1 Limit Cycling Control for Second Order Plants |
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954 | (16) |
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970 | (1) |
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971 | (14) |
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A10.1 Observer Based Robust Control |
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971 | (13) |
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984 | (1) |
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985 | (17) |
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A11.1 Path Planning and Reference Input Trajectory Generation |
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985 | (17) |
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1002 | (1) |
Index |
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1003 | |