文件名称:
Robust Control Design with MATLAB
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文件大小: 5mb
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上传时间: 2011-09-10
详细说明： 1 Introduction ............................................... 3 1.1 Control-system Representations . .......................... 4 1.2 System Stabilities . . . .................................... 6 1.3 Coprime Factorisation and Stabilising Controllers . ........... 7 1.4 Signals and System Norms . . .............................. 9 1.4.1 Vector Norms and Signal Norms . .................... 9 1.4.2 System Norms .................................... 10 2 Modelling of Uncertain Systems ........................... 13 2.1 Unstructure d Uncertainties ............................... 13 2.2 Parametric Uncertainty .................................. 17 2.3 Linear Fractional Transformations . . . ...................... 20 2.4 Structured Uncertainties . . ............................... 23 3 Robust Design Specifications .............................. 25 3.1 Small-gain Theorem and Robust Stabilisation ............... 25 3.2 Performance Consideration ............................... 28 3.3 Structured Singular Values . . . ............................ 29 4 H∞ Design ................................................ 35 4.1 Mixed Sensitivity H∞ Optimisation. . ...................... 35 4.2 2-Degree-Of-Freedom H∞ Design . . ........................ 38 4.3 H∞ Suboptimal Solutions . ............................... 39 4.3.1 Solution Formulae for Normalised Systems ............ 39 4.3.2 Solution to S-over-KS Design....................... 43 4.3.3 The Case of D22 =0............................... 44 4.3.4 Normalisation Transformations . . .................... 45 4.3.5 Direct Formulae for H∞ Suboptimal Central Controller 47 4.4 Formulae for Discrete-time Cases . . ........................ 50xii Contents 5 H∞ Loop-shaping Design Procedures ...................... 55 5.1 Robust Stabilisation Against Normalised Coprime Factor Perturbations . . ......................................... 56 5.2 Loop-shaping Design Procedures .......................... 58 5.3 Formulae for the Discrete-time Case ....................... 61 5.3.1 Normalised Coprime Factorisation of Discrete-time Plant . . .......................................... 61 5.3.2 Robust Controller Formulae . ....................... 62 5.3.3 The Strictly Proper Case ........................... 63 5.3.4 On the Three DARE Solutions ...................... 65 5.4 A Mixed Optimisation Design Method with LSDP ........... 67 6 µ-Analysis and Synthesis .................................. 71 6.1 Consideration of Robust Performance ...................... 71 6.2 µ-Synthesis: D-K Iteration Method . ....................... 74 6.3 µ-Synthesis: µ-K Iteration Method . ....................... 77 7 Lower-order Controllers ................................... 79 7.1 Absolute-error Approximation Methods . ................... 80 7.1.1 Balanced Truncation Method ....................... 81 7.1.2 Singular Perturbation Approximation . . .............. 82 7.1.3 Hankel-norm Approximation . . ...................... 83 7.1.4 Remarks ......................................... 85 7.2 Reduction via Fractional Factors . ......................... 86 7.3 Relative-error Approximation Methods . . . .................. 90 7.4 Frequency-weighted Approximation Methods . . .............. 92 Part II Design Examples 8 Robust Control of a Mass-Damper-Spring System .........101 8.1 System Model ...........................................101 8.2 Frequency Analysis of Uncertain System....................107 8.3 Design Requirements of Closed-loop System ................108 8.4 System Interconnections . . ................................112 8.5 Suboptimal H∞ Controller Design . ........................115 8.6 Analysis of Closed-loop System with Khin ..................117 8.7 H∞ Loop-shaping Design . . ...............................125 8.8 Assessment of H∞ Loop-shaping Design . . ..................128 8.9 µ-Synthesis and D-K Iterations . . . .........................131 8.10 Robust Stability and Performance of Kmu ..................141 8.11 Comparison of H∞, H∞ LSDP and µ-controllers ............150 8.12 Order Reduction of µ-controller ...........................158 8.13 Conclusions .............................................162Contents xiii 9 A Triple Inverted Pendulum Control-system Design .......163 9.1 System Description . .....................................164 9.2 Modelling of Uncertainties . ...............................167 9.3 Design Specifications .....................................180 9.4 System Interconnections . . ................................182 9.5 H∞ Design . . . ..........................................186 9.6 µ-Synthesis . . . ..........................................191 9.7 Nonlinear System Simulation . . . ..........................199 9.8 Conclusions .............................................202 10 Robust Control of a Hard Disk Drive ......................203 10.1 Hard Disk Drive Servo System ............................203 10.2 Derivation of Uncertainty Model ..........................209 10.3 Closed-loop System-design Specifications . . .................215 10.4 System Interconnections . . ................................218 10.5 Controller Design in Continuous-time ......................219 10.5.1 µ-Design . . .......................................221 10.5.2 H∞ Design .......................................228 10.5.3 H∞ Loop-shaping Design...........................228 10.6 Comparison of Designed Controllers .......................229 10.7 Controller-order Reduction . ..............................237 10.8 Design of Discrete-time Controller . . . ......................239 10.9 Nonlinear System Simulation . . . ..........................244 10.10Conclusions .............................................247 11 Robust Control of a Distillation Column ...................249 11.1 Introduction . ...........................................249 11.2 Dynamic Model of the Distillation Column .................250 11.3 Uncertainty Modelling ...................................254 11.4 Closed-loop System-performance Specifications . . ............256 11.5 Open-loop and Closed-loop System Interconnections .........261 11.6 Controller Design . .......................................261 11.6.1 Loop-shaping Design ...............................262 11.6.2 µ-Synthesis .......................................271 11.7 Nonlinear System Simulation . . . ..........................283 11.8 Conclusions .............................................286 12 Robust Control of a Rocket ................................289 12.1 Rocket Dynamics ........................................289 12.2 Uncertainty Modelling ...................................301 12.3 Performance Requirements . . .............................306 12.4 H∞ Design . . . ..........................................310 12.5 µ-Synthesis . . . ..........................................315 12.6 Discrete-time µ-Synthesis . . ...............................324 12.7 Simulation of the Nonlinear System . .......................328xiv Contents 12.8 Conclusions .............................................332 13 Robust Control of a Flexible-Link Manipulator ............335 13.1 Dynamic Model of the Flexible Manipulator ................336 13.2 A Linear Model of the Uncertain System . . .................339 13.3 System-performance Specifications . ........................355 13.4 System Interconnections . . ................................359 13.5 Controller Design and Analysis . ...........................361 13.6 Nonlinear System Simulations . ............................372 13.7 Conclusions .............................................375 References .....................................................377 Index ..........................................................387 ...展开收缩
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