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1 | (22) |
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1.1 General Control Problem |
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1 | (10) |
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2 | (1) |
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3 | (2) |
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5 | (6) |
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11 | (3) |
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1.3 Feedback Loop Trade-off |
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14 | (3) |
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1.4 Objectives of an Applied Theory |
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17 | (2) |
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1.5 Objectives of This Book |
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19 | (4) |
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19 | (1) |
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19 | (2) |
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1.5.3 How to Use This Book |
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21 | (2) |
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23 | (38) |
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23 | (1) |
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24 | (2) |
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2.3 Nominal Internal Stability |
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26 | (3) |
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29 | (13) |
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2.4.1 Phase and Gain Margins |
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29 | (3) |
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2.4.2 Global Dynamic Uncertainty |
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32 | (10) |
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42 | (8) |
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2.5.1 Known Disturbance/Noise/Reference |
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42 | (2) |
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2.5.2 Bounded Disturbances at the Output |
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44 | (3) |
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2.5.3 Other Performance Criteria |
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47 | (3) |
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50 | (5) |
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2.7 Extension to MIMO Systems |
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55 | (2) |
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57 | (4) |
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61 | (32) |
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61 | (2) |
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3.2 Well Posedness and Internal Stability |
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63 | (2) |
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63 | (1) |
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64 | (1) |
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3.3 Open-Loop Stable Plants |
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65 | (3) |
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68 | (10) |
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69 | (6) |
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3.4.2 The Output Feedback Case |
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75 | (3) |
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3.5 Controller Structure and Separation Principle |
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78 | (1) |
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79 | (1) |
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3.7 A Coprime Factorization Approach |
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80 | (8) |
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3.7.1 Coprime Factorizations |
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80 | (8) |
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88 | (2) |
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90 | (3) |
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93 | (34) |
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93 | (4) |
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97 | (1) |
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98 | (1) |
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4.4 Nominal Performance and Robust Stability |
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99 | (1) |
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100 | (5) |
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101 | (1) |
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4.5.2 Actuator Uncertainty |
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102 | (3) |
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105 | (4) |
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109 | (14) |
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4.7.1 Permanent Magnet Stepper Motor |
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109 | (10) |
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119 | (4) |
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4.8 Related Design Procedures |
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123 | (2) |
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125 | (2) |
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127 | (30) |
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127 | (1) |
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5.2 The Classical Linear Quadratic Regulator Problem |
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128 | (5) |
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5.3 The Standard H(2) Problem |
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133 | (8) |
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5.4 Relaxing Some of the Assumptions |
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141 | (1) |
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5.5 Closed-Loop Properties |
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142 | (7) |
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5.5.1 The LQR Case: Kalman's Inequality |
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143 | (2) |
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5.5.2 Some Consequences of Kalman's Inequality |
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145 | (1) |
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5.5.3 Stability Margins of Optimal H(2) Controllers |
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146 | (3) |
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149 | (3) |
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152 | (5) |
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157 | (50) |
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157 | (1) |
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6.2 The Standard H(XXX) Problem |
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158 | (21) |
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6.2.1 Background: Hankel and Mixed Hankel-Toeplitz Operators |
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161 | (15) |
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6.2.2 Proof of Theorem 6.1 |
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176 | (3) |
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6.3 Relaxing Some of the Assumptions |
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179 | (1) |
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6.4 LMI Approach to H(XXX) Control |
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180 | (12) |
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6.4.1 Characterization of All Output Feedback H(XXX) Controllers |
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183 | (5) |
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6.4.2 Connections with the DGKF Results |
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188 | (4) |
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192 | (1) |
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6.6 The Youla Parametrization Approach |
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193 | (10) |
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203 | (4) |
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207 | (38) |
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207 | (8) |
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210 | (5) |
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7.2 Structured Dynamic Uncertainty |
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215 | (8) |
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215 | (4) |
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7.2.2 Analysis and Design |
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219 | (4) |
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7.3 Parametric Uncertainty |
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223 | (14) |
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223 | (2) |
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7.3.2 Research Directions |
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225 | (5) |
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7.3.3 Kharitonov's Theorem |
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230 | (3) |
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233 | (4) |
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7.4 Mixed Type Uncertainty |
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237 | (5) |
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237 | (2) |
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239 | (3) |
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242 | (3) |
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245 | (48) |
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245 | (2) |
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8.2 Robust Stability Revisited |
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247 | (7) |
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8.2.1 Robust Stability Under LTV Perturbations |
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250 | (3) |
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8.2.2 Stability Under Time Invariant Perturbations |
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253 | (1) |
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8.3 A Solution to the SISO l(1) Control Problem |
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254 | (13) |
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8.3.1 Properties of the Solution |
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262 | (4) |
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266 | (1) |
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8.4 Approximate Solutions |
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267 | (15) |
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8.4.1 An Upper Bound of the l(1) Norm |
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268 | (1) |
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269 | (4) |
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8.4.3 Full State Feedback |
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273 | (3) |
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8.4.4 All Output Feedback Controllers for Optimal *-Norm Problems |
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276 | (6) |
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8.5 The Continuous Time Case |
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282 | (6) |
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8.5.1 Solution Via Duality |
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282 | (3) |
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8.5.2 Rational Approximations to the Optimal l(1) Controller |
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285 | (3) |
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288 | (5) |
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293 | (30) |
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293 | (2) |
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9.2 Geometry of State-Space Realizations |
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295 | (9) |
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9.2.1 Controllable/ Unobservable Spaces |
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295 | (2) |
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9.2.2 Principal Components |
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297 | (7) |
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9.3 Hankel Singular Values |
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304 | (6) |
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304 | (2) |
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306 | (4) |
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310 | (8) |
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310 | (1) |
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9.4.2 Hankel Operator Reduction |
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310 | (2) |
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9.4.3 Balanced Realizations |
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312 | (2) |
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9.4.4 Balanced Truncation |
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314 | (4) |
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318 | (3) |
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9.5.1 Approximation Error |
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319 | (2) |
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321 | (2) |
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323 | (54) |
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323 | (1) |
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324 | (15) |
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325 | (1) |
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326 | (2) |
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10.2.3 Identification Error |
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328 | (6) |
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334 | (4) |
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338 | (1) |
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10.3 Frequency-Domain Identification |
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339 | (22) |
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340 | (2) |
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10.3.2 Sampling Procedure |
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342 | (2) |
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344 | (2) |
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10.3.4 Identification Procedures |
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346 | (15) |
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10.4 Time-Domain Identification |
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361 | (11) |
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362 | (4) |
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10.4.2 Identification Procedures |
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366 | (6) |
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10.5 Further Research Topics |
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372 | (5) |
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372 | (1) |
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10.5.2 Nonuniformly Spaced Experimental Points |
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372 | (1) |
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373 | (1) |
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10.5.4 Continuous Time Plants |
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373 | (1) |
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373 | (1) |
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10.5.6 Mixed Time/ Frequency Experiments |
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374 | (1) |
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10.5.7 Mixed Parametric/Nonparametric Models |
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374 | (3) |
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377 | (50) |
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11.1 SAC-C Attitude Control Analysis |
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377 | (12) |
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377 | (1) |
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378 | (3) |
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11.1.3 Design Constraints |
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381 | (2) |
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11.1.4 Robustness Analysis |
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383 | (2) |
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385 | (4) |
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11.2 Controller Design for a D(2)O Plant |
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389 | (11) |
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11.2.1 Model of the Plant |
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389 | (2) |
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11.2.2 Robustness Analysis |
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391 | (6) |
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397 | (3) |
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11.3 X-29 Parametric Analysis |
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400 | (7) |
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400 | (5) |
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405 | (2) |
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11.4 Control of a DC-to-DC Resonant Converter |
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407 | (20) |
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407 | (1) |
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11.4.2 The Conventional Parallel Resonant Converter |
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407 | (2) |
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11.4.3 Small Signal Model |
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409 | (1) |
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11.4.4 Control Objectives |
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410 | (1) |
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11.4.5 Analysis of the Plant |
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411 | (3) |
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414 | (6) |
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11.4.7 Controller Synthesis |
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420 | (1) |
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11.4.8 Simulation Results |
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421 | (6) |
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427 | (18) |
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A Mathematical Background |
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445 | (20) |
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445 | (4) |
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445 | (1) |
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A.1.2 Linear Vector Space |
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446 | (1) |
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A.1.3 Metric, Norm, and Inner Products |
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447 | (2) |
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449 | (8) |
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449 | (1) |
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A.2.2 Banach and Hilbert Spaces |
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449 | (1) |
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A.2.3 Operator and Signal Spaces |
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450 | (2) |
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452 | (1) |
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453 | (2) |
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A.2.6 Some Important Induced System Norms |
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455 | (2) |
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A.3 Duality and Dual Spaces |
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457 | (3) |
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457 | (1) |
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A.3.2 Minimum Norm Problems |
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458 | (2) |
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460 | (5) |
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460 | (1) |
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A.4.2 Properties and Applications |
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461 | (4) |
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465 | (16) |
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465 | (1) |
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466 | (1) |
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467 | (1) |
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467 | (1) |
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467 | (1) |
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467 | (1) |
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468 | (1) |
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468 | (1) |
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469 | (1) |
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B.10 Linear Fractional Transformations |
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470 | (5) |
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475 | (4) |
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B.11.1 H(2) Norm Computation |
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475 | (1) |
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B.11.2 H(x) Norm Computation |
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476 | (1) |
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B.11.3 l(1) Norm Computation |
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476 | (3) |
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479 | (2) |
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481 | (6) |
| Index |
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487 | |