Design of Modern Control Systems - IET Digital Library

7.3.2 Jacobson's necessary condition 136
7.4 Dynamic programming 137
7.5 The Hamilton-Jacobi approach 140
References 142
Problems 14 3
8 Control system design via mathematical programming 14 4
8.1 Introduction 144
8.2 Linear multivariable systems 146
8.3 Non-linear systems
8.4 Semi-infinite programming 152
8.4.1 Feasible-directions algorithms 153
8.4.2 Outer approximations algorithms 155
8.4.3 Non-differentiability 155
8.4.4 Cut-map algorithms 156
8.5 Conclusion 156
References 157
9 Optimisation in multivariable design 159
9.1 Introduction 159
9.1.1 The allocation problem 159
9.1.2 The scaling problem 159
9.1.3 Precompensation design problem 160
9.2 Problem formulation 160
9.2.1 Decomposition 161
9.2.2 Choice of dominance measure 161
9.2.3 General problem 162
9.3 Allocation problem 16 3
9.4 Sealing problem 16 5
9.5 Compensation design 16 7
9.6 Design example 169
References 17 3
Problems 175
10 Pole assignment 177
10.1 Introduction 177
10.2 State-feedback algorithms 179
10.2.1 Dyadic designs 179
10.2.2 Full-rank designs 183
10.3 Output-feedback algorithms 187
10.3.1 Dyadic designs 189
10.3.2 Full-rank designs 192
10.3.3 Example 194
10.4 Concluding remarks 196
References 19 7
Appendix 198
Problems 200
11 Nonlinear systems 202
11.1 Nonlinear behaviour 202
11.2 Fourier series 203
11.3 The describing function 206
11.4 Prediction of limit cycles 210
11.4.1 Frequency response of nonlinear
systems 213
11.5 Nonlinear state-space equations 213
11.6 Lyapunov's method 214