Optimal input signal design in control systems identification Wiktor Jakowluk

Spis treści książki

Preface .................................................................................................................................. 7
List of symbols and acronyms ......................................................................................... 13
1. System identification for control ................................................................................ 17
1.1. A background to optimal input design .............................................................. 17
1.2. Model predictive control ...................................................................................... 19
1.3. Iterative feedback tuning ...................................................................................... 21
1.4. Adaptive parameter estimation ........................................................................... 22
2. Optimal inputs for (ODE) system identification ...................................................... 25
2.1. Single Weighted Cost Function Method ............................................................ 25
2.2. Input friendliness factor and system identification efficiency ........................ 29
2.3. Free final-time problem formulation ................................................................. 31
3. Optimal inputs for (FO) system identification ......................................................... 35
3.1. Fractional-order optimal control problem ........................................................ 35
3.2. Fractional-order operator approximation ......................................................... 38
3.3. Optimal input design problem reformulation .................................................. 42
4. Model-based input design in system identification ................................................. 45
4.1. Prediction error method ....................................................................................... 46
4.2. Input spectrum design problem .......................................................................... 47
4.2.1. Partial correlation parametrization ........................................................... 47
4.2.2. Finite-dimensional parametrization ......................................................... 48
4.3. Application constraints ........................................................................................ 48
5. Least-costly input design for closed-loop system identification ........................... 53
5.1. Model parameter estimation ................................................................................ 53
5.2. Uncertainty in the parameter estimates ............................................................. 55
5.3. Uncertainty of frequency function estimates .................................................... 56
5.4. Spectrum representation ...................................................................................... 57
5.5. Quality constraints in ellipsoidal regions ........................................................... 58
5.6. Optimization problem formulation .................................................................... 59

6. Continuous system identification in the time domain ............................................ 65
6.1. First-order linear system identification ............................................................. 65
6.2. Plant-friendly identification of a first-order system ........................................ 70
6.3. Plant-friendly identification of a second-order nonlinear system ................. 75
6.4. A single degree of freedom linear system identification .................................. 82
6.5. Free final time LTI system identification ........................................................... 90
6.6. Conclusions ........................................................................................................... 98
7. Fractional-order optimal input design problem .................................................... 101
7.1. Fractional-order inertial system optimal control ........................................... 101
7.2. Experimental results for different system orders ............................................ 104
7.3. Conclusions ......................................................................................................... 109
8. Application-oriented input design for open-loop focused on MPC .................. 111
8.1. Cascade tanks system overview ......................................................................... 111
8.2. Cascade tanks model identification .................................................................. 114
8.3. Robust multi-tank system control .................................................................... 121
8.4. Conclusions ......................................................................................................... 124
9. Application-oriented input design for closed-loop with fixed controller .......... 127
9.1. The nonlinear cascaded double tank system application .............................. 127
9.2. Optimal input spectrum design-upper tank case study ................................. 129
9.3. Optimal input spectrum design – interacting tanks case study .................... 132
9.4. Conclusions ......................................................................................................... 134
Summary and suggestions for future work ................................................................. 135
References ........................................................................................................................ 141
List of Tables ................................................................................................................... 151
List of Figures .................................................................................................................. 153
Summary .......................................................................................................................... 157
Streszczenie ..................................................................................................................... 159

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