NONLINEAR CONTROLLER COMPARISON ON A BENCHMARK ...

List of Figures
1.1 TORA System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.1 Photograph of Flexible Beam System . . . . . . . . . . . . . . . . . . 8
2.2 Mechanical Model of Flexible Beam System, . . . . . . . . . . . . . . 9
2.3 Torsional Spring Model of FBS . . . . . . . . . . . . . . . . . . . . . 10
2.4 Translational Oscillation Model for FBS . . . . . . . . . . . . . . . . 11
2.5 Simulink Diagram of FBS . . . . . . . . . . . . . . . . . . . . . . . . 14
4.1 Initial Open Loop Disturbance . . . . . . . . . . . . . . . . . . . . . . 30
4.2 Initial Open Loop Response . . . . . . . . . . . . . . . . . . . . . . . 30
4.3 Linearized Optimal vs. Open Loop Response . . . . . . . . . . . . . . 32
4.4 Linear H1 vs. Open Loop Response . . . . . . . . . . . . . . . . . . 33
4.5 Linear H1 vs. Linearized Optimal . . . . . . . . . . . . . . . . . . . 34
4.6 Passivity Based Control vs. Open Loop Response . . . . . . . . . . . 35
4.7 Passivity Based Control vs. Linear Optimal Control . . . . . . . . . . 35
4.8 Passivity Based Control vs. Linear Robust Control . . . . . . . . . . 36
4.9 Backstepping vs. Open Loop Response . . . . . . . . . . . . . . . . . 37
4.10 Backstepping vs. Linear Optimal Control . . . . . . . . . . . . . . . . 37
4.11 Backstepping vs. Linear Robust Control . . . . . . . . . . . . . . . . 38
4.12 Backstepping vs. Passivity Based Control . . . . . . . . . . . . . . . 38
4.13 SGA: Nonlinear H 2 vs. Open Loop Response . . . . . . . . . . . . . . 39
4.14 SGA: Nonlinear H 2 vs. Linear Optimal control . . . . . . . . . . . . . 40
4.15 SGA: Nonlinear H 2 vs. Linear Robust Control . . . . . . . . . . . . . 40
4.16 SGA: Nonlinear H 2 vs. Passivity Based Control . . . . . . . . . . . . 41
4.17 SGA: Nonlinear H 2 vs. Backstepping Control . . . . . . . . . . . . . 41
4.18 SGA: Nonlinear H1 vs. Open Loop Response . . . . . . . . . . . . . 42
xi