NONLINEAR CONTROLLER COMPARISON ON A BENCHMARK ...
NONLINEAR CONTROLLER COMPARISON ON A BENCHMARK ... NONLINEAR CONTROLLER COMPARISON ON A BENCHMARK ...
control was that it requires only the angle as an input (no state estimation), though perhaps this explains why it is not very e cient in its use of control e ort. 60
Chapter 6 Conclusion and Future Work 6.1 Overview The exible beam system is a nonlinear system subject to the higher-order dynamics of the beam's motion, as well as to the non-linearity caused by the coupling between the rotational actuator and the quasi-linear motion of the mass at the end of the beam. Despite all of these nonlinearities and despite all of the unmodelled dynamics, the linearized approaches work adequately and damp the beam's vibration. It was gratifying to note, however, that the full nonlinear approaches did prove tobe better controllers when implemented in hardware. The successive Galerkin approximations to the HJB and HJI equations pro- duce control algorithms that e ciently regulate the non-linear benchmark problem. The performance of these algorithms as implemented on the FBS is superior to the performance of standard linearized controllers as well as a passivity-based design and a backstepping design. All of the control strategies studied produce robust, stabi- lizing designs, though the passivity based approach is very sensitive to its feedback parameters. In implementing this broad sample of nonlinear control algorithms, the similar- ities and di erences of the studied approaches become more apparent. The standard linearized optimal and robust approaches are simply ways of computing the appro- priate state-feedback gains so that the system is optimally regulated and robust with respect to a given cost function. This approach is thus dependent on an expert fa- miliar with the system to choose an appropriate cost function. This is very similar 61
- Page 21 and 22: Figure 2.2: Mechanical Model of Fle
- Page 23 and 24: Figure 2.4: Translational Oscillati
- Page 25 and 26: 2.3 Software Set-up All of the cont
- Page 27 and 28: Chapter 3 Overview of Control Strat
- Page 29 and 30: The optimal gain matrix was given b
- Page 31 and 32: 3.3 Passivity-Based Control Certain
- Page 33 and 34: limitations, k 1 and k 2 are tuning
- Page 35 and 36: Now we regard as the control variab
- Page 37 and 38: where V satis es the well known Ham
- Page 39 and 40: ecause one can quickly adjust the Q
- Page 41 and 42: Chapter 4 Simulation Results 4.1 Th
- Page 43 and 44: disturbances, whereas the hardware
- Page 45 and 46: Response in cm 4 3 2 1 0 −1 −2
- Page 47 and 48: Response in cm Response in cm 4 3 2
- Page 49 and 50: Response in cm Response in cm 5 4 3
- Page 51 and 52: Response in cm 4 3 2 1 0 −1 −2
- Page 53 and 54: Response in cm Response in cm 4 3 2
- Page 55 and 56: Response in cm Response in cm 4 3 2
- Page 57 and 58: It is seen in Figure 4.23 that the
- Page 59: all of the physical parameters exce
- Page 62 and 63: Response in m 0.05 0.04 0.03 0.02 0
- Page 64 and 65: Response in m 0.05 0.04 0.03 0.02 0
- Page 66 and 67: Response in m Response in m 0.05 0.
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- Page 74 and 75: to the Galerkin approximation techn
- Page 77 and 78: Bibliography [1] P. Kokotovic M. Ja
control was that it requires only the angle as an input (no state estimation), though<br />
perhaps this explains why it is not very e cient in its use of control e ort.<br />
60
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