Nonlinear Control Techniques for Dynamical systems with Uncertain Parameters
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This report explores the control of nonlinear uncertain dynamical systems. Several models representing different types of nonlinearities are considered. In particular, the Duffing oscillator and a system coupled to an electro-rheological device are considered. This latter system nonlinearity is characterized by a nonlinear force versus velocity relationship which is itself a function of an external voltage applied across the device. The stabilization problem is considered, along with the problem of tracking combinations of sinusoidal and uniformly translated trajectories. In all these cases, the dynamical parameters of the systems as well as the input excitation, have been assumed to be specified as estimates of the true values, thus adding a certain level of uncertainty to the problem definition. This uncertainty has been dealt with, in this report, by relying on two robust control algorithms: sliding mode control, and a more general nonlinear robust algorithm. Significant reduction in the oscillation has been achieved in the tasks of stabilization, and satisfactory tracking is noted in the other cases as well. For a nonzero target trajectory, the proposed methods demonstrated the added capability of parameter estimation as well. Time lags associated with the actuator dynamics and signal processing have been accounted for, and attempts have been made to anticipate the values of the excitation over a finite prediction horizon.