Smart structures are currently utilized in many applications from precision positioning control of large space structures to active vibration control of machine components. Despite their relative easiness in controlling, positioning accuracy and longevity can be compromised by the hysteresis. In addition, current active control algorithms are limited predominantly to the control of a single or multiple sinusoidal waves and these are incapable of addressing more complicated multi-spectral signals such as modulated signatures. This dissertation introduces model-based and nonlinear control techniques aimed at the reduction of hysteretic effect and for their application to active motion control.
A nonlinear energy-based hysteresis model is developed for a piezoelectric stack actuator and model predictive sliding mode control is applied to force the system state to reach a sliding surface in an optimal manner and to accurately track the reference signal. This method is employed on pre-stressed curved unimorph actuators (modeled by a second order differential equation) with an additional time delay term to describe the hysteretic effect. Simulations and experiments are conducted to validate this approach, and the results highlight significantly improved hysteresis reduction in the displacement control mode. Also, it has been verified that the performance of the novel control methods is not much affected by the accuracy of actuator model.
Next, enhanced adaptive filtering algorithms are developed with application to active vibration control. A feedback loop with the model predictive sliding mode control is introduced in the adaptive filtering system. The goal of this study is to manage multi-spectral signals while achieving smooth and effective convergence, self-adaptability, and stability. The performance for new adaptive filtering algorithms is validated numerically and experimentally for different signals and other prevailing characteristics. The proposed algorithms are also compared with traditional algorithms for both narrowband and broadband control of signals with complex frequency spectra. The novel technique deals with primary peaks, sidebands, and broadband level simultaneously without a full knowledge of the unwanted signals.