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Control of autonomous helicopters in the presence of environmental and system uncertainties is a challenging task. These uncertainties not only change the dynamics of the system but the trim inputs themselves. In this paper, a viable multivariable adaptive control methodology is proposed that is applicable for general maneuvers with arbitrary speeds and high bandwidth requirements. The control design methodology achieves global stability, and is tested on a high fidelity simulation of a real life autonomous helicopter. The results indicate a satisfactory tracking performance even as the speeds and bandwidth requirements are increased well beyond hover, and as the parametric uncertainties were increased by about 20% of their nominal values. Nomenclature Inverse of adaptation gain matrix ½ Adaptation gain ¾ Adaptation gain ¿ Adaptation gain Ö Adaptation robustness matrix Ö½ Adaptation robustness gain Ö¾ Adaptation robustness gain Ö¿ Adaptation robustness gain Efficiency of Engine
We present a self-tuning scheme for adapting the parameters of a proportional integral (PI) controller proposed by Fung and Yang for stabilization of a Culick-type model of nonlinear acoustic oscillations in combustion chambers. Our adaptation criterion is Lyapunov-based and its objective is the regulation of nonlinear pressure oscillations to zero. We focus on a two-mode model and first develop a design based on an assumption that the amplitudes of the two modes are available for measurement. The adaptation mechanism is designed to stabilize both modes and prevent the phenomenon observed by Candel and coworkers whose adaptive controller stabilizes the first but (under some conditions) apparently destabilizes the second mode. We also prove that the adaptation mechanism is robust to a time delay inherent to the actuation approach via heat release. In order to avoid requirements for sophisticated sensing of the mode amplitudes needed for feedback, we also develop an adaptation scheme which employs only one pressure sensor. In order for the adaptation scheme to be implementable, it is also necessary to know the control input matrix of the system. Rather than performing a linear ID procedure with input excitation, we propose a simple nonlinear ID approach based on limit cycles (internal excitation) which exploits the quadratic character of the nonlinearities. Simulations illustrate the scheme's capability to attenuate limit cycles and its robustness to magnitude-and rate-saturation of the actuator.
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