A new extension of the łrc; adaptive controller to drastically reduce the tracking time lags

Abstract

Abstract:The L 1 adaptive control scheme has proven its effectiveness and robustness in various fields thanks to its particular architecture where robustness and adaptation are decoupled. It was though noted that whenever the trajectory is varying, an inherent lag is present compared to other adaptive schemes due to the presence of a filter in the control architecture. To achieve a better tracking, we propose extending the architecture of the L 1 controller by augmenting it with a control input that could take the form of a nonlinear proportional or a proportional integral term. The extended scheme is validated through simulations via an illustrative example as well as experimental results performed on an underwater vehicle. INTRODUCTIONControlling nonlinear dynamic systems is a challenging task. Indeed, not being able to determnine the behavior of a system especially in presence of varying parameters, makes difficult the design of a suitable controller. For this reason, the idea of online estimating the uncertain or varying parameters from measurements has emerged. Based on these concepts, adaptive control was therefore born. The recently developped L 1 adaptive controller (Hovakimyan and Cao [2010]) stands out among all other developped adaptive methods in its particular architecture where robustness and adaptation are decoupled. The low pass filter introduced in its structure separates the estimation loop from the control loop. This guarantees a fast adaptation and compensation of the unmodeled dynamics while still preserving the stability of the closed-loop system. With such a novel method, various previously noted failures in adaptive control were revisited (Kharisov and Hovakimyan [2010] and Xargay et al. [2009]). Besides, an extensive study has been made in Rohrs et al. [1982] showing that restrictive assumptions were formulated upon the use of a wide range of adaptive controllers. These schemes were seen to exhibit undesirable frequency characteristics. An enough parameter excitation might be needed to ensure parameter convergence. This excitation phase allowing the parameters to adapt, will refect into a bad transient behavior on the system. Consequently, in order to avoid such a behavior, the adaptation gain is usually chosen small which would slow down the system's response. The advantage that the L 1 adaptive controller brings in this regard lies in the fact that the performance of the closed-loop system can be improved by increasing the adaptation gain without degrading the robustness. A zero steady-state tracking error is guaranteed for constant reference inputs. However, similarly to Model Reference Adaptive Control (MRAC), the error is only guaranteed bounded for time varying reference trajectories. A time lag can be noticed with the L 1 controller due to the presence of a filter in the control loop. A very careful filter design should then be done to compromise between this time lag and the desired performance bounds. In this paper, we propose a nonlinear proportional and a proportional integr...

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