Second Level Adaptation as a Parameter Estimation Technique and its Application to Model Reference Adaptive Control
Parameter Estimation, Model Reference Adaptive Control, Second Level Adaptation, Multiple Model Adaptive Control
Adaptive control is used when there is parametric uncertainty in the controlled system. There are two distinct strategies: direct and indirect. Direct adaptive control estimates the controller parameters in real time. In indirect adaptive control the plant parameters are estimated in real time through an identification model and these estimates are used to calculate the controller parameters. There are several identification models that can be used such as parallel, series-parallel and linear regression models. There are several parameter estimation methods that can be used to update these models that are suitable to be used in conjunction with indirect adaptive control such as the least squares method and normalized gradient method. In this context a new method for parameter estimation based on multiple identification models was recently proposed, known as second-level adaptation. In second level adaptation the estimates of the plant parameters are obtained by convex combinations of the estimates from multiple identification models. The coefficients for these convex combinations are also estimated, as a second level of adaptation. In this dissertation we demonstrate the concept of second level adaptation as a parameter estimation method for the case of a plant of degree unity, the case of a plant of degree n with single input and output available for measurement (SISO) and the case of a plant of degree n with p inputs whose state vector is available for measurement (MIMO). We propose a modified form of the adaptive law for second level adaptation. In all cases simulation studies show that the estimates reach their true values faster with second level adaptation compared to individual identification models and that the proposed modification is even faster and also smoother in this regard. Finally, we apply second level adaptation based on linear regression identification models updated through the normalized gradient method to the problem of model reference adaptive control(MRAC) of a degree n SISO plant with relative degree one. The closed-loop stability of the system is demonstrated. Simulation results show that the control signal generated with second level adaptation yields better results of model reference tracking compared to individual identification models.