Analyzing the Noise Behaviour of a Model Reference Adaptive Controller which uses Simultaneous Probing, Estimation and Control
In classical model reference adaptive control, the goal is to design a controller to make the closed-loop system act like a prespecified stable reference model. A recent approach yields a linear periodic controller which simultaneously performs probing, estimation, and control. This linear controller is not only able to handle time-varying systems, but also provides exponential stability. In addition, from simulations, it is found that the controller has excellent noise rejection in certain cases. In this thesis, we used the induced noise gain as the measurement of noise rejection. For plants that are minimum phase with relative degree one, we started with the case where the plant is first order and linear time-invariant. Then we moved to the case where the plant is first order and linear time-varying. Finally, we extended to the general case where the plant is linear time-varying with relative degree one. For the above cases, we quantitatively investigated how certain control parameters affect the induced noise gain.