An Identifier-tracking Based Model Reference Adaptive Control Without The Knowledge Of Relative Degree

Abstract

The purpose of Model Reference Adaptive Control (MRAC) is to create a controller with adjustable parameters to obtain the desired response from a reference model. One of the basic assumptions in MRAC is that the relative degree of the plant is known exactly. However, this assumption is too restrictive for some practical plants, since the relative degree of the plant may not be specified in advance. The study of MRAC with unknown relative degree has been important from both theoretical and practical point of view. This dissertation focuses on a new design approach for the model reference adaptive control of a single-input single-output linear time-invariant plant to relax this crucial assumption. The proposed method, called the "Model reference adaptive control without the knowledge of relative degree", does not require the knowledge of relative degree of the plant. This is achieved by the specific structure of reparameterization for control plant. The n-th order plant with unknown relative degree can have one identical structure for different relative degrees by employing the new method of reparameterization. For this reason, the structure of proposed model reference adaptive controller does not change, even if the unknown relative degree varies from 1 to n. The proposed method is based on a stacked identifier structure. The goal is to make the output of the plant asymptotically track the output of the first identifier, and then driving the output of the first identifier to track that of the second identifier, and so forth, up to the n-th identifier where n is the order of the plant. Lastly, the output of the n-th identifier is forced to converge to the desired response of the reference model.This new MRAC scheme guarantees the signal boundness and zero tracking error. All the parameter update laws are derived based on Lyapunov stability theory. Simulation studies are illustrated to show the effectiveness of the proposed method.