Abstract
In this paper we propose a design method of a robust adaptive control system. And We consider a design method of a control system in which the norm of the output error between the object and the model converges to any small region. The controlled object under consideration here is a linear time invariant system with relative degree less than three and bounded disturbances.
In the case of the relative degree being one, it is presented that the design purpose is established by using of σ-modification approach and a unity feedback of the output error. In the traditional method, a control system is construtted by giving attention to the expanded error in the case where the relative degree is more than two. But it is difficult to guarantee the convergence of the norm of the output error, even if the control system can be constructed so that the convergence of the norm of the expanded error to any small region is guaranteed. Therefore in the case of the relative degree being two, estimated parameters, which are the sum of the output error and the estimated parameters of σ-modification approach, are used in order to construct the control system by giving attention to the output error. Moreover state feedback is used in order to guarantee the convergence of the norm of the output orror. In the case of the relative degree being three the control system is constructed so that the output signal of the first lag system tracks the inputof the case of the relative degree being two, where the input of the object is added to a first lag system, and by means of constructing such the control system, it is shown for plants with relative degree being three that the design purpose is also established.
Finally, computer simulation results are presented to illustrate the effectiveness of the proposed method.
