Abstract
This paper presents a model reference adaptive control system (MRACS) for an SISO continuous-time linear plant in the presence of bounded disturbances. The assumptions made regarding the plant and disturbances are (i) the plant is minimum phase, (ii) an upper bound on the plant order is known, and (iii) the maximum amplitude of the equivalent disturbance at the controlled output is known.
Because the plant relative degree is not known a priori, the adaptive algorithm is based on the switching of parameter adjustment rules, one of which ensures the global stability of the MRACS. And “dead zone” method is applied in the adaptive algorithm for bounded disturbances.
In the stability analysis, the followings are proved: (1) the parameter adjustment rules are switched at most finite times, (2) the adaptive parameters are bounded, (3) the time derivative of the parameters are square integrable, (4) state variables of the control system are globally bounded on [0, ∞), and (5) the output error enters into a certain bound.
Numerical analysis is performed to compare the proposed method and the method in which no dead zone is used. It will illustrate the robustness of this method for bounded disturbances.
