1984 Volume 20 Issue 10 Pages 905-911
A problem of designing an adaptive tracking system with internal stability is considered by an indirect method for the single-input single-output discrete-time linear system described in Lüders-Narendra canonical state form.
Under the assumptions that system parameters and the state are known, appropriate state-feedback gains and pre-compensator's gains that replace all the system poles by the desired ones and, at the same time, control the output to follow the reference signal generated through a known dynamical system with an unknown initial condition are first characterized in a form easy for computation. In the adaptive design, these system parameters and the state are all replaced by the estimates. The least square estimation scheme is used for parameter estimation and the state is reconstructed via the method of an adaptive observer. It is then established that in the proposed scheme, all the variables remain bounded, the closed-loop poles approach the desired ones and the output tracks the reference trajectory asymptotically. A computer simulation result is also provided to illustrate the tracking behavior to the desired reference trajectory.
