Abstract
A basic controller structure of a direct adaptive pole-placer for a single input and single-output linear system of unknown order is first investigated to obtain an error equation for estimating pole-placing feedback gains. As the system order is overestimated, the resulting closed-loop system using such estimated feedback gains in control has, in general, undesirable poles other than desirable ones. The estimated gains are thus adjusted solving a linear minimization problem so that the undesirable poles appearing in closed-loop system may be removed. By introducing a reduced order state vector, a minimal state space representation of the closed-loop system is then derived, and its generic observability in the parameter space is demonstrated when a signal comprised of an appropriate linear combination of the past input and output data is regarded as the system output.
Finally, a global asymptatic stability of the overall control system consisting of the poleplacing feedback estimator and controller is established under the assumption that the closed-loop system is uniformly observable with respect to the system output. Since the colsed-loop system is generically observable in the parameter space as demonstrated above, this assumption is sufficiently weak and will practically be satisfied by virtue of the adjustment process on the estimated feedback gains.
A result of a computer simulation in which a non-minimum phase system of second order is treated as the fifth order system illustrates the usefulness of the proposed scheme.
