Stability and robustness of adaptive pole-zero placement algorithm
Thesis DisciplineElectrical Engineering
Degree GrantorUniversity of Canterbury
Degree NameDoctor of Philosophy
A computationally efficient pole-zero placement algorithm for explicit adaptive control of discrete-time plants is presented, It is effectively an implicit algorithm in the sense that the controller design stage is trivial. Although the algorithm is restricted to open-loop stable plants, it is applicable to nonminimum phase plants. Results concerning the adaptive control of linear, time-invariant plants having purely deterministic or stochastic disturbances are given. In the deterministic case, it is shown that the adaptive control algorithm ensures that the purely deterministic disturbances are removed from the system output and that asymptotic perfect tracking is achieved. In the stochastic case, it is shown that the adaptive control algorithm leads to the required stability properties of the closed-loop system. The robustness properties of the modified adaptive control algorithm in the presence of bounded external disturbances and unmodelled dynamics are also given. It is shown that if the modelling error is sufficiently small relative to the normalizing signals, then the algorithm ensures the boundedness of the input-output signals.