A SELF-TUNING POLE-PLACEMENT CONTROL DESIGN

Abstract

In pole-placement control design based on input-output model, a generalised matrix equation is first derived, and it is then used to design controllers of any order. The poles of the closed-loop system can be assigned arbitrarily to any desired location within the Restricted Stability Zone but it is constrained by the limits of the control signal. When the pole-placement controller is applied to a non-minimum phase process, it is found that the inherent negative derivative effect can be reduced by assigning the poles to the right-most location in the Restricted Stability Zone. The pole-placement control design is also incorporated with an adaptive self-tuner. A multi-rate parameter estimator scheme that allows longer updating interval for the parameter estimator than the sampling interval of the controller is adopted. It is shown that its normalised prediction error remains bounded and the convergence properties for the multi-rate self-tuning pole-placement control scheme is established. Simulation results show that the initial estimated parameters must be properly assigned within the local convergence region. The size of the region depends on the selection of the multi-rate ratio (that is, controller sampling rate versus estimator updating rate), and the desired pole location.