10. DUAL POLE-PLACEMENT AND LQG CONTROLLERS WITH INDIRECT ADAPTATION

Abstract

Adaptive pole-placement controllers (APPC) exhibit important properties and provide closed-loop system dynamics according to the desired position of the poles. Moreover, the pole locations can be determined to ensure optimal or robust properties of the system (see, for example, Yu et al., 1987). In systems with indirect adaptation, the plant parameters are estimated and used for computation of the controller parameters, whereas in systems with direct adaptation the controller parameters are estimated directly (usually together with some additional parameters) without estimation of the plant parameters. Usually the indirect APPC requires the estimation of less parameters in comparison with the direct APPC, but it is necessary to solve the Diophantine equation online in real time. Therefore, the indirect APPC can provide a more rapid adaptation and may be applied in cases where this requirement is important. The bicriterial approach for the synthesis of the direct dual APPC was already presented in Chapter 6, whereas the dual version of the indirect APPC was derived only for the simplified approach presented in Chapter 9. Below, this problem will be investigated first without the simplified calculation of the nominal output. The importance of APPC is also display ed in their direct application for the LQG control law (Keuchel and Stephan, 1994; Yu et al., 1987). The LQG control law can be obtained using a spectral factorization for the pole placement. Therefore, in the following at first the dual APPC is derived, and then the LQG controller can be obtained formally by application of the spectral factorization mentioned above (Keuchel and Stephan, 1994; Yu et al., 1987). Both controller types, the indirect APPC and the dual LQG controller, will be applied to a thyristor-driven DC motor in Chapter 11.