Simultaneous recovery of loop transfer property and disturbance attenuation property by high gain observer

Abstract

The loop transfer property of a full state feedback control system can be recovered by an observer based controller, provided the system is minimum phase and the observer gain is chosen appropriately. It is possible that the closed loop transfer function from the disturbance to the controlled output cannot be recovered by the same observer as above, even if the loop transfer function is recovered. The disturbance attenuation property is shown to be recovered if the Riccati equation that is to be solved in designing the observer is modified appropriately. Although the observer succeeds in recovering the disturbance attenuation property, it may fail to recover the loop transfer property. Simultaneous recovery of both properties is, therefore, desirable in practical control system design. It is shown that simultaneous recovery is possible if the number of independent measurement outputs is greater than or equal to the number of independent control and disturbance inputs. The dual result is also given; both properties can be simultaneously recovered if the system has a sufficient number of control inputs. Finally, a condition for simultaneous recovery is given also in terms of the geometric concept of an (A, B)-invariant subspace.