H_∞ and H₂ Controllers

Abstract

In the LQG controller design we assumed that the control inputs were collocated with disturbances, and that the control outputs were collocated with the performance. This assumption imposes significant limits on the LQG controller possibilities and applications. The locations of control inputs do not always coincide with the disturbance locations, and the locations of controlled outputs are not necessarily collocated with the location where the system performance is evaluated. This was discussed earlier, when the generalized structure was introduced. The H₂ and H_∞ controllers address the controller design problem in its general configuration of non-collocated disturbance and control inputs, and noncollocated performance and control outputs. Many books and papers have been published addressing different aspects of H_∞ controller design, and [12], [30], [94], [99], [100], [104], [122], and [129] explain the basic issues of the method. The H_∞ method addresses a wide range of the control problems, combining the frequency- and time-domain approaches. The design is an optimal one in the sense of minimization of the H_∞ nonn of the closed-loop transfer function. The H_∞ model includes colored measurement and process noise. It also addresses the issues of robustness due to model uncertainties, and is applicable to the single-input-single-output systems as well as to the multiple-input-multiple-output systems.