Robust observer-controller compensator design using the loop shaping design procedure and the algebraic method

Abstract

This paper investigates robust observer-controller compensator design using Vidyasagar's structure (VS). VS has a unit matrix parameter H similar to the Q parameter for the Youla-Kucera parameterization. VS can be designed based on the left coprimeness of the central controller in the H(infinity)-loop shaping design procedure (H(infinity)-LSDP) and therefore can preserve the intrinsic properties of the H(infinity)-LSDP. This paper introduces algebraic methods to simplify the design of H in the VS controller by solving specific algebraic equations. In particular, the algebraic design of H can achieve two things. First, a dynamic H adjusts the tracking performance and yields the integral action. Second, a dynamic H rejects the input and output sinusoidal disturbances with known frequencies. These attributes are indications of the flexibility of the proposed method since the output-feedback controller design of the H(infinity)-LSDP cannot easily deal with such conditions. This paper discusses the achieved loop and the closed-loop behavior of the system with VS, and also gives two numerical examples. The first example shows that the proposed method results in a better design in many aspects than the resulting from H(infinity)-LSDP. The second example shows the application of the proposed method to rejecting input and output step disturbances, and input and output multiple sinusoidal disturbances, for which the H(infinity)-LSDP can hardly be used. Copyright (C) 2009 John Wiley & Sons, Ltd.