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

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_∞‐loop shaping design procedure (H_∞‐LSDP) and therefore can preserve the intrinsic properties of the H_∞‐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_∞‐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_∞‐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_∞‐LSDP can hardly be used. Copyright © 2009 John Wiley & Sons, Ltd.