Loop recovery via H^∞/H² sensitivity recovery

Abstract

Loop transfer recovery (LTR) techniques are known to enhance the input or output robustness properties of linear quadratic gaussian (LQG) designs. Here, novel loop recovery techniques are applied to LQG designs based on H ^∞ /H ² optimization methods. The motivation is to exploit the power of the H ^∞ /H ² approach so as to avoid high estimator or control loop gains, to cope systematically with non-minimum phase plants, and to maintain availability of the optimal state estimates when required. In the new methods, the simplicity of the original loop recovery approach is retained, in that a scalar parameter can be adjusted to achieve a compromise between optimality for the nominal plant model and robustness at the plant input or output. There is also a built in frequency shaping in the sensitivity function-based performance index used for the H ^∞ /H ² optimization. This emphasizes crossover frequencies. However, in our method there is an increase in the controller complexity of at most 2n–1 (n being the order of the plant), unless controller reduction techniques are applied.

In the case of minimum phase plants, full or asymptotic loop recovery can be achieved and the H ^∞ /H ² optimization is trivial. However for non-minimum phase plants, only a partial loop recovery is possible, and the H ^∞ /H ² optimization seeks to achieve a ‘best’ possible recovery property. This paper focuses on H ^∞ optimization. Design examples are included to illustrate the relative strength of the new H ^∞ sensitivity recovery methods for loop recovery.