Polynomial solution of the 3 1/2-DOF H2/H∞ feedforward control problem

Abstract

Feedforward controllers are more sensitive to modelling errors than feedback designs and an H∞ solution of the feedforward problem, where robustness can be improved, is therefore desirable. A novel optimisation problem is required to provide the necessary independent tuning flexibility. The optimisation problem is based on an extended cost function which allows separate costing of the terms due to the feedback, reference and feedforward controllers. This enables the amount of feedforward action to be varied relative to the feedback action and the robustness of the feedback loop to be shaped independently of the tracking performance. The use of separate cost terms that enable the amount of feedforward control, relative to feedback action, to be tuned is essential in some applications. The solution of a new 3 1/2-degree-of-freedom H∞/H2 stochastic optimal control problem is discussed which may be either H2 or H∞ optimal. The system includes a 2 1/2-degree-of-freedom tracking controller and a feedforward control action. The feedback controller must be robust and is therefore normally designed to minimise an H∞ criterion. However, the solution obtained is sufficiently general that the feedback, tracking or feedforward control functions can be chosen to minimise either an H2 or an H∞ criterion.