On the structure of robust controllers and weight selection in the mixed sensitivity minimization

Abstract

In this paper we examine the structure of robust controllers obtained from the mixed sensitivity minimization for a class of mechanical systems consisting of rigid body dynamics, weak flexible modes, and small time delays (or non-minimum phase effects due to non-collocated actuator and sensor). In particular, we study the weight selection in the mixed sensitivity design and illustrate that for certain performance and robustness objectives, the resulting H∞ optimal controller is in the form of a classical PID controller cascaded by a filter suppressing the uncertain flexible modes. Furthermore, we provide a link between this H∞ optimal controller and the conventional three-loop controller/autopilot (3LC) scheme frequently used in aerospace applications. More precisely, the 3LC scheme is shown to be equivalent to a two-degree-of freedom (2DoF) control structure where the H∞ controller is used in the feedback loop and the reference signal is filtered outside the loop.