A generalized mixed-sensitivity convex approach to hierarchical multivariable inner-outer loop control design subject to simultaneous input and output loop breaking specifications

摘要

In this paper, we present a generalized mixed-sensitivity multivariable framework for designing hierarchical inner-outer loop control systems for linear time invariant (LTI) plants subject to simultaneous input and output convex specifications. The methodology presented can handle a broad class of closed loop (e.g. ℋ∞, ℋ2, frequency- and time-domain) objectives. This is accomplished by exploiting the Youla-Jabr-Bongiorno-Kucera (YJBK) parameterization, the resulting convexification, and state-of-the-art polynomial-time convex solvers that can be applied to smooth and non-differentiable problems. It is well known that ill-conditioned plants (with large relative gain array entries (RGA)) can be particularly troublesome when specifications must be met at multiple loop breaking points (e.g. inputs/controls, outputs/errors). The associated tradeoffs can be quite severe for such systems. A hierarchical control architecture can exploit the additional feedback information in order to significantly help in making reasonable tradeoffs between properties at these loop-breaking points. The utility of the framework is illustrated by designing a control system for the longitudinal dynamics of a 3-DOF scramjet-powered hypersonic vehicle model - one that is unstable, non-minimum phase and flexible. For such a challenging vehicle, the method is shown to generate very good designs - designs that would be difficult to obtain without the new framework presented. Comparisons to other methods are made to further illustrate its power and transparency. While the focus of the paper is on finite-dimensional LTI multivariable plants and frequency domain specifications, the methods presented can also be applied to infinite-dimensional plants subject to time-domain specifications. In short, the paper provides a systematic approach to a large class of important control design problems.