On the stabilization of linear unstable systems with control constraints

Julio H. Braslavsky and Rick H. Middleton
Abstract
In this paper we consider the problem of stabilisation of linear systems with constrained control. Previous works have frequently suggested the use of low-gain feedback to avoid problems caused by saturation. This is a useful technique for open-loop stable plants, but has sensitivity problems when used for open-loop unstable plants. In this paper, we discuss this issue, together with a new control methodology. This new methodology uses two controllers, one based on a minimum-time optimal control, and another using any standard linear controller design. A switching strategy, with hysteresis, is suggested so that locally, the linear control behaviour is achieved, but non-locally, the maximal possible region of attraction is achieved. This control strategy, as well as the analysis of other controllers, requires computations of certain regions in the state space. In the 2nd order case, methods for computing these regions are given, while for higher orders, quadratic approximations may be used. An example illustrates the above ideas.

Keywords: Control system design, Stability, Linear systems, Control nonlinearities, Saturation, Bang-bang control.

15 pages
18 references
81 Kb


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