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