Design of a class of stabilizing nonlinear state feedback controllers with bounded inputs

This paper addresses the problem of designing stabilizing global linearization controllers subject to bounded inputs. It is well-known that saturation of the input variables usually leads to a serious performance degradation of even instability of processes if undesired attractors are present. Instability occurs in open-loop unstable plants once the controller hits the constraints. If the plant is open-loop stable, saturation may also lead to instability in the form of limit cycles. This paper provides conditions under which the existence of stable global linearization controllers for SISO and MIMO plants is ensured. These conditions will setup the basis to derive a tuning technique that, preserving stability, renders a quite acceptable performance in terms of closed-loop response. Two problem categories, and solution strategies, will be considered: (1) If the set of constrained inputs U-b is given, a feasible region in the state space is calculated and a low-gain static controller computed to preserve stability. Performance is then improved by adding and saturating and external controller. (2) If the feasible set in the state space and the desired dynamic behavior are given, a feasible set, U-b, and thus a global linearization controller, is computed. Performance is improved through an external and possibly saturated controller. The methodology we propose represents a simple way of designing nonlinear state feedback controllers for systems affected by severe nonlinearities and undesired attractors such as chemical reactors and it is particularly attractive for open-loop unstable plants. It applies to SISO as well as to MIMO systems and is illustrated through two simulation examples that involve continuous-stirred tank reactors. The first of them consists of the control of a non-isothermal reactor at the unstable state, while the second consists of the control of level and concentration.