Quantitative non-linear compensation design for saturating unstable uncertain plants

Consider an unstable uncertain plant controlled by an element Np, which saturates when its input |x| ≥ M. The system can be stabilized by means of feedback, which, however, is absent during Np saturation. If the saturation interval is long enough, it is impossible to recover system stability via Np. This paper presents a synthesis technique for ensuring that Np does not saturate despite very large command inputs. The basic idea is to prevent |x|>M, via an added saturating element N with saturation level m, which in turn is determined by |x|. A systematic, quantitative design technique is presented for unstable plants with large uncertainty, to achieve (a) desired performance tolerances over the linear range (small command inputs) and (b)acceptable but unavoidably slower response for large command inputs. Both (a) and (b) are achieved over the specified extent of plant uncertainty. The design technique makes use of several previously developed quantitative synthesis theories for minimum- and non-minimum-phase uncertain plants in linear operation, and for uncertain minimum-phase stable plants subject to saturation.