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A new class of nonlinear PID controllers are derived for nonlinear systems using a Nonlinear Generalised Predictive Control (NGPC) approach. First the disturbance decoupling ability of the nonlinear generalised predictive controller is discussed. For a nonlinear system where the disturbance cannot be decoupled, a nonlinear observer is designed to estimate the offset. By selecting the nonlinear gain function in the observer, it is shown that the closed-loop system under optimal generalised predictive control with the nonlinear observer is asymptotically stable.It is pointed out that this composite controller is equivalent to a nonlinear controller with integral action. As a special case, for a nonlinear system with a low relative degree, the proposed nonlinear controller reduces to a nonlinear PI or PID predictive controller, which consists of a nonlinear PI or PID controller and a prediction controller. The design method is illustrated by an example nonlinear mechanical system.

• This is a journal article. It was published in the journal, IEE proceedings: control theory and applications and is subject to Institution of Engineering The stability condition presented in this paper enables the "fictitious" terminal control to be nonlinear, rather than only linear, and thus the stability region is greatly enlarged. Furthermore it is pointed out that nominal stability is still guaranteed even though the global, or even the local, minimisation of the objective cost is not achieved within the prescribed computational time.Keywords: Nonlinear systems, generalised predictive control, computational delay, optimisation, stability, constrained control online optimisation problem:subject to system dynamics,andfor τ ∈ [0, δ] where δ denotes the sampling time interval, R > 0, Q > 0 or Q ≥ 0 and non-zero x is detectable in the performance index and P > 0Fact 1: The constraint (3) is convex if the matrix P satisfies (4). Submitted to IEE Part D: Control Theory and Applications 3The constraint (3) can be written as

This paper addresses the terminal region of model-based predictive control (MPC) for non-linear systems with control input and state constraints. Based on a stability condition of non-linear MPC, a method to determine the terminal weighting term in the performance index and the terminal stabilizing control law to enlarge the terminal region and thus the domain of attraction of the non-linear MPC is proposed. An LMI based optimization approach is developed to choose the terminal weighting item and fictitious terminal stabilizing control law so as to enlarge the terminal region of the non-linear MPC method. The proposed method is illustrated by a numerical example and compares favourably with existing results.