ADVANCES in MATHEMATICAL and COMPUTATIONAL METHODS
Model Based Predictive Control for a Class of Maximum Phase nonlinear SISO Systems I. I. SILLER-ALCALÁ, A. FERREYRA-RAMÍREZ, R. ALCÁNTARA-RAMÍREZ, AND J. JAIMES-PONCE Departamento de Electrónica, Grupo Control de Procesos Universidad Autónoma Metropolitana Av. San Pablo No. 180, Col. Reynosa Tamaulipas, Del. Azcapotzalco, C. P.0200, México D.F. MÉXICO
[email protected] Abstract: - This paper presents a nonlinear control design for a class of nonlinear systems with a completely unstable zero dynamics (Maximum Phase). The control scheme developed here, it was done by using a canonical form for nonlinear systems and applying nonlinear predictive controller, this combination obtains an approximately linear input-output response and internal stability. The efficacy of the method is demonstrated by means of a numerical example. Key-Words: - Nonlinear control, Predictive control, Non-minimum phase, Zero dynamics, Continuous system.
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for maximum phase nonlinear systems, i.e. systems with a completely unstable zero dynamics. The NCGPC (Nonlinear Continuous Time Generalized Predictive Control), [10-12] is an alternative nonlinear predictive controller capable of dealing with non-minimum phase nonlinear systems. The NCGPC was developed in a different way than conventional nonlinear predictive controllers. The NCGPC [10-12] is based in the prediction of the system output and due to the fact that it was not derived with the objective of canceling nonlinearities, as feedback linearization techniques do, which require the nonlinear system must have stable dynamics zero for the input-output linearized system to be internally stable. NCGPC has two main advantages. The first advantage is that it can constrain the predicted control through Nu, when Nu=0 the predicted input is constrained to be constant in the future. It is possible to infer that u(t) is indirectly constrained by Nu. Additionally, the response becomes slow and the control is not very active. The second advantage is, when Nu
