Digital Control of Nonlinear Control Systems using a PIM Based Fuzzy Method

A new approach for digital control of a class of nonlinear systems is proposed. For this purpose, a combination of the well-known Parallel Distributed Compensation (PDC) method, and a particular linear digital redesign approach, namely, the plant-input mapping (PIM) method, is employed. In this methodology, a group of linear continuous-time controllers for fuzzy blending using the PDC method is designed and using the PIM method, every linear controller is discretised using the PIM method, with a unique property of guaranteeing the closed-loop stability of every subsystem for all non-pathological sampling periods. Closed loop stability of the resulting digital control system is studied, using the second Lyapunov stability theorem, extended for fuzzy-switching systems. The superiority of the resulting nonlinear digital control system is demonstrated through an example.