Microprocessor-Based Fuzzy Decentralized Control of 2-D Piezo-Driven Systems

In this paper, the trajectory tracking of a 2-D piezo-driven system (2DPDS) using microprocessor-based fuzzy decentralized control (MBFDC) is developed. It is known that the piezoelectric actuator contains hysteresis, which is not one-to-one mapping and memoryless nonlinearity. Due to this nonlinearity and the coupling characteristic of the 2DPDS, an effective decentralized control is difficult to design. From the very beginning, the suitable coefficients of switching surface are assigned to stabilize the dynamics of switching surface and to shape the response of tracking error. Based on the data of input/output, two scaling factors are employed to normalize the switching surface and its derivative. According to the concept of if-then rule, an appropriate rule table for the ith subsystem is then achieved. This table is skew symmetric about the diagonal line; the absolute value of this table is proportional to the distance to the diagonal line. According to the system stability, the output-scaling factor is determined. Finally, a sequence of experiments including the trajectory tracking using MBFDC, proportional-integral-differential control, and classic fuzzy control is carried out to confirm the usefulness of the proposed control system.