Using second order sliding mode principle to design tracking controller for a kind of piezoelectric actuators

A new second order sliding mode tracking controller (SOSMC) is presented for a kind of piezoelectric actuator (PEA) model with hysteretic nonlinearity. The second-order nonlinear dynamic model of the PEA is introduced and a second order sliding mode control law with dual-phase sliding movement is designed. In order to prove the system's stability, a determinant theorem is presented. By theoretical analysis, the second order sliding mode controller is proved to be stable in the sense that all signals involved are bounded. The simulation results show the validity of the SOSMC for this kind of nonlinear dynamic model of PEA.