Adaptive PI-Based Sliding Mode Control for Nanopositioning of Piezoelectric Actuators

Abstract

This paper proposes an adaptive proportion-integral (PI)-based sliding mode control design (APISMC) used for nanopositioning of piezoelectric actuators (PEAs). Nonlinearities, mainly hysteresis, can drastically degrade the system performance. As well as the model imperfection, hysteresis can be treated as uncertainties of the system. These uncertainties can be addressed by sliding mode control (SMC) since SMC is promising for positioning and tracking control. To further improve the response speed, suppress chattering, and reduce the steady-state error, the adaptive PI-based SMC is employed to replace the discontinuous control. Actually, the adaptive PI-based SMC offers a fast convergence of the sliding surface. Further, another advantage of the proposed controller lies in that its implementation only requires the online tuning PI parameters without acquiring the knowledge of bounds on system uncertainties. A linear second-order system is utilized as the estimated model to compensate for the process nonlinearity and estimate the control gain. The robust stability of the APISMC is proved through a Lyapunov stability analysis. Simulation results demonstrate that the modified SMC is superior to the original one for both positioning and tracking applications. Compared with the original, the proposed controller provides better performance—less chattering, faster response, and higher precision.