Adaptive Sliding Mode Control of Hysteresis in Piezoelectric Actuator

Nominal-Model-Based Sliding-Mode Control for Traveling-Wave Ultrasonic Motor

Traveling-wave ultrasonic motors (TWUSMs) have strong nonlinearity and uncertainty, which are sensitive to the environment, disturbances, and load changes. Thus, precision control of TWUSMs is hard to achieve with traditional methods for complex driving mechanisms. A nominal-model-based sliding-mode control strategy with strong robustness is proposed to achieve accurate speed control of TWUSMs. Firstly, a second-order nominal model of the speed difference and output torque was deduced to construct a nonlinear sliding-mode surface; then, a nonlinear sliding-mode controller was designed with the collaborative regulation of frequency and the amplitude of two-phase control voltages. The global asymptotic stability of the controller was proved under bounded disturbances and parameter uncertainty. Finally, the effectiveness and accurate control were testified to and verified by the simulations and experiments, which showed good robustness and a disturbance rejection of the strategy for TWUSMs, with strong nonlinearity and uncertainty.

Finite-time adaptive sliding mode control for high-precision tracking of piezo-actuated stages

Piezo-actuated stages are widely used in nanopositioning applications. However, they not only have inherent static hysteresis characteristics but also have dynamic rate-dependent hysteresis nonlinearity. Therefore, to address dynamic hysteresis nonlinearity and uncertainty in the model parameters, an adaptive switching-gain sliding mode controller with a proportional-integral-derivative surface is designed. In particular, the combination of Bouc-Wen model and second-order linear system is used to describe the dynamic hysteresis process. To improve the robustness and reduce chattering in the sliding mode control method, an adaptive switching-gain is added to the controller without knowing in advance the upper bound of uncertainties. Finite-time convergence conditions of the closed-loop system are also analyzed. Finally, the proposed control method is implemented in real time on an ARM experimental platform. Comparative experimental results demonstrate excellent tracking performance and robustness. The dynamic hysteresis characteristics are suppressed effectively, and this result provides a powerful reference for engineering applications.

Identification of Preisach Model Parameters Based on an Improved Particle Swarm Optimization Method for Piezoelectric Actuators in Micro-Manufacturing Stages

The Preisach model is a typical scalar mathematical model used to describe the hysteresis phenomena, and it attracts considerable attention. However, parameter identification for the Preisach model remains a challenging issue. In this paper, an improved particle swarm optimization (IPSO) method is proposed to identify Preisach model parameters. Firstly, the Preisach model is established by introducing a Gaussian−Gaussian distribution function to replace density function. Secondly, the IPSO algorithm is adopted to Fimplement the parameter identification. Finally, the model parameter identification results are compared with the hysteresis loop of the piezoelectric actuator. Compared with the traditional Particle Swarm Optimization (PSO) algorithm, the IPSO algorithm demonstrates faster convergence, less calculation time and higher calculation accuracy. This proposed method provides an efficient approach to model and identify the Preisach hysteresis of piezoelectric actuators.

Multi-stroke anti-hysteresis algorithm based on inverse model

The control strategy of multi-stroke repetitive driving is often required in the micro-nano-system. However, the current research only focuses on the modeling algorithm of a single stroke; thus, it is difficult to realize the hysteresis compensation at any stroke of the piezoelectric actuator. This paper proposes a multi-stroke compensation algorithm combined with the inverse model: through the analysis of the hysteresis model, the rising trajectory with better linearity is defined as the target line to find a mathematical expression with fewer parameters to describe the falling trajectory, then to find the relationship between maximum stroke voltage and the above parameters to establish a mathematical model that can describe any stroke, and finally, to verify that the above model applies to any unknown stroke, thereby realizing multi-stroke compensation. The experimental results show that the hysteresis corrected rate after the above algorithm compensation is mostly over 85%, of which the maximum hysteresis corrected rate is 93.81% and the hysteresis error is less than 2.5%. Experiments prove the effectiveness of the above multi-stroke compensation algorithm based on the inverse model and extend the research on piezoelectric hysteresis characteristics to multi-stroke compensation.