Improved sliding mode dynamic matrix control strategy: Application on spindle loading and precision measuring device based on piezoelectric actuator

Abstract

Spindle workload simulation and precision measurement are important in evaluating the precision of the spindle under different working conditions. Controlling the loading and measuring system accurately is difficult due to the robustness requirements of the controller, the complex dynamic model of the spindle loading system, the difficulty of obtaining system parameters, and the hysteresis of the piezoelectric actuator (PEA). To overcome this challenge, this study refers to the dynamic matrix control (DMC) method and proposes a highly versatile, robust, improved sliding mode DMC predictive controller (ISLDMC). ISLDMC is a non-inverse model control method with strong stickiness and good tracking characteristics. To help the controller achieve good versatility, this study regards nonlinear links, such as hysteresis of PEA, as an unknown disturbance and collects the step response signals of the piezoelectric system as the model state equation. In consideration of the practical application of the piezoelectric system, the prediction function of the state equation is used at the feedforward end of the controller, and the sliding mode function and incremental output are unified at the output end via weighted form optimization. In the feedback part, a variable correction coefficient is introduced into the state equation of the controller to enhance the tracking characteristics of the controller. This improvement is independently verified in a simulation environment. The design method of the controller is provided, the Schur stability of the closed-loop control system is proven. Moreover, the proposed controller is applied to machine tool spindle workload simulation and a precision-measuring device based on piezoelectric actuators. ISLDMC-based displacement-tracking and force-tracking controllers are designed. The experiment showed that the tracking performance and anti-interference, anti-model mismatch, and linear compensation capabilities of ISLDMC are better than those of the DMC controller, PI controller, and controllers from other studies. Furthermore, the linear compensation and anti-disturbance characteristics of the ISLDMC controller with the step response as the state equation are verified through force tracking experiments, which reveal that ISLDMC has good force tracking performance and anti-disturbance and linear compensation characteristics. The effectiveness of the introduction of dynamic correction coefficients is verified through a separate simulation involving displacement tracking and piezoelectric load experiments. The findings confirm that compared with the DMC controller, the ISLDMC controller improves tracking characteristics to a certain extent and has higher robustness.