Fractional-Order Sliding Mode Control Of Linear-Motor-Drive Systems With Uncertainties

Linear-motor-drive system has been widely used in the modern manufacturing industry,and it is also the development direction of future technology.There are many sources of uncertainties in the linear motor drive system in practice,such as the thrust fluctuation,the environmental disturbance,the friction force,the parameter uncertainties,and the high-frequency response characteristics.In some complex tasks,more uncertainties are introduced due to payload changes and coupling between motion axes.These uncertainties have a great negative influence on the performance of the system.Considering that the linear motor driver directly drives the system without other components,the uncertainties in the system need to be handled by a robust control algorithm to ensure its performance in various working conditions.This paper proposes a variety of control methods and control structures based on the fractional-order sliding mode to solve the motion control problems in the linear-motor-drive system for precise and complex tasks,according to the actual situation and industrial application.Firstly,two new motion control algorithms based on fractional-order super-twisting sliding mode control are designed for the wafer scanning stage,which is a particular industrial case of the linear-motor-drive system.In the first algorithm,an adaptive neural network scheme is proposed to compensate for the system’s uncertainties,and the platform’s high precision control is realized through the proposed sliding mode control scheme.In particular,due to the existence of the designed adaptive scheme,the stability of the proposed control scheme is guaranteed.In the second algorithm,the problem of the "waterbed effect" in the wafer scanning platform is solved effectively by introducing variable-gain terms and fractional-order control algorithm.Both the repetitive and nonrepetitive uncertainties in the system are well handled.Finally,the experimental results show that the two control algorithms can perform better than the traditional methods.The wafer scanner introduced above is a particular piece of equipment,but the situations are different in the general single-degree-of-freedom linear motor drive system.Next,the motion control problem of the specific linear motor drive equipment is extended to the general equipment,and the position tracking control of the single-degree-of-freedom system is studied.In this paper,a new fractional-order sliding mode control method is proposed for the application of digital controllers in the discrete-time environments.This paper analyzes the stability of the discrete-time fractional-order sliding mode surface,which is not mentioned in the previous literature.In this paper,a new switching control law is proposed to suppress the chattering of the system further.Meanwhile,the theoretical accuracy of the whole motion control scheme and its theoretical advantages over other schemes are analyzed.The advantages over the traditional control methods are verified in the general linear-motor-drive system.Then,the motion control problem of the single-degree-of-freedom system is extended to the multi-degree-of-freedom system.Aiming at the complex task of linear-motor-drive system,the contouring control,a new fractional-order sliding mode contouring control method based on the simplified Newton method is proposed in this paper.In this method,the proposed contouring error estimation is well combined with the discrete-time system,and the numerical estimation of contouring error can be calculated accurately and quickly without requiring the derivative.Moreover,since this method is a dynamic estimation scheme,it can effectively ensure the accuracy of the contouring error estimation when the reference contour is with a significant curvature rate and a large feed rate.Finally,the system achieves higher precision of the contouring error control under the further action discrete-time fractional-order sliding mode control.In particular,during the process of studying the control scheme in high-dimensional systems,this paper also shows an easyto-use stability analysis method of the fractional-order sliding mode surface.Further,it gives the theoretical analysis of the contouring error.The effectiveness of the control scheme is verified in multiple groups of comparative experiments.Additionally,on the gantry driven by linear motors,two linear motors often drive a beam together,which involves the synchronization control.Therefore,a novel secondorder discrete-time fractional-order sliding mode synchronous control scheme is proposed to solve this problem.In this paper,a universal definition of the synchronization error is proposed,which can guarantee precision in multi-dimensional systems.Also,it is effectively combined with contouring error estimation so that the same scheme can realize the synchronization control and the contouring control at the same time.Under the action of the cross-coupling second-order fractional sliding mode control,the physical coupling between the motors is well handled,and excellent control performance is achieved.Moreover,the design of the special switching control law also separates the uncertainties and states in the system,ensuring the high performance and robustness of the closed-loop system.Finally,the effectiveness of the synchronization control scheme is proved by sufficient simulation and experiment results.