Research And Application Of Adaptive Fractional-order Terminal Sliding Mode Control

With the development of natural science and social science,fractional calculus has been widely used in many aspects of scientific research and engineering technology.Different from the property research of integer order calculus,fractional calculus has a large space for exploration,and has become one of the hot topics concerned by researchers.Compared with integer-order sliding mode control,the fractional-order sliding mode controller provides more degrees of freedom due to its additional design parameters.Therefore,the fractional-order can be adjusted to obtain the best dynamic response,while the robustness remains unchanged.In fact,adaptive control technology is usually used in sliding mode control,because adaptive sliding mode control combines the advantages of adaptive control and sliding mode control.Based on the adaptive fractional-order terminal sliding mode control,this paper mainly makes the following research:1)The trajectory tracking problem of the cable-driven manipulator with unknown concentration force and unknown upper limit of external disturbance is studied.First,when the upper limit of external disturbance is unknown,an adaptive fractional-order non-singular fast terminal sliding mode(AFONFTSM)control strategy is designed.The upper limit is estimated through adaptive control,and the new adaptive control law avoids the singularity problem,the adopted fractional-order non-singular fast terminal sliding mode(FONFTSM)control can achieve fast convergence and effectively suppress jitter.Secondly,an AFONFTSM control strategy with delay estimation is designed.The delay estimation unit can be used to appropriately compensate for the centralized unknown dynamics of the system to obtain ideal model-free characteristics.The characteristic of these two control strategies is to use the adaptive control law to estimate the upper limit of uncertainty only by measuring the speed and position,so as to achieve the effect of rapid convergence,high precision and elimination of jitter.Finally,the simulation results show the effectiveness of the proposed control scheme.2)Aiming at the problem that the trajectory tracking of a linear motor(LM)with strong uncertainty is difficult to control.First,a practical adaptive fractional-order terminal sliding mode control(AFOTSM)strategy is proposed.In order to ensure the high-precision convergence of sliding mode variables in fixed time,the adaptive control rate is designed,and the stability of fixed time is analyzed by using Lyapunov stability theory.Secondly,based on the AFOTSM control strategy,the boundedness analysis of the error is carried out.The results show that even if the system is uncertain,the designed motion control system can achieve higher convergence accuracy.Finally,the simulation results show that the controller design is easy to implement,has high tracking accuracy and strong robustness.3)A series of problems concerning the asymmetry,density,load vibration and internal displacement uncertainty of each component during the flight of the quadrotor,and the change of the center of gravity caused by the change of load.First,an adaptive fractional-order sliding mode control strategy is proposed,which is designed to reduce the influence of wind disturbance,load and inertial momentum changes.Secondly,the influence of variable load on the trajectory tracking of the four rotors under wind load is considered.In the presence of interference paths,the four-rotor mass parameters are used to correct the coefficient load,and the coefficients are estimated online based on the adaptive Lyapunov method,so that the four-rotor can track the rotor and achieve the ideal state.