Research On Finite-time Synchronous Robust Sliding Mode Control Of Uncertain Dual Parallel Mechanisms

The dual parallel mechanism is composed of two sets of symmetrical parallel mechanisms,exhibiting a symmetrical multi-branch closed chain structure.Due to the coordinated movement of two sets of symmetrical parallel mechanisms,the dual parallel mechanism has superior carrying capacity and can realize multi-mode motion,thus it is especially suitable for industrial applications such as complex conveying operation of large and heavy objects.From the control point of view,compared to kinematic control,the impact of system nonlinear dynamic factors on control performance can be compensated by dynamic control;compared to asymptotic control methods,superior performance,such as convergence speed,control accuracy and anti-disturbance performance,can be attained by finite time control.Therefore,the finite time dynamic control of the dual parallel mechanism is studied in this paper.The following problems are investigated:(1)The uncertainty problem.Because of the symmetrically distributed multi-branch closed chain structure,the dynamic modeling of the double parallel mechanism is complicated and the modeling errors are inevitable.Besides,the friction and the external disturbance exist during the operation process.These uncertainties will affect the precision of dynamic control.(2)The synchronous coordination problem.Compared with general parallel mechanisms,the operation of the dual parallel mechanism is equivalent to the synchronous operation of two parallel mechanisms.The pose of its end effector is adjusted via the coordinated motion of the active joints and two sets of parallel mechanisms.Therefore,higher requirements are put forward for the synchronization of the dual parallel mechanism.(3)Input saturation problem.Input constraints are common in actual mechanical systems,i.e.,the output of the actuator is limited physically.The control input acting on the dual parallel mechanism needs to manipulate two sets of parallel mechanisms to coordinate movement simultaneously.When the required control inputs exceed the output limit of the actuator,the input saturation problem occurs,which can destroy the dynamic control performance and even the stability of the system.In order to solve the above problems,based on the disturbance estimation technique and the finite time nonsingular terminal sliding mode control theory,the following control methods are proposed in this paper,i.e.,the finite time robust sliding mode control for the uncertain dual parallel mechanism,the finite time synchronous robust sliding mode control for the uncertain dual parallel mechanism,and the finite time synchronous robust sliding mode control for the dual parallel mechanism with uncertainties and input constraints.The control goal of improving the robustness and synchronization under the input saturation condition can be achieved.It is noteworthy that,as for the dynamic control of uncertain parallel mechanisms,there are few literatures to solve the issues of uncertainty,synchronization coordination and input saturation simultaneously.The main research of this paper is as follows:(1)The finite-time robust sliding mode control method for the uncertain dual parallel mechanism is proposed.In order to solve the uncertainty problem and realize the finite-time dynamic control of the uncertain dual parallel mechanism,a nonlinear disturbance observer is first designed to estimate the lumped disturbance;and then by extending the exponential power included in the terminal sliding mode surface parameters from a fractional exponential power to a real exponential power,a non-singular terminal sliding mode control algorithm with real exponential power is designed;the finite-time robust sliding mode control method for the uncertain dual parallel mechanism is finally proposed.The restriction on change rate of the lumped disturbance is relaxed from approximately zero to only bounded under the designed controller.The sign function is not included in the proposed control law,and the lumped disturbance in the dynamic system is estimated and compensated by the proposed control scheme.Consequently,the system robustness is improved and the chattering of sliding mode control is alleviated.As for the finite-time robust sliding mode control of the uncertain dual parallel mechanism,the finite time stability of the closed-loop system is proved via the finite time Lyapunov stability theorem.Compared with the asymptotically convergent robust sliding mode control based on the linear sliding mode surface,the simulation results show that the proposed control method has superior performance in terms of control accuracy,convergence speed and chattering suppression.(2)The finite-time synchronous robust sliding mode control method for the uncertain dual parallel mechanism is proposed.Based on the above research,in order to further solve the synchronous coordination problem and realize the finite-time dynamic control of the uncertain dual parallel mechanism,a non-singular terminal sliding mode control algorithm with real exponential power is designed based on a composite error,which is composed of the tracking error of each joint and the synchronization errors among the joints.By combining with a nonlinear disturbance observer,the finite time synchronous robust sliding mode control method for the uncertain dual parallel mechanism is proposed.As for the finite-time synchronous robust sliding mode control of the uncertain dual parallel mechanism,the finite time stability of the closed-loop system is proved via the finite time Lyapunov stability theorem.Compared with the finite-time robust sliding mode control method based on the tracking errors for the uncertain dual parallel mechanism,the simulation results show that the proposed control method can not only maintain good performance in terms of convergence speed and chattering suppression ability,but also improve the synchronization,and further improve the control accuracy.(3)The finite-time synchronous robust sliding mode control method for the dual parallel mechanism with uncertainties and input constraints is proposed.Because the above two control methods do not consider the input saturation problem in the actual system,the control effect of the uncertain dual parallel mechanism will be inaccessible to the theoretical expectation in practice and even destroy the system stability.Based on the above research,in order to further solve the input saturation problem and realize the finite-time dynamic control,by adding the fractional exponential power to the auxiliary system with asymptotic convergence,a novel auxiliary system with finite-time convergence is constructed to compensate the input saturation;then,by combining with the nonlinear disturbance observer and the non-singular terminal sliding mode control algorithm with real exponential power,the finite time synchronous robust sliding mode control method for the dual parallel mechanism with uncertainties and input constraints is presented.As for the finite time synchronous robust sliding mode control method for the dual parallel mechanism with uncertainties and input constraints,the finite time stability of the closed-loop system is proved via the finite time Lyapunov stability theorem.Compared with the finite-time synchronous robust sliding mode control method for the uncertain dual parallel mechanism without input constraints,the simulation results show that the proposed control method can guarantee the theoretically expected synchronous coordination performance and control accuracy even in the case of input constraints.(4)The motion control experiment is conducted on the prototype system of the dual parallel mechanism for automobile electro-coating conveying.Based on the distributed "PC+UMAC" prototype system platform of the dual parallel mechanism for automobile electro-coating conveying,the above three proposed control methods are validated in a comparative way.The experimental results show that the proposed finite-time synchronous robust sliding mode control method for the dual parallel mechanism with uncertainties and input constraints shows better control performance under the influence of uncertainty problem,synchronous coordination problem and input saturation problem.