Research On Space-time-scaling Synchronization Cascade Sliding Mode Control Of Uncertain Parallel Mechanisms

Compared with the serial mechanism,the parallel mechanism has the advantages of high stiffness,strong load capacity and high positioning accuracy.It has great advantages in many applications such as motion imitation,precision machining and high-speed assembly,etc.The parallel mechanism is a multi-branch coupling nonlinear object with rigid constraints,and has many uncertain factors,such as modeling error,friction and external random disturbance.Amongst such uncertain factors,the modeling error includes parameter perturbation,high-frequency or fast-varying internal disturbance,the friction contains essentially nonlinear Coulomb one,and the external random disturbances contains various periodic and high-frequency or fast-varying external ones,etc.There is non-uniform time-varying constraint internal forces coupling among the branches and the total effects of above-mentioned uncertain factors on the joint motions of the parallel mechanism are not always consistent.Thus,under the above-mentioned comprehensive influences of the structural and unknown uncertain factors,if the joint error of each branch is only corrected in its own control loop,and other loops do not respond,it will lead to asynchronous motions between all the branches.Because the end execution accuracy of the parallel mechanism is determined by all the motion branches,the joint motion asynchronization will inevitably lead to the decline of the end motion accuracy,and even damage the whole parallel mechanism in serious cases.At present,there are still some difficulties in the research of synchronization control on the uncertain parallel mechanism,which mainly include that there are some problems such as of control-parameter coupling and vague physical meaning in the existing methods that combine cross-coupling control with different control methods to solve the uncertainty problem under the Lyapunov-stability theory,which is not universal for different parallel mechanisms;there are many parameters difficult to be adjusted,chattering and differential expansion problem in practice amongst the existing sliding mode control methods with disturbance observer for the uncertain parallel mechanisms.Therefore,a construction method of control law is proposed to solve the synchronization control problem by using space-time-scaling transformation in this thesis,and based on such idea,the space-time-scaling synchronization sliding mode control combined with extended state observer,the space-time scaling synchronization cascade sliding mode control and the space-time scaling synchronization cascade sliding mode control based on extended state observer are successively proposed for the uncertain parallel mechanism.The main work of this thesis is as follows:1.The space-time scaling synchronization sliding mode control combined with extended state observer for the uncertain parallel mechanism is proposedTo solve the uncertain problem,there are many parameters difficult to be adjusted in practice amongst the existing sliding mode control methods with disturbance observer for the uncertain PMs.Therefore,the dynamic model of uncertain PM is firstly established,and then transformed into chained-integrators via the dynamic-linearization method.Furthermore,the sliding mode control combined with extended state observer(ESO-SMC)for the uncertain parallel mechanism is proposed,which only needs to be tuned with one-dimensional bandwidth parameter.To further solve the synchronization problem,there are some problems such as of control-parameter coupling and vague physical meaning in the existing methods that combine cross-coupling control with different control methods to solve the uncertainty problem under Lyapunov-stability theory,which is not universal for different parallel mechanisms.For such reasons,the relationship between the cross-coupling control,consensus control and time-scale control are explored in this thesis,on such basis a construction method of control law of using the space-time scaling transformation to solve the synchronization problem is proposed,i.e.,the space-time scaling synchronization control can be constructed from the original control method by the space-time scaling transformations,which only needs to be tuned with the time-scale parameter that has clear physical meaning.Thus,there is no more need to adjust multiple control parameters,and with it,the universal problem on how to combine the cross-coupling control with different control methods is then resolved for synchronization.Based on the construction method of control law,this thesis further combines the ESO-SMC method with the space-time scaling synchronization control construction method and then proposes the space-time scaling synchronization sliding mode control combined with extended state observer to solve the uncertainty problem and synchronization problem at the same time for the parallel mechanism.The simulation results show that compared with the method of sliding mode control combined with extended state observer,the space-time scaling synchronization sliding mode control combined with extended state observer can not only achieve good tracking performance with less control parameters,but also improve the synchronization performance of uncertain parallel mechanism.2.The space-time scaling synchronization cascade sliding mode control for the uncertain parallel mechanism is proposedIn the proposed space-time scaling synchronization sliding mode control combined with extended state observer for the uncertain parallel mechanism,the drive control variable has chattering problem due to the existence of the sliding mode symbol term,which is not conducive to increase the bandwidth of sliding mode control.For such reasons,the cascade sliding mode control method that only needs to be tuned with the one-dimensional bandwidth parameter which can be further increased,is first proposed to solve the uncertainty problem of the parallel mechanism.In such method,the several same 1^st order quasi sliding mode surfaces are cascaded to weaken the chattering layer by layer,and thus the bandwidth can then be increased due to the chattering's weakening.Based on the construction method of control law of using space-time scaling transformation to solve the synchronization control problem,this thesis further combines the cascade sliding mode control with the space-time scaling synchronization control construction method and then proposes the space-time scaling synchronization cascade sliding mode control for the uncertain parallel mechanism to solve the uncertainty problem and synchronization problem at the same time for the parallel mechanism.The simulation results show that compared with the method of space-time scaling synchronization sliding mode control combined with extended state observer,due to the increase of bandwidth,the proposed control method can not only make the parallel mechanism with better tracking performance and synchronization performance,but also effectively reduces the chattering.3.The space-time scaling synchronization cascade sliding mode control based on extended state observer for the uncertain parallel mechanism is proposedThe proposed space-time scaling synchronization cascade sliding mode control for the uncertain parallel mechanism is sensitive to noise due to its multiple derivatives of output since it is nested from several first-order quasi sliding mode surface,which leads to the differential expansion problem that constraints the bandwidth of cascade sliding mode control.Therefore,this thesis first proposes the cascade sliding mode control based on extended state observer for the uncertain parallel mechanism,which only needs to be tuned with the one-dimensional bandwidth parameter that can be further increased.In such method,the cascade sliding mode control is designed in the extended state observer in parallel with the system to solve the differential expansion problem,and the bandwidth can be further increased due to the solution of the differential expansion problem.Based on the construction method of control law of using space-time scaling transformation to solve the synchronous control problem,this thesis further combines the cascade sliding mode control based on extended state observer with the space-time scaling synchronization control construction method and then proposes the space-time scaling synchronization cascade sliding mode control based on extended state observer for the uncertain parallel mechanism to solve the uncertainty problem and synchronization problem at the same time for the parallel mechanism.The simulation results show that compared with the method of the space-time scaling synchronization cascade sliding mode control for the uncertain parallel mechanism,the proposed control method can not only solve the chattering problem and differential expansion problem at the same time,but also make the tracking performance and synchronization performance of the parallel mechanism better due to the further improvement of bandwidth.4.The experimental study on the space-time scaling synchronization sliding mode control method based on the automobile electro-coating conveying parallel mechanism prototype systemBased on the distributed"PC+UMAC"automobile electro-coating conveying parallel mechanism prototype system,the space-time scaling synchronization sliding mode control combined with extended state observer,the space-time scaling synchronization cascade sliding mode control and the space-time scaling synchronization cascade sliding mode control based on extended state observer for the uncertain parallel mechanism are validated in a comparative way.The experimental results show that the method of the space-time scaling synchronization cascade sliding mode control based on extended state observer for the uncertain parallel mechanism has better comprehensive tracking performance and synchronization performance.