Dynamic Analysis And Contouring Control Of A2-DoF Planar Parallel Manipulator Driven By Linear Motors

Precision motion platform are key components of modern manufacturing equipments,which determine the accuracy and production efficiency of precision CNC machine toolsand electronic manufacturing equipments. From the viewpoint of mechanism, precisionmotion platform can be devided into serial platforms and parallel platforms (which is alsocalled parallel manipulator). From the viewpoint of drive type, they can be devided intodirect-drive motion platforms and indirect-drive motion platforms. The motion platformdirect driven by linear motors can improve the rigidity and reliability of transmission system,resulting in better control performances, higher transmission and positioning accuracy of themotion platform. At the same time, the multi-loop kinematic structure of parallel mechanismcan compensate for the error accumulation effects and achieve better tracking performance,which results a potential solutions to high-speed and high-precision motion applications. Thedevelopment of precision motion platform driven by linear motors can meet therequirements of modern manufacturing equipments and is of great theoretical and industrialsignificance.The subject investigated in this dissertation is a2-DoF high-precision planar parallelmanipulator direct driven by linear motors. Several fundamental problems, including thedimensional synthesis, inverse dynamic analysis and dynamic optimization of parallelmechanism, the task space dynamic model-based trajectory tracking control and thecontouring control of the2-DoF planar parallel manipulator are fully investigated andintensively studied. Experimental results are presented to validate the proposed trajectorytracking control and contouring control stragegies.Based on the structural analysis of the parallel manipulator, explicit expression ofinverse and direct kinematics of2-DoF planar parallel manipulator are derived. TheLagrangian formulation is applied to derive explicit expressions of task space dynamicmodel of the2-DoF planar parallel manipulator. The kinematic and dynamic performanceindices, including the workspace, the conditioning index, the dynamic manipulability and dynamic dexterity are analyzed. A global and comprehensive performance index (GCPI) anda global and comprehensive dynamic performance index (GCDPI) are proposed for thedimendional synthesis and dynamic optimization. Simulation results show that the2-DoFplanar parallel manipulator with optimized kinematic and inertial variables has larger, moreisotropic and more uniform dynamic manipulability in the prescribed task space of theparallel manipulator.In order to achieve high precision trajectory tracking control of the2-DoF parallelmanioulator, a task space dynamic model-based feedforward controller (MFC) is proposedin this dissertation. The model-based feedforward controller is combined with a cascadePID/PI controller and a velocity feedforward controller (VFC) to construct a hybridPID/PI+VFC/MFC trajectory tracking controller. The task space dynamic model and currentloop controller of linear motor are used to derive the transfer function of model-basedfeedforward controller. Experimental results show that, when the moving platform iscommanded to track a circle with a radius of50mm at an angular velocity of=10rad/s, avelocity ofvm ax=250mm/s and an acceleration ofam ax=2510mm/s2, the Root Mean Square(RMS) values of axial tracking errors are0.0118mm and0.0141mm, respectively, themaximum absolute values of axial tracking errors are0.0366mm and0.0424mm,respectively. Compared with conventional hybrid PID/PI+VFC/AFC trajectory trackingcontroller, the hybrid PID/PI+VFC/MFC trajectory tracking controller has superior trackingperformance, which reduces axial tracking errors by at least15%in the high-feedratecircular tracking experiments.In order to achieve high precision contouring control of the2-DoF parallel manipulator,a global task space based cross-coupled contouring controller (CCC) is proposed in thisdissertation. The contouring controller is based on a PI type cross-coupled controller andcircular approximation of contour error in the global task space of the parallel manipulator.The generalized contour error transfer function (GCETF), which establishes the relationshipbetween the contour error of uncoupled controuring control system and cross-coupledcontrouring control system, is used to derive the control parameters and stability analysis ofthe cross-coupled controller. The task space based contouring controller is combined withthe hybrid PID/PI+VFC/MFC trajectory tracking controller to achieve high-precisioncontouring control of the2-DoF planar parallel manipulator. Experimental results show that,when the moving platform is commanded to tracking an ellipse with long-axis of50mm andshort-axis of40mm at an angular speed of=10rad/s, a velocity ofvm ax=201.06mm/s and an acceleration ofam ax=2008.6mm/s2, the Root Mean Square (RMS) and maximum absolutevalues of the contour errors are0.0047mm and0.0255mm, respectively. When the movingplatform is commanded to tracking a lemniscate of Bernoulli with fixed length of60mm inthe X-axis at an angular speed of=5rad/s, a velocity ofvm ax=175.95mm/s and anacceleration ofa max=1768.6mm/s2, the RMS and maximum absolute values of the contourerrors are0.0037mm and0.0326mm, respectively. Compared with uncoupled contouringcontroller, the cross-coupled controller has superior contouring tracking performance, whichreduces contouring errors by at least24.29%and17.95%in the high-feedrate elliptical andlemniscate contouring experiments.The research results of this dissertation is useful for the development and application ofnew-type precision motion platform. It is of great reference value to the structural synthesisof parallel mechanism and to the theoretical and experimental studies of high-speed andhigh-precision motion control algorithms.