A modified similitude analysis method for the electro-mechanical performances of a parallel manipulator to solve the control period mismatch problem

Due to the discrete feature and performance limitation of the numerical controller,the control period sometimes cannot meet the constraints of the scaled model in similitude analysis,which brings the control period mismatch problem.The traditional similitude analysis methods are not able to solve this problem since the controller is treated as continuous system in these methods.This paper proposes a modified similitude analysis method to solve the control period mismatch problem,and the electro-mechanical performances of a 2-DOF parallel manipulator is predicted.Based on the model of dynamic and control system,most of the similitude laws are derived by taking the controller as continuous system.Then the transfer function of the controller in discrete form is established,and the similitude law related to control period is derived to figure out the cause of mismatch problem.The modified method,named long period equivalent,is proposed to solve the mismatch problem by using the least square method and superposition principles.Finally,the scaled model of the parallel manipulator is determined based on the modified similitude analysis method.