PLACING MULTIBODY SYSTEM TO EQUILIBRIUM STATE BY USING MULTIPLE PID CONTROLLERS AND GENETIC ALGORITHM

摘要

During development of MBS (Multibody System) dynamics simulation tool that evaluates contact forces between bodies, a procedure had to be developed for placing general MBS to equilibrium state. The procedure would be executed before dynamics simulation starts, to ensure stable and convergent simulation from its beginning. As very broad range of stiffnesses is coupled within the same model and additionally contact forces are evaluated, placing system to satisfactory initial state is not a simple task. Algorithm for initial conditions must place bodies to positions that would provide smallest possible (zero) resultant force on each body. After several approaches being tested, usage of PID (Proportional-Integral-Derivative) controllers showed greatest potential for solving the problem in a stable and fast manner. Such controller would be attached to each body and will move bodies to positions with smallest resultant force. To completely model PID controller, three parameters must be evaluated - gains for each controller action. For optimal combination of three parameters - conditions on force convergence and resultant force end value (zero) must be satisfied. Analysis showed that parameters for controller actions cannot be fixed and work successfully for MBSs with different number of DOF (Degrees of Freedom). Based on that, PID controller parameter range has been evaluated by Genetic Algorithm after repeated tests on systems of different types and number of DOF. Parameters choice and PID controller behavior were checked on models of engine timing drives (belt and chain drives with lashes) with several hundred DOF and simple model of Single Valve Train with just few DOF. Tests showed correct choice of PID parameters and stable iteration procedure regardless of DOF number and type of MBS. This paper focuses on determination of PID controller parameters by analyzing influence of MBS structure to procedure for reaching equilibrium state. Analysis is mainly focused on convergence and stability of the procedure.