A planar parallel manipulator - dynamics revisited and controller design

In this paper, the dynamic modelling and control design of a planar parallel manipulator used as a pick-and-place machine, is addressed. First, in a departure from standard modelling techniques utilized for planar parallel mechanisms, it is demonstrated that since the translational axes of the manipulator are driven by DC motors through industry standard ball screws, the nonlinear dynamics and coupling effects of the nonlinear dynamics of the manipulator are greatly reduced by a very large effective gear ratio factor, in this case, 1.097 xlO6. The dynamics of the driving motors thus become the dominant dynamics in the system. Hence, the dynamics of the entire system can be approximated as a set of three identical linear dynamic equations, each of which represents the dynamics of one kinematic chain, with constraints representing the coupling of these axes. Then a robust closed-loop controller designed with a Convex Integrated Design (CID) method is determined, such that multiple closed-loop performance specifications, together with a robustness specification, are simultaneously satisfied. The robustness of the closed-loop controller thus guarantees that the controller, although determined based on a simplified linear model, performs as expected on the practical system, i.e., the manipulator, hence results in satisfactory closed-loop performance. Both simulation and experiments conducted demonstrate that the multiple simultaneous closed-loop performance specifications are satisfied thus validating the simplified modeling strategy and verifying the effectiveness of the control design approach.