Trajectory Tracking Control for a 3-DOF Planar Parallel Manipulator Using the Convex Synchronized Control Method

In this paper, in order to satisfy multiple closed-loop performance specifications simultaneously while improving tracking accuracy during high-speed, high-acceleration tracking motions of a 3-degree-of-freedom (3-DOF) planar parallel manipulator, we propose a new control approach, termed convex synchronized (C-S) control. This control strategy is based on the so-called convex combination method, in which the synchronized control method is adopted. Through the adoption of a set of $n$ synchronized controllers, each of which is tuned to satisfy at least one of a set of $n$ closed-loop performance specifications, the resultant set of $n$ closed-loop transfer functions are combined in a convex manner, from which a C-S controller is solved algebraically. Significantly, the resultant C-S controller simultaneously satisfies all $n$ closed-loop performance specifications. Since each synchronized controller is only required to satisfy at least one of the $n$ closed-loop performance specifications, the convex combination method is more efficient than trial-and-error methods, where the gains of a single controller are tuned to satisfy all $n$ closed-loop performance specifications simultaneously. Furthermore, during the design of each synchronized controller, a feedback signal, termed the synchronization error, is employed. Different from the traditional tracking errors, this synchronization error represents the degree of coordination of the active joints in the parallel manipulator based on the manipulator kinematics. As a result, the trajectory tracking accuracy of each active joint and that of the manipulator end-effector is improved. Thus, possessing both the advantages of the convex combination method and synchronized control, the proposed C-S control method can satisfy multiple closed-loop performance specifications simultaneously while improving tracking accuracy. In addition, unavoidable dynamic modeling errors are addressed through the introduction of a robust performance specification, which ensures that all performance specifications are satisfied despite allowable variations in dynamic parameters, or modeling errors. Experiments conducted on a 3-DOF P-R-R-type planar parallel manipulator demonstrate the aforementioned claims.