Stability analysis of a dual-loop P-PI controller with variable gains for parallel manipulators

This work reports a novel variable-gains two-loop Proportional-Proportional Integral (P-PI) tracking controller, applied to a parallel manipulator. The dual-loop structure gives the controller the ability to tune separately the velocity loop and the position loop. This allows us to obtain a more decoupled control of these two variables for tracking control tasks on parallel robots. The dynamic model of a 3 DOF (Degrees Of Freedom) parallel manipulator is obtained. The stability analysis in the sense of Lyapunov of the proposed controller applied to the parallel robot is developed, which results in the conditions for the uniform ultimate boundedness of the solutions of the closed-loop system.