Robust Control and Estimation Framework for Parallel Manipulators: A Comparative Study of Super-Twisting and Fractional-Order PID Strategies ^†

This research investigates the problem of robust control of a nonlinear, fast-dynamics, high-precision planar manipulator with a limited workspace. Starting from a mathematical model formulated in terms of Euler-Lagrange dynamics, the proposed approach considers, given the limitations of the physical system, that some states are unavailable for direct measurement, and the system is perturbed by external disturbances. Consequently, a reduced-order state observer and an estimator with time-varying gains are proposed. Using these estimates in the control stage, four types of control laws are synthesized. Two are derived from super-twisting control theory (STC), the third is an integer-order PID (IOPID) controller, and the fourth is based on a fractional-order PID (FOPID) approach with optimization-based tuning. The first three strategies require accurate information about the mathematical model of the system. All the considered control strategies address external perturbations to ensure the robustness of the system. Several tests have been conducted to validate the overall estimation and control scheme. Based on the dynamic evolution of the manipulator tip and the analyzed performance metrics, the numerical results show that all the proposed controllers provide suitable solutions to robust tracking problems.