Active Disturbance Rejection Control Combined with a Singular Perturbation Approach for Cable-Driven Parallel Robots with Elastic Cables

Cable elasticity is the principal obstacle to accurate positioning in large cable-driven parallel robots (CDPRs). The composite controller derived from singular perturbation theory addresses it by adding a vibration-damping correction to a rigid controller, but for a machine with long and highly compliant cables, the correction must be made strong: the velocity and damping gains Kv and Kd have to be raised and the proportional gain Kp lowered, which yields a slow and imprecise platform response. This paper augments that composite controller with active disturbance rejection control (ADRC). An extended state observer reconstructs the lumped elastic torque acting on each winch from the measured cable length, and the estimate is injected into the control law. The compensation introduces an additional tunable proportional gain Kpq, which acts on the closed-loop stiffness directly, so that Kv and Kd can be reduced and Kp increased without loss of stability, giving a faster and more accurate response. The proposed controller complements rather than replaces the composite structure: the damping correction remains necessary, and removing it destabilises the loop even when ADRC is active. Asymptotic stability of the overall closed loop is established by Lyapunov’s second method through a composite function combining the slow and fast subsystems. The controller is evaluated in simulation on the IPAnema3 spatial cable-driven parallel robot, without ADRC, with ADRC, and with ADRC under an added payload of 35 kg. Under these simulated conditions, and relative to the baseline composite controller without ADRC, the proposed controller reduces the root mean square position error by a factor of 8.2 and the integral of time-weighted absolute error by a factor of 7.7.