Integral Manifold Based Control Design of Fully-Constrained Cable Robots with Elastic Cables

In this paper, a composite nonlinear control design for fully-constrained cable-driven parallel robots with elastic cables is investigated in detail. Based on the previous researches, dominant dynamics of the cables in longitude is considered in the robot modeling and the result is transformed into a standard singular perturbation model. Based on this theory, the system model is divided into two subsystems including slow and fast dynamics and a controller is designed for each of them. Firstly, the fast response of the system is extracted and is damped by a relevant control. As a result, the system response converges to an integral manifold and remains in it. Moreover, a compensative term is employed to control the vibrations due to the elasticity of the cables as well as a nonlinear controller which is applied to the slow subsystem. For each subsystem, the stability of the proposed controller is analyzed and finally, the stability of the complete closed-loop system is proven using the Lyapunov second method. The simulation results illustrate that the proposed composite control algorithm is effective and is capable of compensating the vibrations caused by the elasticity in the cables and stabilize the system.