Three link flexible arm robust regulation via proportional retarded control scheme.

In this paper, a delayed distributed proportional control is developed for a class of multiple-input-multiple-output systems in order to reduce the effects of external disturbances and uncertain dynamics. The system under consideration is a three degrees-of-freedom planar robot, consisting of an active joint driving the first link and passive flexible joints for the second and third links. The control challenge for this system is to drive the flexible arm around the desired setpoint or trajectory by controlling the first link. Actually, by using a specific Lyapunov-Krasovskii storage functional associated with a constrained optimization problem, the robustness of the proposed proportional retarded control action is achieved. This analysis, together with the attractive ellipsoid concept allows to conclude with Ultimately-Uniformly-Bounded stability. The closed-loop control algorithm is tested in numerical simulation and a comparative study with some existing recent control schemes based on the performance error is presented. • The proposed control scheme belongs to a class of multivariable proportional time delay distributed controller. • After finite time the trajectories of a flexible manipulator stay within reduced size attractive ellipsoid. • Ultimate Uniformly Bounded Stability of the controlled system is demonstrated by using a Lyapunov-Krasovskii functional. • The proposed algorithm can also be adapted for a class of nonlinear uncertain/disturbed multivariable output systems. • A sufficient condition to guarantee the feasibility of specific Bilinear Matrix Inequality is presented. [ABSTRACT FROM AUTHOR]