A Robust Offline Precomputed Optimal Feedforward Control Action for the Real Time Feedback/Feedforward Control of Double Pendulum Gantry Cranes

Abstract

This paper deals with FeedBack/ FeedForward (FB/FF) control of double pendulum gantry crane systems with payloads taking values over arbitrarily large intervals. The new proposed 2DoF control architecture is aimed at: 1) to speed up the horizontal payload transportation while minimizing the tracking error with respect to a desired trajectory; 2) to minimize the sway angles amplitude. The main features of the control design procedure are: 1) the dynamic output FB control is designed in order to ensure the robust stability of the closed loop system and the steady-state exact payload positioning; 2) the FF control action is given by the optimally weighted sum of the two contributions due to FF Plant Inversion (FFPI) and FF Closed Loop Inversion (FFCLI) control schemes; 3) the optimal robust FF control input is obtained as the solution of a min max optimization problem that can be solved offline with numerically efficient procedures; 4) the provided analytical closed form of the FF input in terms of a linear combination of polynomial B-splines basis functions allows an easy implementation on commercial devices.

Keywords

• Gantry crane
• 2DoF control
• trajectory tracking
• model inversion
• B-spline input shaping