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

Valentina Orsini

doi:10.1109/access.2021.3131032

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 a (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.

Highlights

The two main control requirements for a gantry crane system are: 1) a fast and very accurate point-to-point payload transition, 2) the minimization of the sway angles amplitude. Reconciling these two opposite control specifications calls for particular control techniques that can be summarily classified as FF, FB and FB/FF techniques
The present contribution situates in the category of 2DoF FF/FB, where the FF input is obtained through a dynamic inversion procedure [30]- [33]
This paper has presented a new approach to the robust FB/FF control of double-pendulum gantry cranes where the payload can take values over a given arbitrarily large interval

Summary

Introduction

The two main control requirements for a gantry crane system are: 1) a fast and very accurate point-to-point payload transition, 2) the minimization of the sway angles amplitude. FF open-loop techniques are mainly based on input-shaping algorithms [1]- [9] and are the most used both for their simplicity and because they do not require sensors for measuring the sway angles. These techniques are sensitive to external disturbances and parametric uncertainties. Reference [36] proposes the application

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