Nonlinear Optimal Control of an H-Type Gantry Crane Driven by Dual PMLSMs

Abstract

Gantry cranes of the H-type with dual electric-motor actuation are widely used in industry. In this article, the control problem of an H-type gantry crane which is driven by a pair of linear permanent magnet synchronous motors (dual PMLSMs) is considered. The integrated system that comprises the H-type gantry crane and its two LPMSMs is proven to be differentially flat. The control problem for this robotic system is solved with the use of a nonlinear optimal control method. To apply the nonlinear optimal control method, the dynamic model of the H-type gantry crane with dual LPMSM undergoes approximate linearization at each sampling instant with the use of first-order Taylor series expansion and through the computation of the associated Jacobian matrices. The linearization point is defined by the present value of the system's state vector and by the last sampled value of the control inputs vector. To compute the feedback gains of the optimal controller an algebraic Riccati equation is repetitively solved at each time-step of the control algorithm. The global stability properties of the nonlinear optimal control method are proven through Lyapunov analysis. The proposed control scheme achieves stabilization of the H-type gantry crane with dual LPMSMs without the need of diffeomorphisms and complicated state-space model transformations.Gerasimos Rigatos has been partially supported by Grant Ref. 301022 ‘Nonlinear optimal and flatness-based control methods for complex dynamical systems’ of the Unit of Industrial Automation of the Industrial Systems Institute, Pierluigi Siano and Mohammed AL-Numay acknowledge financial support from the Researchers Supporting Project Number (RSP2024R150), King Saud University, Riyadh, Saudi Arabia