Flatness-Based Control in Successive Loops of an H-Type Gantry Crane with Dual PMLSM

Purpose In this article, the feedback control and stabilization problem of dual PMLSM-driven H-type gantry cranes is treated with the use of a flatness-based control method which is implemented in successive loops. Dual-drive gantry cranes can achieve high torque and high precision in the tasks’ execution. Such a type of crane can be used in several industrial applications. The solution to the associated nonlinear control problem is a particularly challenging research objective. Methods The integrated system that comprises the H-type gantry crane and two PMLSMs is shown to be differentially flat. The control problem for this robotic system is solved with the use of a flatness-based control approach which is implemented in successive loops. To apply the multi-loop flatness-based control scheme, the state-space model of the H-type gantry crane with dual PMLSM is separated into subsystems, which are connected in cascading loops. Results For each subsystem, control can be performed with inversion of its dynamics as in the case of input–output linearized flat systems. The state variables of the preceding (ith) subsystem become virtual control inputs for the subsequent (i+1)th subsystem. In turn, exogenous control inputs are applied to the last subsystem. The whole control method is implemented in successive loops and its global stability properties are also proven through Lyapunov stability analysis. Conclusion A novel nonlinear optimal control method has been developed for the dynamic model of a dual PMLSM-driven gantry crane. The proposed method achieves stabilization of the H-type gantry crane with dual PMLSM without the need for diffeomorphisms and complicated state-space model transformations. Using the local differential flatness properties of each one of the subsystems that constitute the gantry crane's model, the design of a stabilizing feedback controller is enabled.