Nonlinear Optimal Control for the Underactuated Double-Pendulum Overhead Crane

PurposeDouble-pendulum overhead cranes find use in industry, construction works, and in supply-chain operations. Control and stabilization of the overhead crane and double-pendulum system exhibit elevated difficulty because of nonlinearities and underactuation. In this article, a nonlinear optimal control approach is proposed for the dynamic model of such crane systems.MethodsThe dynamic model of the crane and double-pendulum system undergoes approximate linearization around a temporary operating point that is recomputed at each time step of the control method. The linearization relies on Taylor series expansion and on the associated Jacobian matrices. For the linearized state-space model of the system, a stabilizing optimal (H-infinity) feedback controller is designed.ResultsThis controller stands for the solution to the nonlinear optimal control problem under model uncertainty and external perturbations. To compute the controller's feedback gains, an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis. Finally, to implement state estimation-based control without the need to measure the entire state vector of the overhead crane and double-pendulum system, the H-infinity Kalman filter is used as a robust state estimator.ConclusionsThe proposed nonlinear optimal control method achieves fast and accurate tracking of reference setpoints for all state variables of the double-pendulum overhead crane under moderate variations of the control inputs.

Automated summary

A nonlinear optimal control method is proposed for the dynamic model of double-pendulum overhead crane system. The method solves the control and stabilization problem by approximately linearizing the system at each time step and designing a stabilizing optimal feedback controller based on the linearized state-space model. The control gains are computed by solving an algebraic Riccati equation and the H-infinity Kalman filter is used for robust state estimation-based control.