Nonlinear H-infinity control for 4-DOF underactuated overhead cranes

Abstract

The article proposes a nonlinear H-infinity control method for four degrees of freedom underactuated overhead cranes. The crane’s system is underactuated because it receives only two external inputs, namely a force that allows the motion of the bridge along the x-axis and a force that allows the motion of the trolley along the y-axis. A solution to the control problem of this underactuated system is obtained by applying nonlinear H-infinity control. The dynamic model of the overhead crane undergoes approximate linearization round local operating points which are redefined at each iteration of the control algorithm. These temporary equilibria consist of the last value of the crane’s state vector and of the last value of the control signal that was exerted on it. For the approximate linearization of the system’s dynamics, a Taylor series expansion is performed through the computation of the associated Jacobian matrices. The modelling errors are compensated by the robustness of the control algorithm. Next, for the linearized equivalent model of the crane an H-infinity feedback controller is designed. This requires the solution of an algebraic Riccati equation at each iteration of the computer control program. It is shown that the control scheme achieves H-infinity tracking performance, which implies maximum robustness to modelling errors and external perturbations. The stability of the control loop is proven through Lyapunov analysis.