Nonlinear Control Strategy with Guaranteed Transient Performance for Double Pendulum Cranes

This paper proposes a control strategy with guaranteed transient performance for double pendulum crane systems. This control strategy not only completes the control objectives, but also improves the convergence performance. First, applying the prescribed performance bound (PPB) technology, the state variable errors of the system are transformed. This technology can eliminate the steady static errors and guarantee transient performance. This technology enables the trolley to reach the specified desired position quickly, and limits the first and second pendulum angles, ensuring the safety performance of the system. Then, in the controller design, more swing angle information is used as feedbacks. In this way, the first and second pendulum angles are restrained, the double pendulum effect is solved. So, this way improves the safety of the system. The stability analysis proves that the errors of the system state variables can reach a very small neighborhood of zero with the specified exponential speed according to prescribed performance bound technology. Finally, the simulation results validate that this control strategy achieves the control objectives, restrains the first and second pendulum angles, and ensures the transient performances of the system.