Model reference command shaping for control of a multimode double-pendulum overhead crane

Abstract

Cranes with double-pendulum dynamics are extensively used in industrial applications to transport massive or hazardous materials from one location to another. In such situations, the hook and payload generate significant oscillations during fast transportation with different modes of frequency. The crane control challenge increases under payload hoisting and payload mass variations as the system’s natural frequency and damping ratio change during these conditions. Most existing feedforward approaches need measurements of system’s parameters for controller design. This thesis proposes a new Model Reference Command Shaping (MRCS) based on a reference model for a multimode Double-Pendulum Overhead Crane (DPOC). This technique avoids the need for measurement or estimation of system’s frequency and damping ratio in contrast to the existing input and command shaping approaches. Several formulations are used to find the shaper’s numerator to ensure an exact cancellation of system poles that significantly contributes to the reduction of hook and payload oscillations. As the MRCS design involves complicated procedures and mathematical formulations, a simpler MRCS approach using the Particle Swarm Optimization (PSO) algorithm namely MRCS-PSO is subsequently designed. Furthermore, in an attempt to achieve the objectives of precise trolley positioning with minimal hook and payload oscillations of DPOC, a hybrid control structure of MRCS and Proportional-Integral-Derivative (PID) feedback control called MRCS+PID is proposed and implemented. The hybrid controller is designed such that all the control parameters can be tuned concurrently to ensure optimal responses of both objectives. Simulations using a nonlinear DPOC model and experiments on a laboratory DPOC are carried out to investigate the effectiveness and robustness of the proposed controllers. In all investigations, crane operating conditions under payload hoisting and payload mass variations which pose difficult crane control are considered. Performance assessments of the controllers are performed based on the maximum and overall oscillations of the hook and payload, together with the speed and final position of the trolley response. The simulation and experimental results demonstrate a higher robustness of MRCS as compared to the established multimode Zero Vibration and Zero Vibration Derivative input shapers designed with the average travel length technique. The MRCS achieved 21.1% and 1.2% reductions in the overall hook oscillations, as well as 27.1% and 9.2% in the overall payload oscillations respectively. The advantage of the MRCS-PSO approach is confirmed by achieving a near exact pole-zero cancellation that provides almost a similar performance in the oscillation reductions when compared to the MRCS approach. For the hybrid controller, experimental results show that the MRCS+PID control design enables the trolley to move with a smoother response and it is 15.9% faster than the PID+PID feedback control. Moreover, the MRCS+PID control is found to be superior with reductions of the maximum and overall payload oscillations by 36.6% and 83.8% respectively. It is envisaged that the MRCS and the hybrid MRCS with a feedback controller can be utilized for efficient oscillation and vibration control of various multimode systems.