Design of control for load movement by overhead crane
Problem of a load movement is discussed where the load is attached like a pendulum to cart and an external force can push the cart along horizontal direction. Such problem is related with the huge set of mechanical systems, for example, overhead crane control operation, suppression of pendulum oscillations by the horizontal movement of the cart, etc. The following problems are discussed in the paper such as mathematical model of pendulum on the cart, control problem statement, and controller design methodology for providing movement of the load in the desired position and suppressing load oscillations simultaneously. Cascaded control system structure is proposed where modified proportional-integral-derivative controllers without ideal differentiation are used. Controller parameters are selected such that two-time-scale motions are artificially induced in the closed-loop system where the damping of fast transients yields the desired slow-motion behavior in accordance with prescribed performance specifications. Analysis of the closed-loop system properties is provided via method of time-scale separation. Numerical simulation is provided based on MatLab/Simulink Tools. Set of simulations are provided under wide range variations of lading weight and length of pendulum. From simulation results follow that the desired behavior of transients in the closed-loop system is provided in spite of lading weight and length of pendulum variations. The proposed controller design methodology can be applied of other examples of underactuated mechanical systems as well.