Analysis of the operation of the microprocessor control system of a bridge crane using optimum control laws

Abstract

This work presents the results of studies on the influence of the error of the main parameters of the bridge crane on the quality of optimal control. The quality of control refers to the exact positioning of the load at the stopping point and the magnitude of the final fluctuations of the load after the crane stops. The concept of optimal control is based on L.S. Pontryagin's maximum principle, which is when the goal is achieved by switching the acceleration-braking control of the load suspension point according to a specific algorithm. To achieve the maximum speed of operation of the crane, certain restrictions and conditions have been removed, namely, the refusal to eliminate load fluctuations during crane acceleration, which simplifies the subsequent elimination of load fluctuations during crane braking. However, this is an unnecessary waste of time, and therefore, acceleration is carried out at the maximum possible acceleration without eliminating load fluctuations. Of course, at the same time, significant fluctuations in the cargo occur, and they continue throughout the entire time the crane is moving. Moreover, the final goal is achieved only at the end of the cycle by switching the acceleration-deceleration modes - the cargo is delivered precisely to the specified point without fluctuations after the crane stops. A PC program that generates optimal control laws for a specific crane has been developed. This program can be used for any lifting machine where the suspension point moves in a straight line, and flexible load suspension is used, such as overhead or gantry cranes, hoists, etc. The results of the research were tested on several objects: a 0.5t crane, a 5t bridge grab crane, and models of bridge cranes. In each case, a good coincidence of theoretical and experimental results was observed, resulting in effective management of the object. The original microprocessor system implemented the optimal control laws, built first based on the MKP-1 microcontroller and then based on Arduino. However, a good result is guaranteed only if the fundamental parameters of the crane coincide with the theoretical ones. This is not easy to achieve during the actual operation of the crane. They vary within a specific range. The article examines how the error in each of the main parameters of the crane affects the result and how the control system can be improved to reduce the negative impact to a minimum. Keywords: optimal control, elimination of load fluctuations, accurate positioning, crane, microprocessor, reloading cycle