Performance Evaluation of the Optimal Control of a Gantry Crane

For a gantry crane, optimal control of the crane motion requires that the speed of the cart be maximized, and the swing of the hanging payload be minimized. The problem lends itself naturally to optimal linear quadratic (LQ) controllers. This paper examines the performance of four different approaches to the design of an LQ controller, including two optimization approaches as based on: 1) minimal energy of cart and payload and 2) integrated absolute error of payload angle. Both simulation and experimental results are presented. A demonstration is also given as to how the results taken from laboratory scale gantry crane experiments must be treated with caution. Laboratory based studies have generally worked with systems where the moving cart mass is much larger than the suspended payload mass. In the case of industrial scale gantry cranes, the reverse can be true. This has implications with respective to the robustness of the controller. In the case where the cart mass is much greater than the payload mass, the effect of the payload on the cart is correctly neglected. However, there are stability implications if this is not the case. The implications with respect to the tuning of LQ controllers for this application are discussed.