Robust Control of Mechanical Systems: an Experimental Study

Abstract

Two adaptive control schemes for nonlinear mechanical systems, proposed by Slotine and Li [1, 2] and Kelly [3], are investigated, with emphasis on robustness for unmodeled dynamics. The investigation is performed along the following lines, • select a system for testing the controllers, it must be possible to change the dynamics of this system easily, • design and tune the control schemes for the system without unmodeled dynamics, • evaluate the tracking performance of the control schemes for the system with unmodeled dynamics. The system used for designing and tuning the controllers is a two degrees of freedom manipulator, a XY-table, with two prismatic joints. The control task is to follow a periodic trajectory, e.g., a circle. Both adaptive control schemes are based on a model, of which the parameters are adapted, and a feedback component, including PD action, for the remaining tracking error. A pure PD control is used for reference. All three control schemes can use friction compensation. The design parameters for the PD component of the controllers are used to get specific eigen frequencies and damping parameters for a closed loop linear design model. The design parameters for the adaptation are chosen such that the adaptation is fast, without increasing the bandwidth of the closed loop model. Finally, the design parameters are tuned by test runs to get good tracking behavior. The system used for robustness evaluation is again the XY- table, which was also used for the design and tuning of the controllers. It is possible to change the stiffness of the spindle of the XY-table and make the link “stiff” or “flexible”. We design and tune the control schemes when the link is stiff, and next assess the robustness if the link is flexible. The experimental results suggest that there are no advantages in using one of the adaptive control schemes, instead of PD control, from a robustness viewpoint. The tracking error achieved with the adaptive control schemes is, however, much smaller. There is also some difference between the two adaptive schemes. The scheme of Kelly seems more robust and has also a slightly better tracking performance.