Experimental evaluation of the robustness of discrete sliding mode control versus linear quadratic control

Sliding mode control (SLM) uses a switching control action to direct a process along a user-specified path from an arbitrary initial state to the desired state. Researchers have developed continuous and discrete SLMs, namely CSLM and DSLM, as well as multi-input/multi-output (MIMO) versions. Proponents of SLM claim excellent robustness in that the controller is able to maintain good performance in the presence of unmodeled dynamics, model errors, and bounded disturbances. This paper evaluates experimentally the robustness of DSLM with respect to the more conventional linear-quadratic (LQ) controller as applied to the inverted pendulum apparatus. The original version of DSLM was modified to use a variable sliding gain methodology. This acted to eliminate high controller sensitivity to parameter tuning. To further improve the results, different weights were applied to each of the states. This combination of the two techniques is new in that by themselves, the state weights and the varying sliding gain were not able to produce satisfactory results. The results of the experimental study demonstrate that the performance of SLM improves considerably with the addition of state weights and a varying sliding gain methodology and that DSLM* is indeed more robust than the conventional LQ controller.