On a new adaptive sliding mode control for MIMO nonlinear systems with uncertainties of unknown bounds

Abstract

This paper proposes a new approach of adaptive sliding mode controller designs for multiple-input multipleoutput nonlinear systems with uncertainties of unknown bounds and limited available inputs. The goal is to obtain robust, smooth, and fast transient performance for real sliding mode control so that the phenomena of the slow response and the gain overestimation in most adaptive sliding mode controller designs can be greatly improved. We introduce an Integral/Exponential adaptation law with boundary-layer targeting the reduction of the chatter levels of the sliding mode by significantly reducing the gain overestimation while simultaneously speeding up the system response to the uncertainties. The gain is further reduced when the system state is in the boundary layer. The simulation and experimental results demonstrate the proposed design.NEW ADAPTIVE SLIDING MODE CONTROL FOR NL UNC SYSTEMS 943 the sliding surface is also suggested in some papers [8,12,13,15]. In [8], a low-pass filter is adopted to tune the switching gain in the control and allow a decrease in the switching gain once the sliding mode is established. Therefore, the adaptation law does not overestimate the magnitude of the perturbations, and the gain does not go to infinite. However, it still requires knowledge of the bounds of perturbations, and the use of a low-pass filter introduces a time delay which affects the transient phenomenon. Recently,in [12,13,15], a boundary layer scheme neighboring the sliding surface in switching-gain dynamics was proposed so that the switching gain is gradually reduced when it is inside the boundary layer. These boundary-layer ASMC designs do not require a priori knowledge of the bounds of perturbations. However, the system response to perturbations is relatively slow; the overshoot is relatively large; and the chattering level is relatively high.Generally speaking, most ASMC adaptation processes consist of two phases: compensating phase where the switching gain increases its value until it completely compensates for the perturbations and the sliding variable reaches its maximum value, and the reaching phase where the sliding variable converges to the sliding surface (or to its immediate vicinity) [6,16]. Thus, the overall reaching time includes a compensating time and a converging time. On the one hand, in most existing ASMC designs, the system response to perturbations is relatively slow. In particular, the overshoot due to the perturbations is relatively large and the compensating time is relatively long. On the other hand, the overestimation of the control gain still exists, particularly, at the moment when the sliding variable reaches the sliding manifold. Even the switching gain will gradually decrease its value after reaching phase, the large switching gain at the reaching phase still creates large magnitude of chattering proportional to the magnitude of the switching gain [17]. Targeting to overcome the earlier two problems, the proposed algorithm significantly reduces the magnitude of the switching gain...

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