Abstract
In this paper, a generalized regular form is proposed to facilitate sliding mode control (SMC) design for a class of nonlinear systems. A novel nonlinear sliding surface is designed using implicit function theory such that the resulting sliding motion is globally asymptotically stable. Sliding mode controllers are proposed to drive the system to the sliding surface and maintain a sliding motion thereafter. Tracking control of a two-wheeled mobile robot is considered to underpin the developed theoretical results. Model-based tracking control of a wheeled mobile robot is first transferred to a stabilization problem for the corresponding tracking error system, and then the developed theoretical results are applied to show that the tracking error system is globally asymptotically stable even in the presence of matched and mismatched uncertainties. Both experimental and simulation results demonstrate that the developed results are practicable and effective.
Highlights
Sliding mode control (SMC) is a powerful technique because of its fast convergence and strong robustness [1], [2]
Such an effect can be included in the system uncertainty which can be overcome by redesign of the sliding mode control if necessary
The control performance of the motors may be affected by parameter variations, the uncertainties caused by friction between the wheels and ground in the motor system will not affect the performance of the wheeled mobile robot (WMR) system since the SMC is robust to uncertainties implicit in the input channel
Summary
Sliding mode control (SMC) is a powerful technique because of its fast convergence and strong robustness [1], [2]. It is not necessary to satisfy Brockett’s well known necessary condition [20] if the reference trajectory does not involve stabilisation to a rest configuration [21], it is challenging to use PID control or linear control methods to obtain desired tracking performance for WMR systems because of the inherent nonlinearity caused by the nonholonomic constraints. In [26], sliding mode techniques were applied to a WMR system using a feedback linearisation approach and results have been obtained for the tracking control problem and for regulation tasks This requires that the propulsive force of the WMR can be measured as one of the states in the system so that the strict relative degree condition required for feedback linearisation can be satisfied. Experimental and simulation results on the WMR show that the proposed controller is insensitive to matched uncertainties, and can tolerate a certain level of mismatched uncertainties in both theory and application
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