Sliding Mode Based Decentralized Tracking Control of Underactuated Four-Body Systems

Abstract

In this paper, output tracking control of four-body systems with flexible links is considered, where only the first and last bodies are with actuators. The systems are mathematically modelled based on the Newton's second law, which is described as an interconnected system with two subsystems. Due to the mechanical wear and changes of the external environment, it is necessary to consider uncertainties in the systems which are assumed to be bounded by known functions. Based on sliding mode techniques, a decentralized control scheme is proposed such that the outputs of the controlled systems can track the desired signals uniformly ultimately. Using specific coordinate transformations, the considered systems are transformed to a new system with a special structure to facilitate the design of sliding surfaces and sliding mode controllers. A set of conditions is developed under which the designed decentralized controller drives the tracking errors onto the sliding surface and stay on the surface thereafter while the system states are bounded. For simulation purposes, the desired signals are selected as part of a hyperbolic function which is time-varying and in consistence with the real situations. Simulation demonstrates that the proposed control strategy is effective and feasible.

Sliding Mode-Based Distributed Trajectory Tracking Control of Four-body Train Systems

“…Therefore, this paper focuses on a distributed control approach using sliding mode techniques to tackle the speed tracking challenge of a fourbody train system where some extensions and improvements of the time-varying desired signals and unknown interconnections are explored. According to the prior works [14,15] , the train system is modelled as an interconnected system with unknown uncertainties and disturbances. Then, a sliding surface is synthesised based on the tracking and the Barbashin-Krasovskii theorem is introduced to guarantee the occurrence of a reaching phase and sliding motion with the proposed distributed control.…”

Decentralized discrete adaptive sliding mode control for interconnected nonlinear systems

“…The second phase consists of synthesizing a discontinuous control law that enforces and maintains the system states on the sliding surface. 2,3,22 Moreover, SMC is considered robust due to its insensitivity to system uncertainties, its ability to counteract disturbances, its robustness to modeling errors, its fast response and chattering suppression, and its performance in nonlinear and uncertain systems. These characteristics make SMC an attractive choice for control applications where robustness is essential.…”

“…2 In Ji et al, 3 a decentralized state feedback stabilization using SMC is developed for nonlinear interconnected systems. A decentralized SMC for underactuated four-body systems is given in Ding et al 22 However, all the proposed methods are developed in continuous time. As well, there are a limited number of research works dealing with discrete SMC for interconnected nonlinear systems described by Hammerstein nonlinear subsystems.…”