Adaptive type-2 neural fuzzy sliding mode control of a class of nonlinear systems
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ORIGINAL PAPER
Adaptive type-2 neural fuzzy sliding mode control of a class of nonlinear systems Muhammad Umair Khan
· Tolgay Kara
Received: 31 January 2020 / Accepted: 3 August 2020 © Springer Nature B.V. 2020
Abstract The objective of this study is to design an optimal control scheme for the control of a class of nonlinear flexible multi-body systems with extremely coupled dynamics and infinite dimensions. The assumed mode method (AMM) acquires a finite-dimensional model, but there are uncertainties in the truncated model that make the system a difficult control problem. The proposed control scheme is a hybrid of the sliding mode control (SMC) and the type-2 neural fuzzy system (NFS). A new modified conjugate gradient (CG) algorithm is used to optimize the NFS parameters. The control law of the proposed control scheme requires the estimation of the uncertain system functions, which is provided by the NFS. Moreover, NFS plays an essential role in avoiding the chattering phenomenon commonly observed in conventional SMC. The control scheme stability is assured by the Lyapunov stability theorem. Various other intelligent control schemes have also been tested to make a comparison with the proposed control scheme. The simulation results evidently indicate that the proposed control scheme has enhanced tracking efficiency while managing the inherent deflections of the system and is therefore concluded as a reliM. U. Khan (B) · T. Kara Department of Electrical and Electronics Engineering, Faculty of Engineering, Gaziantep University, Gaziantep, Turkey e-mail: [email protected] T. Kara e-mail: [email protected]
able control technique for the nonlinear, flexible multibody class of systems. Keywords Sliding mode control · Neural fuzzy systems · Assumed mode method · Flexible manipulator · Conjugate gradient · Steepest descent
1 Introduction Many physical systems have a high level of uncertainty and nonlinearity, making it difficult to control them. This has led to considerable efforts by researchers in recent years to improve the behavior of nonlinear systems by designing appropriate nonlinear control schemes [1–3]. The vast amount of uncertainty in some nonlinear systems complicates the development of an accurate mathematical model for such systems. This motivates the need for control schemes that are robust against uncertainties. SMC introduced by Utkin is preferred in the literature because of its simplicity, better disturbance rejection, and robustness against parameter uncertainties [4]. The desired tracking of the trajectory is achieved in two phases in the SMC: the approaching phase during which the system states are controlled to approach the predefined sliding surface, and the sliding phase in which the trajectories reside on the sliding surface. Conventional SMC has the drawback that the control requires infinite switching to maintain the dynamics of the system on the sliding surface. This phe-
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nomenon known as chattering is more likely in practical implementations due t
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