Abstract
In this paper, a novel adaptive neuro network nonsingular fast terminal sliding mode control based on barrier Lyapunov functions is proposed for flexible double-clamped beam systems with input saturation and distributed disturbance. First, the Galerkin projection method is employed to reduce the partial differential dynamic equations of the beam into ordinary differential equations. Second, a novel barrier Lyapunov function is employed to design a nonsingular fast terminal sliding mode controller that ensures the closed-loop system is stable with state constraints. In addition, an auxiliary system is proposed to guarantee the stability of the beam system subject to input saturation. Third, an adaptive neural network is used to deal with the possible unknown part of the model parameters. It is proved that the proposed control law can handle input saturation and state constraints simultaneously without knowing the model exactly. Finally, numerical simulations illustrate the effectiveness of the proposed control laws.
Highlights
With the rapid development of the aerospace industry, heavy spacecraft and aircraft have gained much attention in recent years
SIMULATION ANALYSIS Numerical simulations for the double-clamped beam actuated by a piezoelectric actuator with input saturation and unknown distributed disturbance are given to demonstrate the effectiveness of the barrier function-based nonsingular fast terminal sliding mode control law (BNFTSMC) (33) and adaptive neuro network barrier function based nonsingular fast terminal sliding mode control law (Adaptive NN BNFTSMC) (44)
In this paper, a vibration control problem arising in a flexible double-clamped beam system has been investigated. Both barrier function based nonsingular fast terminal sliding mode control and barrier function based adaptive NN nonsingular fast terminal sliding mode control have been developed for the double-clamped beam system
Summary
With the rapid development of the aerospace industry, heavy spacecraft and aircraft have gained much attention in recent years. S. Li et al.: Barrier Function-Based Adaptive Neuro Network Sliding Mode Vibration Control for Flexible Double-Clamped Beams differential equations (ODEs) form which effectively simplifies the mathematical model. Motivated by the aforementioned literature, a novel vibration control approach for the nonlinear double-clamped beam with a piezoelectric actuator is developed to deal with model uncertainties, input saturation, state constraints, and distributed disturbances simultaneously. The proposed control laws guarantee the system state variables convergence in finite-time and improve the performance of vibration suppression in the nonlinear double-clamped beam system. 2) The proposed fast nonsingular terminal sliding mode control laws achieves the stability of nonlinear doubleclamped beam system within finite-time. 4) The barrier fast nonsingular sliding mode control law based on the adaptive RBF neural network is developed to approximate the unknown nonlinear part of the system model which is significant for the applications. For a matrix A ∈ Rn×n, A 1 denotes the maximum absolute column sum norm. (·)
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