nonlinear controller
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Abstract This paper proposes an active modal vibration control method based on a modal sliding mode controller applied to a smart material composite structure with integrated piezoelectric transducers as actuators and sensors. First, the electromechanical coupled system is identified using a modal reduced-order model. The sliding surface is based on the modal-filtered states and designed using a general formulation allowing the control of multiple vibration modes with multiple piezoelectric sensors and actuators. The performance and stability of the nonlinear controller are addressed and confirmed with the experimental results on a composite smart spoiler-shaped structure. The nonlinear switching control signal, based on the modal-shaped sliding surface improves the performances of the linear part of the control while maintaining not only stability but also robustness. The attenuation level achieved on the target modes on all piezoelectric sensors starts from -14dB up to -22dB, illustrating the strong potential of nonlinear switching control methods in active vibration control.

In order to solve the problem that backstepping method cannot effectively guarantee the robust performance of the closed-loop system, a novel method of determining parameter is developed in this note. Based on the ship manoeuvring empirical knowledge and the closed-loop shaping theory, the derived parameters belong to a reduced robust group in the original stabilizing set. The uniformly asymptotic stability is achieved theoretically. The training vessel “Yulong” and the tanker “Daqing232” are selected as the plants in the simulation experiment. And the simulation results are presented to demonstrate the effectiveness of the proposed algorithm.

The authors have addressed an important topic that is needed for backstepping algorithm to guarantee the robust performance of the closed-loop system. A novel method of determining parameters was presented based on ship maneuvering empirical knowledge and closed-loop shaping theory, and theoretical proof had shown the uniformly asymptotic stability of an established nonlinear Nomoto model. However, the following important points are suggested for the improvement of this paper.

Abstract In this paper, the general decay projective synchronization of a class of memristive competitive neural networks with time delay is studied. Firstly, a nonlinear feedback controller is designed, which does not require any knowledge about the activation functions. Then, some new and applicable conditions dependent on the Lyapunov function and the inequality techniques are obtained to guarantee the general decay projective synchronization of the considered systems under the developed controller. Unlike other forms of synchronization, projective synchronization can improve communication security due to the scaling constant’s unpredictability. In addition, the polynomial synchronization, asymptotical synchronization, and exponential synchronization can be seen as the special cases of the general decay projective synchronization. Finally, a numerical example is given to demonstrate the effectiveness of the proposed control scheme.