Robust synchronization of fractional-order unified chaotic systems via linear control

AbstractA new scheme for accomplishing synchronization between two fractional-order unified chaotic systems is proposed in this paper. The scheme does not require that the nonlinear dynamics of the synchronization error system must be eliminated. Moreover, the parameter of the systems does not have to be known. A controller is a linear feedback controller, which is simple in implementation. It is designed based on an LMI condition. The LMI condition guarantees that the synchronization between the slave system and the master system is achieved. Numerical simulations are performed to demonstrate the effectiveness of the proposed scheme

Time-varying sliding mode controller for heat exchanger with dragonfly algorithm

This article proposes the design of a sliding mode controller with a time-varying sliding surface for the plate heat exchanger. A time-varying sliding mode controller (TVSMC) combines the benefit of the control system’s robustness and convergence rate. Using Lyapunov stability theory, the stability of the designed controller is proved. In addition, the controller parameters of the designed controller are specified optimally via the dragonfly algorithm (DA). The input constraint’s effect is considered in the controller design process by applying the concept of the auxiliary system. The bounded disturbances are applied to investigate the robustness of the proposed techniques. Moreover, the quasi-sliding mode controller (QSMC) is developed as a benchmark to evaluate the convergence behavior of the proposed TVSMC technique. The simulation results demonstrate the proposed TVSMC with the optimal parameters provided by the DA algorithm (TVSMC+DA) can regulate the temperature to the desired level under bounded disturbances. When compared to the QSMC method, the TVSMC+DA performs significantly faster convergence speed and greater reduction in chattering occurrence. The results clearly indicate that the proposed controller can enhance convergence properties while being robust to disturbances

Control of shimmy vibration in aircraft landing gears based on tensor product model transformation and twisting sliding mode algorithm

Shimmy vibration is a common phenomenon in landing gear systems during either the take-off or landing of aircrafts. The shimmy vibration is undesirable since it can damage the landing gear and discomforts the pilots and passengers. In this work, tensor product model transformation (TPMT) and twisting sliding mode algorithm (TSMA) are utilized to design a robust controller for suppression of the shimmy vibration. The design has two steps. First, the TPMT is applied to determine the first part of the controller to suppress the vibration of the undisturbed system. After that, the TSMA is adopted to obtain another part of the controller to eliminate the remaining vibration caused by disturbances. By integrating these two parts, the proposed controller is obtained. Simulation studies are provided to demonstrate the effectiveness of the controller

Adaptive Vibration Control of Piezoactuated Euler-Bernoulli Beams Using Infinite-Dimensional Lyapunov Method and High-Order Sliding-Mode Differentiation

This paper presents an adaptive control scheme to suppress vibration of flexible beams using a collocated piezoelectric actuatorsensor configuration. A governing equation of the beams is modelled by a partial differential equation based on Euler-Bernoulli theory. Thus, the beams are infinite-dimensional systems. Whereas conventional control design techniques for infinite-dimensional systems make use of approximated finite-dimensional models, the present adaptive control law is derived based on the infinitedimensional Lyapunov method, without using any approximated finite-dimension model. Thus, the stability of the control system is guaranteed for all vibration modes. The implementation of the control law requires a derivative of the sensor output for feedback. A high-order sliding mode differentiation technique is used to estimate the derivative. The technique features robust exact differentiation with finite-time convergence. Numerical simulation and experimental results illustrate the effectiveness of the controller