A new hyperchaotic system and its linear feedback control

This paper reports a new hyperchaotic system by adding an additional state variable into a three-dimensional chaotic dynamical system, studies some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov exponents, bifurcation diagram and the hyperchaotic attractor evolving into periodic, quasi-periodic dynamical behaviours by varying parameter k. Furthermore, effective linear feedback control method is used to suppress hyperchaos to unstable equilibrium, periodic orbits and quasi-periodic orbits. Numerical simulations are presented to show these results.

Control and Stabilization of Chaotic System Based on Linear Feedback Control Method

In this paper, two kinds of chaotic systems are controlled respectively with and without time-delay to eliminate their chaotic behaviors. First of all, according to the first-order approximation method and the stabilization condition of the linear system, one linear feedback controller is structured to control the chaotic system without time-delay, its chaotic behavior is eliminated and stabilized to its equilibrium. After that, based on the first-order approximation method, the Lyapunov stability theorem, and the matrix inequality theory, the other linear feedback controller is structured to control the chaotic system with time-delay and make it stabilized at its equilibrium. Finally, two numerical examples are given to illustrate the correctness and effectiveness of the two linear feedback controllers.

Decoupled nonsingular terminal sliding mode control for affine nonlinear systems

A decoupled nonsingular terminal sliding mode control（DNTSMC） approach is proposed to address the tracking control problem of affine nonlinear systems.A nonsingular terminal sliding mode control（NTSMC） method is presented,in which the nonsingular terminal sliding surface is defined as a special nonsingular terminal function and the convergence time of the system states can be specified.The affine nonlinear system is firstly decoupled into linear subsystems via feedback linearization.Then,a nonsingular terminal sliding surface is defined and the NTSMC method is applied to each subsystem separately to ensure the finite time convergence of the closed-loop system.The verification example is given to demonstrate the effectiveness and robustness of the proposed approach.The proposed approach exhibits a considerable advantage in terms of faster tracking error convergence and less chattering compared with the conventional sliding mode control（CSMC）.

Linear-control-based synchronization of coexisting attractor networks with time delays

This paper introduces the concept of linear-control-based synchronization of coexisting attractor networks with time delays. Within the new framework, closed loop control for each dynamic node is realized through linear state feedback around its own arena in a decentralized way, where the feedback matrix is determined through consideration of the coordination of the node dynamics, the inner connected matrix and the outer connected matrix. Unlike previously existing results, the feedback gain matrix here is decoupled from the inner matrix; this not only guarantees the flexible choice of the gain matrix, hut also leaves much space for inner matrix configuration. Synchronization of coexisting attractor networks with time delays is made possible in virtue of local interaction, which works in a distributed way between individual neighbours, and the linear feedback control for each node. Provided that the network is connected and balanced, synchronization will come true naturally, where theoretical proof is given via a Lyapunov function. For completeness, several illustrative examples are presented to further elucidate the novelty and efficacy of the proposed scheme.

A Suitable Active Control for Suppression the Vibrations of a Cantilever Beam

In our consideration,a comparison between four different types of controllers for suppression the vibrations of the cantilever beam excited by an external force is carried out.Those four types are the linear velocity feedback control,the cubic velocity feedback control,the non-linear saturation controller(NSC)and the positive position feedback(PPF)controller.The suitable type is the PPF controller for suppression the vibrations of the cantilever beam.The approximate solution obtained up to the first approximation by using the multiple scale method.The PPF controller effectiveness is studied on the system.We used frequency-response equations to investigate the stability of a cantilever beam.We notified that,there is a good agreement between the analytical solution and the numerical solution.

Control of magnetic levitation positioning stage with an eddy current damper

To enhance the system damping,a permanent magnet set which served as an eddy current damper was added to the magnetic levitation positioning stage which consists of a moving table,four Halbach permanent magnetic arrays,four stators and displacement sensors.The dynamics model of this stage was a complex nonlinear,strong coupling system which made the control strategy to be a focus research.The nonlinear controller of the system was proposed based on the theory of differential geometry.Both simulation and experimental results show that either the decoupling control of the movement can be realized in horizontal and vertical directions,and the control performance was improved by the damper,verifying the validity and efficiency of this method.

Stabilization of Nonuniform Euler-Bernoulli Beam with Locally Distributed Feedbacks

In this article, we study the stabilization problem of a nonuniform Euler-Bernoulli beam with locally distributed feedbacks. Firstly, using the semi-group theory, we establish the well-posedness of the associated closed loop system. Then by proving the uniqueness of the solution of a related ordinary differential equations, we derive the asymptotic stability of the closed loop system. Finally, by means of the piecewise frequency domain multiplier method, we prove that the corresponding closed loop system can be exponentially stabilized by only one of the two distributed feedback controls proposed in this paper.

A novel integrated self-powered brake system for more electric aircraft

Traditional hydraulic brake systems require a complex system of pipelines between an aircraft engine driven pump（EDP） and brake actuators, which increases the weight of the aircraft and may even cause serious vibration and leakage problems. In order to improve the reliability and safety of more electric aircraft（MEA）, this paper proposes a new integrated self-powered brake system（ISBS） for MEA. It uses a hydraulic pump geared to the main wheel to recover a small part of the kinetic energy of a landing aircraft. The recovered energy then serves as the hydraulic power supply for brake actuators. It does not require additional hydraulic source, thus removing the pipelines between an EDP and brake actuators. In addition, its self-powered characteristic makes it possible to brake as usual even in an emergency situation when the airborne power is lost. This paper introduces the working principle of the ISBS and presents a prototype. The mathematical models of a taxiing aircraft and the ISBS are established. A feedback linearization control algorithm is designed to fulfill the anti-skid control. Simulations are carried out to verify the feasibility of the ISBS, and experiments are conducted on a ground inertia brake test bench. The ISBS presents a good performance and provides a new potential solution in the field of brake systems for MEA.

Robust Control for Static Loading of Electro-hydraulic Load Simulator with Friction Compensation

Load simulator is a key test equipment for aircraft actuation systems in hardware-in-the-loop-simulation. Static loading is an essential function of the load simulator and widely used in the static/dynamic stiffness test of aircraft actuation systems. The tracking performance of the static loading is studied in this paper. Firstly, the nonlinear mathematical models of the hydraulic load simulator are derived, and the feedback linearization method is employed to construct a feed-forward controller to improve the force tracking performance. Considering the effect of the friction, a LuGre model based friction compensation is synthesized, in which the unmeasurable state is estimated by a dual state observer via a controlled learning mechanism to guarantee that the estimation is bounded. The modeling errors are attenuated by a well-designed robust controller with a control accuracy measured by a design parameter. Employing the dual state observer is to capture the different effects of the unmeasured state and hence can improve the friction compensation accuracy. The tracking performance is summarized by a derived theorem. Experimental results are also obtained to verify the high performance nature of the proposed control strategy.

OPTIMAL INVERSE LQG CONTROL FOR CERTAIN ODE AND PDE STATIONARY PROCESSES

Following work carried out earlier on linear-quadratic optimal control for linear finitedimensional stationary systems we report,in this article,on extension of some of those results to certaininfinite dimensional systems;in particular a class of PDE systems of elliptic type.These systems arestudied in the now familiar framework developed by J.L.Lions and E.Magenes,specialized to asubclass of such systems important in a variety of applications.As an extended example this paperstudies an optimal redistribution problem in a groundwater flow system governed by Darcy's equation,presenting both analytic and computational work related to such problems.