Transfer function of FBS-3A feedback broadband seismometer

FBS-3A feedback broadband seismometer has been widely utilized in observation networks up to now. Therefore, it is very important and practically meaningful for the application of this kind of sensor to fulfill some relative research work about its transfer function and for the analysis to the data recorded and the further development of the seismometer. In this paper, from the viewpoint of achieving its working principle, method of systematic analysis is applied to deduce the transfer functions, including both the transfer function for calibration and that for measurement. Moreover, on the basis of that, the distribution of its zeroes and poles in a complex frequency domain is analyzed, which provides a convincing evidence to simplify this seismometer system from a high-order one to a two-order one. And the emulation of the frequency characteristics of FBS-3A is presented in this paper. On the whole, the aim of this article is to do some theoretical work about the earthquake observation sensor, and also to introduce the method of making systematic analysis in a complex frequency domain to the research and the development of the seismometers.

Design of bounded feedback controls for linear dynamical systems by using common Lyapunov functions

For a linear dynamical system,we address the problem of devising a bounded feedback control,which brings the system to the origin in finite time.The construction is based on the notion of a common Lyapunov function.It is shown that the constructed control remains effective in the presence of small perturbations.

Transfer Function Model of Multirate Feedback Control Systems

Based on the suitably defined multivariable version of Kranc operators and the extended input and output vectors, the multirate sampling plant is transformed to a equivalent time invariant single rate one, then the transfer function model of the multivariable multirate sampling plant is obtained. By combining this plant model with the time invariant description of the multirate controller in terms of extended vectors, the closed loop transfer function model of the multirate feedback control system can be determinated. This transfer function model has a very simple structure, and can be used as a basis for the analysis and synthesis of the multirate sampling feedback control systems in the frequency domain.

Synchronizing spatiotemporal chaos in the coupled map lattices using nonlinear feedback functions

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Method of Designing Generators of Pseudorandom Sequences for Information Protection Based on Shift Register with Non-Linear Feedback Function

This paper proposes an efficient, high-tech method of construction of pseudorandom binary sequences generators with a repetition period 2n?for n-bit shift register with a nonlinear feedback function. The developed method is illustrated by constructing a nonlinear function feedback shift register. It is proved that the offered method requires the realization of a memory size proportional to n2?that allows making successful use of suitable generators for practical use on the shift register of the longer word.

Adaptive functional link network control of near-space vehicles with dynamical uncertainties

The control law design for a near-space hypersonic vehicle（NHV） is highly challenging due to its inherent nonlinearity,plant uncertainties and sensitivity to disturbances.This paper presents a novel functional link network（FLN） control method for an NHV with dynamical thrust and parameter uncertainties.The approach devises a new partially-feedback-functional-link-network（PFFLN） adaptive law and combines it with the nonlinear generalized predictive control（NGPC） algorithm.The PFFLN is employed for approximating uncertainties in flight.Its weights are online tuned based on Lyapunov stability theorem for the first time.The learning process does not need any offline training phase.Additionally,a robust controller with an adaptive gain is designed to offset the approximation error.Finally,simulation results show a satisfactory performance for the NHV attitude tracking,and also illustrate the controller＇s robustness.

Observer design and output feedback stabilization for linear singular time-delay systems with unknown inputs

The design of a functional observer and reduced-order observer with internal delay for linear singular timedelay systems with unknown inputs is discussed. The sufficient conditions of the existence of observers, which are normal linear time-delay systems, and the corresponding design steps are presented via linear matrix inequality（LMI）. Moreover, the observer-based feedback stabilizing controller is obtained. Three examples are given to show the effectiveness of the proposed methods.

State Feedback Sliding Mode Control without Chattering by Constructing Hurwitz Matrix for AUV Movement

This paper presents a new method to eliminate the chattering of state feedback sliding mode control （SMC） law for the mobile control of an autonomous underwater vehicle （AUV） which is nonlinear and suffers from unknown disturbances system. SMC is a well-known nonlinear system control algorithm for its anti-disturbances capability, while the chattering on switch surface is one stiff question. To dissipate the well-known chattering of SMC, the switching manifold is proposed by presetting a Hurwitz matrix which is deducted from the state feedback matrix. Meanwhile, the best switching surface is achieved by use of eigenvalues of the Hurwitz matrix. The state feedback control parameters are not only applied to control the states of AUV but also connected with coefficients of switching surface. The convergence of the proposed control law is verified by Lyapunov function and the robust character is validated by the Matlab platform of one AUV model.

The feedback control of fractional order unified chaotic system

This paper studies the stability of the fractional order unified chaotic system. On the unstable equilibrium points, the equivalent passivity＇＇ method is used to design the nonlinear controller. With the definition of fractional derivatives and integrals, the Lyapunov function is constructed by which it is proved that the controlled fractional order system is stable. With Laplace transform theory, the equivalent integer order state equation from the fractional order nonlinear system is obtained, and the system output can be solved. The simulation results validate the effectiveness of the theory.

State Feedback Control for a Class of Fractional Order Nonlinear Systems

Using the Lyapunov function method, this paper investigates the design of state feedback stabilization controllers for fractional order nonlinear systems in triangular form, and presents a number of new results. First, some new properties of Caputo fractional derivative are presented, and a sufficient condition of asymptotical stability for fractional order nonlinear systems is obtained based on the new properties. Then, by introducing appropriate transformations of coordinates, the problem of controller design is converted into the problem of finding some parameters, which can be certainly obtained by solving the Lyapunov equation and relevant matrix inequalities. Finally, based on the Lyapunov function method, state feedback stabilization controllers making the closed-loop system asymptotically stable are explicitly constructed. A simulation example is given to demonstrate the effectiveness of the proposed design procedure. © 2014 Chinese Association of Automation.

Robust Output Feedback Control for Fractional Order Nonlinear Systems with Time-varying Delays

Robust controller design problem is investigated for a class of fractional order nonlinear systems with time varying delays. Firstly, a reduced-order observer is designed. Then, an output feedback controller is designed. Both the designed observer and controller are independent of time delays. By choosing appropriate Lyapunov functions, we prove the designed controller can render the fractional order system asymptotically stable. A simulation example is given to verify the effectiveness of the proposed approach. © 2014 Chinese Association of Automation.

Time-Delayed Feedback Control in a Single-Mode Laser System

The effects of time-delayed feedback control in a single-mode laser system is investigated.Using the smalltime delay approximation,the analytic expression of the stationary probability distribution function of the laser field isobtained.The mean,normalized variance and skewness of the steady-state laser intensity are calculated.It is found thatthe time-delayed feedback control can suppress the intensity fluctuation of the laser system.The numerical simulationsare in good agreement with the approximate analytic results.

Modified Function Projective Synchronization of Complex Networks with Multiple Proportional Delays

This paper deals with the modified function projective synchronization problem for general complex networks with multiple proportional delays. With the existence of multiple proportional delays, an effective hybrid feedback control is designed to attain modified function projective synchronization of networks. Numerical example is provided to show the effectiveness of our result.

Stabilization of a class of discrete-time switched systems via observer-based output feedback

In this paper, observer-based static output feedback control problem for discrete-time uncertain switched systems is investigated under an arbitrary switching rule. The main method used in this note is combining switched Lyapunov function （SLF） method with Finsler＇s Lemma. Based on linear matrix inequality （LMI） a less conservative stability condition is established and this condition allows extra degree of freedom for stability analysis. Finally, a simulation example is given to illustrate the efficiency of the result.

Hybrid Predictive Control Based on High-Order Differential State Observers and Lyapunov Functions for Switched Nonlinear Systems

In this paper, a hybrid predictive controller is proposed for a class of uncertain switched nonlinear systems based on high-order differential state observers and Lyapunov functions. The main idea is to design an output feedback bounded controller and a predictive controller for each subsystem using high-order differential state observers and Lyapunov functions, to derive a suitable switched law to stabilize the closed-loop subsystem, and to provide an explicitly characterized set of initial conditions. For the whole switched system, based on the high-order differentiator, a suitable switched law is designed to ensure the whole closed-loop’s stability. The simulation results for a chemical process show the validity of the controller proposed in this paper.

Non-fragile Dynamic Output Feedback H∞Control for a Class of Un­certain Switched Systems with Time-varying Delay

The problem of non-fragile dynamic output feedback H∞control for a class of uncertain switched systems with time-varying delay is discussed.Firstly,the form of non-fragile dynamic output feedback H∞controller is given.Under the condition that the upper bound of time delay and the upper bound of delay derivative are limited simultaneously,Lyapunov functional and its corresponding switching rules are constructed by using single Lyapunov function method and convex combination technique;Secondly,we use the inequality lemma to scale the derived Lyapunov functional in order to eliminate the time-varying delay term in the in­equality,and then introduce the J-function to obtain a nonlinear matrix in­equality that satisfies the H∞performance indexγ,we also employ Schur complement lemma to transform the nonlinear matrix inequality into set of linear matrix inequalities consisting of two linear matrix inequalities,a sufficient condition for the existence of a non-fragile dynamic output feedback H∞controller and satisfying the H∞performance indexγis concluded for a class of uncertain switching systems with variable time delay;Finally,a switched system composed of two subsystems is consid­ered and the effectiveness and practicability of the theorem are illustrated by numerical simulation with LMI toolbox.

Time-delay identification for vibration systems with multiple feedback

An approach for time-delay identification is proposed in multiple-degree-of-freedom (MDOF) linear systems with multiple feedback. The applicability of the approach is discussed in detail. Based on the characteristics of frequency domain in feedback controlled system with multiple time-delays, this paper proposes a time-delay identification approach, which is based on the pseudo impedance function of reference point. Treating feedback time-delays as the 'frequencies' of the oscillation curve, the time-delays can be obtained from the 'frequencies' of the curve. Numerical simulation is conducted to validate the proposed approach. The application scope of the approach is discussed with regard to different forms of feedback.

The permanence and global attractivity of a competitive system with feedback controls and toxic substance

In this paper,we consider a nonautonomous competitive system with feedback controls and toxic substance.Some average couditions for the permanence and global attractivity of the system are obtained.It is shown that our results are generalization or improvement of those of Zhao,Jiang and Lazer [Nonlinear Analysis:Real World Applications,5(4)(2004),265-276],Xia,Cao,Zhang and Chen [Journal of Mathematical Analysis and Applications,294(2)(2004),503-522] and Chen [Nonlinear Analysis:Real World Applications,in press]