THE STUDY ON A KIND OF CONTROL SYSTEM WITH NONLINEAR PARABOLIC DISTRIBUTED PARAMETERS

The modelling of one kind of nonlinear parabolic distributed parameter control system with moving boundary, which had extensive applications was presented, Two methods were used to investigate the basic characteristics of the system: I) transforming the system it? the variable domain into that in the fixed domain; 2) transforming the distributed parameter system into the lumped parameter system. It is found that there are two critical values for the control variable : the larger one determines whether or not the boundary would move, while the smaller one determines whether or not the boundary, would atop automatically. For one-dimensional system of planar, cylindrical and spherical cases the definite solution problem can be expressed as a unified form. By means of the computer simulation the open-loop control system and close-cycle feedback control system have been investigated. Numerical results agree well with theoretical results. The computer simulation shows that the system is well posed, stable, measurable and controllable.

Harmonic Amplification Analysis of Cable Lines with Distributed Parameters Based on Kalman Filter and Convolution Inversion

Harmonic amplification phenomena could appear at the point of common connection(PCC) of the cable line terminal. However, the distributed parameter model of the cable line contains hyperbolic functions with plural variables, which makes it challenging to obtain the harmonic amplification factor(HAF). Hence, a time-domain method combining the Kalman filter and convolution inversion(KFCI) methods is proposed to address this problem. First, the Kalman filter method optimizes the square wave pulse response(SWPR) with measurement error. Then, the optimized SWPR data are used to get the HAF by the convolution inversion method. Next, the harmonic amplification characteristics of cable lines are explored. Finally, an experimental simulation model is built on the PSCAD software, verifying the optimization effectiveness of Kalman filter for the SWPR with error and the accuracy of the HAF calculated by the proposed method. The analysis rationality of harmonic amplification properties is also demonstrated.

Observer-based dynamic event-triggered control for distributed parameter systems over mobile sensor-plus-actuator networks

We develop a policy of observer-based dynamic event-triggered state feedback control for distributed parameter systems over a mobile sensor-plus-actuator network.It is assumed that the mobile sensing devices that provide spatially averaged state measurements can be used to improve state estimation in the network.For the purpose of decreasing the update frequency of controller and unnecessary sampled data transmission, an efficient dynamic event-triggered control policy is constructed.In an event-triggered system, when an error signal exceeds a specified time-varying threshold, it indicates the occurrence of a typical event.The global asymptotic stability of the event-triggered closed-loop system and the boundedness of the minimum inter-event time can be guaranteed.Based on the linear quadratic optimal regulator, the actuator selects the optimal displacement only when an event occurs.A simulation example is finally used to verify that the effectiveness of such a control strategy can enhance the system performance.

Stabilization of stochastic Hopfield neural network with distributed parameters

In this paper, the stability of stochastic Hopfield neural network with distributed parameters is studied. To discuss the stability of systems, the main idea is to integrate the solution to systems in the space variable. Then, the integration is considered as the solution process of corresponding neural networks described by stochastic ordinary differential equations. A Lyapunov function is constructed and Ito formula is employed to compute the derivative of the mean Lyapunov function along the systems, with respect to the space variable. It is difficult to treat stochastic systems with distributed parameters since there is no corresponding Ito formula for this kind of system. Our method can overcome this difficulty. Till now, the research of stability and stabilization of stochastic neural networks with distributed parameters has not been considered.

Mathematical modeling of an armature assembly in pilot stage of a hydraulic servo valve based on distributed parameters

The dynamic performance of a nozzle-flapper servo valve can be affected by several factors such as the disturbance of the input signal,the motion of the armature assembly and the oscillation of the jet force.As the part of vibrating at high frequency,the armature assembly plays a vital role during the operation of the servo valve.In order to accurately predict the transient response of the armature assembly during the vibration,a mathematical model of armature assembly is established based on the distributed parameters method(DPM)and Hamilton principle.The new mathematical model is composed of three main parts,the modal eigenfunction,modal mechanical response expressions of the spring tube and the motion equation of the other armature assembly.After programing,the purpose of using the DPM to predict the dynamic response of different positions located on the armature assembly is achieved.For verifying the validity of the mathematical model,the finite element method(FEM)and classic model(CM)of armature assembly are applicated by commercial software under the same condition.The comparison results prove that the DPM can effectively predict the axial and tangential deflection of the armature assembly different positions which the CM can’t duing to its over-simplification.A certain error is generated when predicting the axial deformation at different heights by DPM,which is caused by an approximate method to simulate the torsion of the spring tube.The comparison results of the spring tube deflection at different vibration frequencies shows that the adaptability of DPM is significantly higher than the classic model,which verify the model is more adaptable for predicting the dynamic response of the armature assembly.

Extraction of distributed parameters for multi-conductor transmission lines by the difference iteration method

The distributed parameters of the transmission lines have the significant impact to the signal propagation. In the conventional method of the distributed parameter extraction,the discontinuity of inverse trigonometric or hyperbolic can arise the problem about phase ambiguity which causes significant errors for transmission models. A difference iteration method（ DIM） is proposed for extracting distributed parameters of high frequency transmission line structure in order to overcome the phase ambiguity in the conventional method（ CM）. The formulations of the proposed method are first derived for two-conductor and multi-conductor lines. Then the validation is performed for the models of micro-strip transmission line. Numerical results demonstrate that the proposed DIM can solve the problem about the phase ambiguity and the extracted distributed parameters are accurate and efficient for a wide range of the frequencies of interest and line lengths.

Working Condition Real-Time Monitoring Model of Lithium Ion Batteries Based on Distributed Parameter System and Single Particle Model

Lithium ion batteries are complicated distributed parameter systems that can be described preferably by partial differential equations and a field theory. To reduce the solution difficulty and the calculation amount, if a distributed parameter system is described by ordinary differential equations （ODE） during the analysis and the design of distributed parameter system, the reliability of the system description will be reduced, and the systemic errors will be introduced. Studies on working condition real-time monitoring can improve the security because the rechargeable LIBs are widely used in many electronic systems and electromechanical equipment. Single particle model （SPM） is the simplification of LIB under some approximations, and can estimate the working parameters of a LIB at the faster simulation speed. A LIB modelling algorithm based on PDEs and SPM is proposed to monitor the working condition of LIBs in real time. Although the lithium ion concentration is an unmeasurable distributed parameter in the anode of LIB, the working condition monitoring model can track the real time lithium ion concentration in the anode of LIB, and calculate the residual which is the difference between the ideal data and the measured data. A fault alarm can be triggered when the residual is beyond the preset threshold. A simulation example verifies that the effectiveness and the accuracy of the working condition real-time monitoring model of LIB based on PDEs and SPM.

Reliability-based Robust Optimization Design of Automobile Components with Non-normal Distribution Parameters

In the reliability designing procedure of the vehicle components, when the distribution styles of the random variables are unknown or non-normal distribution, the result evaluated contains great error or even is wrong if the reliability value R is larger than 1 by using the existent method, in which case the formula is necessary to be revised. This is obviously inconvenient for programming. Combining reliability-based optimization theory, robust designing method and reliability based sensitivity analysis, a new method for reliability robust designing is proposed. Therefore the influence level of the designing parameters’ changing to the reliability of vehicle components can be obtained. The reliability sensitivity with respect to design parameters is viewed as a sub-objective function in the multi-objective optimization problem satisfying reliability constraints. Given the first four moments of basic random variables, a fourth-moment technique and the proposed optimization procedure can obtain reliability-based robust design of automobile components with non-normal distribution parameters accurately and quickly. By using the proposed method, the distribution style of the random parameters is relaxed. Therefore it is much closer to the actual reliability problems. The numerical examples indicate the following: (1) The reliability value obtained by the robust method proposed increases (】0.04%) comparing to the value obtained by the ordinary optimization algorithm; (2) The absolute value of reliability-based sensitivity decreases (】0.01%), and the robustness of the products’ quality is improved accordingly. Utilizing the reliability-based optimization and robust design method in the reliability designing procedure reduces the manufacture cost and provides the theoretical basis for the reliability and robust design of the vehicle components.

Distributed Secondary Control and Optimal Power Sharing in Microgrids

We address the control problem of microgrids and present a fully distributed control system which consists of primary controller, secondary controller, and optimal active power sharing controller. Different from the existing control structure in microgrids, all these controllers are implemented as local controllers at each distributed generator. Thus, the requirement for a central controller is obviated. The performance analysis of the proposed control systems is provided, and the finite-time convergence properties for distributed secondary frequency and voltage controllers are achieved. Moreover, the distributed control system possesses the optimal active power sharing property. In the end, a microgrid test system is investigated to validate the effectiveness of the proposed control strategies. © 2014 Chinese Association of Automation.

Exponential stabilization of distributed parameter switched systems under dwell time constraints

The exponential stabilization problem for finite dimensional switched systems is extended to the infinite dimensional distributed parameter systems in the Hilbert space. Based on the semigroup theory, by applying the multiple Lyapunov function method, the exponential stabilization conditions are derived. These conditions are given in the form of linear operator inequalities where the decision variables are operators in the Hilbert space; while the stabilization properties depend on the switching rule. Being applied to the two-dimensional heat switched propagation equations with the Dirichlet boundary conditions, these linear operator inequalities are transformed into standard linear matrix inequalities. Finally, two examples are given to illustrate the effectiveness of the proposed results.

SLIDING MODE CONTROL OF A CLASS OF ITO TYPE DISTRIBUTED PARAMETER SYSTEMS WITH DELAY

Sliding mode control problem of a class of Ito^ type partial differential equations with delay is probed. The variable structure controller is designed. The existence of motion of sliding mode is shown. And the character of invariance of sliding control system about uncertainty on the sliding switching surface and stability are analyzed.

Improved control of distributed parameter systems using wireless sensor and actuator networks:An observer-based method

In this paper,the control problem of distributed parameter systems is investigated by using wireless sensor and actuator networks with the observer-based method.Firstly,a centralized observer which makes use of the measurement information provided by the fixed sensors is designed to estimate the distributed parameter systems.The mobile agents,each of which is affixed with a controller and an actuator,can provide the observer-based control for the target systems.By using Lyapunov stability arguments,the stability for the estimation error system and distributed parameter control system is proved,meanwhile a guidance scheme for each mobile actuator is provided to improve the control performance.A numerical example is finally used to demonstrate the effectiveness and the advantages of the proposed approaches.

One high-efficiency analysis method for high-speed circuit networks containing distributed parameter elements

In the field of high-speed circuits, the analysis of mixed circuit networks containing both distributed parameter elements and lumped parameter elements becomes ever important. This paper presents a new method for analyzing mixed circuit networks. It adds transmission line end currents to the circuit variables of the classical modified nodal approach and can be applied directly to the mixed circuit networks. We also introduce a frequency-domain technique without requiring decoupling for multiconductor transmission lines. The two methods are combined together to efficiently analyze high-speed circuit networks containing uniform,nonuniform,and frequency-dependent transmission lines. Numerical experiment is presented and the results are compared with that computed by PSPICE.

SPECTRUM DISTRIBUTION OF THE SEDOND ORDER GENERALIZED DISTRIBUTED PARAMETER SYSTEMS

Spectrum distribution of the second order generalized distributed parameter system was discussed via the functional analysis and operator theory in Hilbert space. The solutions of the problem and the constructive expression of the solutions are given by the generalized inverse one of bounded linear operator. This is theoretically important for studying the stabilization and asymptotic stability of the second order generalized distributed parameter system.

Improved control for distributed parameter systems with time-dependent spatial domains utilizing mobile sensor-actuator networks

A guidance policy for controller performance enhancement utilizing mobile sensor-actuator networks （MSANs） is proposed for a class of distributed parameter systems （DPSs）, which are governed by diffusion partial differential equations （PDEs） with time-dependent spatial domains. Several sufficient conditions for controller performance enhancement are presented. First, the infinite dimensional operator theory is used to derive an abstract evolution equation of the systems under some rational assumptions on the operators, and a static output feedback controller is designed to control the spatial process. Then, based on Lyapunov stability arguments, guidance policies for collocated and non-collocated MSANs are provided to enhance the performance of the proposed controller, which show that the time-dependent characteristic of the spatial domains can significantly affect the design of the mobile scheme. Finally, a simulation example illustrates the effectiveness of the proposed policy.

Cramer-Rao bound and signal-to-noise ratio gain in distributed coherent aperture radar

This paper studies the estimation performance of the coherent processing parameter （CPP）, including time delay differences and phase synchronization errors among different apertures of the distributed coherent aperture radar （DCAR）. Firstly, three architectures of signal processing in the DCAR are introduced. Secondly, the closed-form Cramer-Rao bound （CRB） of the CPP estimation is derived and compared. Then, the closed-form CRB is verified by numerical simulations. Finally, when the next generation radar works in a fully coherent mode, the closed-form signal-to-noise ratio （SNR） gain of the three architectures is presented.

Optimal switching policy for performance enhancement of distributed parameter systems based on event-driven control

This paper aims to improve the performance of a class of distributed parameter systems for the optimal switching of actuators and controllers based on event-driven control. It is assumed that in the available multiple actuators, only one actuator can receive the control signal and be activated over an unfixed time interval, and the other actuators keep dormant. After incorporating a state observer into the event generator, the event-driven control loop and the minimum inter-event time are ultimately bounded. Based on the event-driven state feedback control, the time intervals of unfixed length can be obtained. The optimal switching policy is based on finite horizon linear quadratic optimal control at the beginning of each time subinterval. A simulation example demonstrate the effectiveness of the proposed policy.

Simulation of a class of delay stochastic system with distributed parameter

Simulation of a class of delay stochastic system with distributed parameter is discussed. Difference schemes for the numerical computation of delay stochastic system are obtained. The precision of the difference scheme and the efficiency of the difference scheme in simulation of delay stochastic system with distributed parameter are analyzed. Examples are given to illustrate the application of the method.

Failure Prediction Modeling of Lithium Ion Battery toward Distributed Parameter Estimation

Lithium ion battery has typical character of distributed parameter system, and can be described precisely by partial differential equations and multi-physics theory because lithium ion battery is a complicated electrochemical energy storage system. A novel failure prediction modeling method of lithium ion battery based on distributed parameter estimation and single particle model is proposed in this work. Lithium ion concentration in the anode of lithium ion battery is an unmeasurable distributed variable. Failure prediction system can estimate lithium ion concentration online, track the failure residual which is the difference between the estimated value and the ideal value. The precaution signal will be triggered when the failure residual is beyond the predefined failure precaution threshold, and the failure countdown prediction module will be activated. The remaining time of the severe failure threshold can be estimated by the failure countdown prediction module according to the changing rate of the failure residual. A simulation example verifies that lithium ion concentration in the anode of lithium ion battery can be estimated exactly and effectively by the failure prediction model. The precaution signal can be triggered reliably, and the remaining time of the severe failure can be forecasted accurately by the failure countdown prediction module.

A MAXIMUM PRINCIPLE FOR DISTRIBUTED PARAMETER SYSTEMS WITH MIXED PHASE-CONTROL CONSTRAINTS ANDENDPOINT CONSTRAINTS

This paper considered the optimal control problem for distributed parameter systems with mixed phase-control constraints and end-point constraints. Pontryagin's maximum principle for optimal control are derived via Duboviskij-Milujin theorem.