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.

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.

A modified lumped parameter model of distribution transformer winding

The modelling of the distribution transformer winding is the starting point and serves as important basis for the transformer characteristics analysis and the lightning pulse response prediction.A distributed parameters model can depict the winding characteristics accurately,but it requires complex calculations.Lumped parameter model requires less calculations,but its applicable frequency range is not wide.This paper studies the amplitude-frequency characteristics of the lightning wave,compares the transformer modelling methods and finally proposes a modified lumped parameter model,based on the above comparison.The proposed model minimizes the errors provoked by the lumped parameter approximation,and the hyperbolic functions of the distributed parameter model.By this modification it becomes possible to accurately describe the winding characteristics and rapidly obtain the node voltage response.The proposed model can provide theoretical and experimental support to lightning protection of the distribution transformer.

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.

A Note on the Controllability of Distribution Parameter Control System

This paper gives the relation between the precise controllabilities of two distrib-ution parameter systems.

One-sided empirical Bayes test for location parameter in Gamma distribution

In this paper, we devote to constructing the one-sided empirical Bayes(EB) test for the location parameter in the Gamma distribution by nonparametric method. Under some mild conditions, we prove that the EB test is asymptotically optimal with the rate of the order O(n^(-δs/(2s+1))), where 1/2 ≤ δ < 1 and s > 1 is a given natural number. An example is also given to illustrate that the conditions of the main theorems are easily satisfied.

High-Accuracy Confidence Regions for Distribution Parameters

With the help of today’s computers, it is always relatively easy to find maximum-likelihood estimators of one or more parameters of any specific statistical distribution, and use these to construct the corresponding approximate confidence interval/region, facilitated by the well-known asymptotic properties of the likelihood function. The purpose of this article is to make this approximation substantially more accurate by extending the Taylor expansion of the corresponding probability density function to include quadratic and cubic terms in several centralized sample means, and thus finding the corresponding -proportional correction to the original algorithm. We then demonstrate the new procedure’s usage, both for constructing confidence regions and for testing hypotheses, emphasizing that incorporating this correction carries minimal computational and programming cost. In our final chapter, we present two examples to indicate how significantly the new approximation improves the procedure’s accuracy.

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.

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.

Multi-Model Based PSO Method for Burden Distribution Matrix Optimization With Expected Burden Distribution Output Behaviors

Burden distribution is one of the most important operations, and also an important upper regulation in blast furnace(BF) iron-making process. Burden distribution output behaviors(BDOB) at the throat of BF is a 3-dimensional spatial distribution produced by burden distribution matrix(BDM),including burden surface output shape(BSOS) and material layer initial thickness distribution(MLITD). Due to the lack of effective model to describe the complex input-output relations,BDM optimization and adjustment is carried out by experienced foremen. Focusing on this practical challenge, this work studies complex burden distribution input-output relations, and gives a description of expected MLITD under specific integral constraint on the basis of engineering practice. Furthermore, according to the decision variables in different number fields, this work studies optimization of BDM with expected MLITD, and proposes a multi-mode based particle swarm optimization(PSO) procedure for optimization of decision variables. Finally, experiments using industrial data show that the proposed model is effective, and optimized BDM calculated by this multi-model based PSO method can be used for expected distribution tracking.

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.

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.

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.

Development of a mass model in estimating weight-wise particle size distribution using digital image processing

Particle size distribution of coarse aggregates through mechanical sieving gives results in terms of cumu- lative mass percent. But digital image processing generated size distribution of particles, while being fast and accurate, is often expressed in terms of area function or number of particles. In this paper, a mass model is developed which converts the image obtained size distribution to mass-wise distribution, mak- ing it readily comparable to mechanical sieving data. The concept of weight/particle ratio is introduced for mass reconstruction from 2D images of particle aggregates. Using this mass model, the effects of several particle shape parameters （such as major axis, minor axis, and equivalent diameter） on sieve-size of the particles is studied. It is shown that the sieve-size of a particle strongly depend upon the shape param- eters, 91% of its variation being explained by major axis, minor axis, bounding box length and equivalent diameter. Furthermore, minor axis gives an overall accurate estimate of particle sieve-size, error in mean size （D-50） being just 0.4%. However, sieve-size of smaller particles （〈20 ram） strongly depends upon the length of the smaller arm of the bounding box enclosing them and sieve-sizes of larger particles （〉20 mm） are highly correlated to their equivalent diameters. Multiple linear regression analysis has been used to generate overall mass-wise particle size distribution, considering the influences of all these shape parameters on particle sieve-size. Multiple linear regression generated overall mass-wise particle size distribution shows a strong correlation with sieve generated data. The adjusted R-square value of the regression analysis is found to be 99 percent （w.r,t cumulative frequency）. The method proposed in this paper provides a time-efficient way of producing accurate （up to 99%） mass-wise PSD using digital image processing and it can be used effectively to renlace the mechanical sieving.

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.

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.

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.