Control Of Distributed Parameter Systems Research Articles

A distributed-parameter control system using electromagnetic neural stimulation for human–machine perception interface

ABSTRACT This article presents a new design of a distributed-parameter control system for human–machine perception interface, which is capable of precisely stimulating the neural systems with electromagnetic fields. By discretising the neural systems, a state-space representation of the electromagnetic stimulation is developed to facilitate the following design and analysis. A forward controller with multiple inputs and multiple outputs is consequently designed to estimate the excitation current. This novel approach enables the applications of the well-established control theory to analyse the system. The feasibility and accuracy of the control system are numerically illustrated and validated with the applications of Transcranial Magnetic Stimulation (TMS) and retinal stimulation. The results indicate that the newly designed control system can not only generate electromagnetic stimulation with better attenuation and focality than the most widely used Figure-8 coil, but also transmit the patterns extracted from images with electromagnetic stimulations to human retinas.

Axial power distribution control in fast nuclear reactor based on proportional spatial-derivative method

Axial power distribution control is one of the key issues for Nuclear Power Plant (NPP) operation. In the most of NPPs, the axial power distribution control is realized by the Lumped Parameters Control (LPC) method, which often takes the axial power difference between adjacent nodes as the controlled object. However, the nuclear reactor core has a typical distributed parameters feature. With the number of discrete nodes increases, the control system design is more and more complex. Therefore, it is necessary to develop the Distributed Parameter Control (DPC) method. In this work, a DPC method based on the Proportional Spatial-Derivative (PSD) controller is presented. Experiments show that the power distribution control system based on the PSD control method can inhibit the power peak. Meanwhile, the comparison between the PSD and PID controllers shows that the DPC system based on the PSD method has better dynamic performance than LPC system.

Analysis of the error in an iterative algorithm for asymptotic regulation of linear distributed parameter control systems

Applications of regulator theory are ubiquitous in control theory, encompassing almost all areas of systems and control engineering. Examples include active noise suppression [Banks et al., Decision and Control, Active Noise Control: Piezoceramic Actuators in Fluid/structure Interaction Models, IEEE, Los Alamitos, CA (1991) 2328–2333], design and control of energy efficient buildings [Borggaard et al., Control, Estimation and Optimization of Energy Efficient Buildings. Riverfront, St. Louis, MO (2009) 837–841.] and control of heat exchangers [Aulisa et al., IFAC-PapersOnLine 49 (2016) 104–109.]. Numerous other examples can be found in [Aulisa and Gilliam, A Practical Guide to Geometric Regulation for Distributed Parameter Systems. Chapman and Hall/CRC, Boca Raton (2015).]. In the geometric approach to asymptotic regulation the main object of interest is a pair of operator equations called the regulator equations, whose solution provides a control solving the tracking/disturbance rejection regulation problem. In this paper we present an iterative algorithm, called the β-iteration method, which is based on the geometric methodology, and delivers accurate control laws for approximate asymptotic regulation. This iterative scheme has been successfully applied to a wide range of linear and nonlinear multi-physics examples and in practice only one or two iterations are usually required to deliver sufficiently accurate results. One drawback to these research efforts is that no proof was given of the convergence of the method. This work contains a detailed analysis of the error in the iterative scheme for a large class of linear distributed parameter systems. In particular we show that the iterative errors converge at a geometric rate. We demonstrate our estimates on three control problems in multi-physics applications.

Optimal control for a higher-order nonlinear parabolic equation describing crystal surface growth

In this paper, we shall study the optimal control of the initial-boundary value problem of a higher-order nonlinear parabolic equation describing crystal surface growth. The existence and uniqueness of weak solutions to the problem are given. According to the variational method, optimal control theories and distributed parameter system control theories, we can deduce that the norm of the solution is related to the control item and initial value in the special Hilbert space. The optimal control of the problem is given, the existence of optimal solution is proved and the optimality system is established.

Assessment of severity of nonlinearity for distributed parameter systems via nonlinearity measures

The performance of controlled distributed parameter systems (DPSs) not only depends on the controller, but also on the dynamic nature of the process itself. One of the primary factors affecting DPS control is process nonlinearity. In many situations, the extent and severity of nonlinearity is the crucial characteristic in deciding whether linear system analysis and controller synthesis methods are adequate. However, due to their spatio-temporal coupling, traditional nonlinearity measures cannot be directly applied to nonlinear DPSs. In this study, a nonlinearity measure method to quantify the severity of nonlinearity for a class of DPSs is proposed. First, time/space separation and model reduction are carried out using proper orthogonal decomposition (POD). Thus, an optimal linear time-invariant model with a low-order is obtained through the optimization of a spatio-temporal error while full state feedback is incorporated in order to stabilize the linear model. Finally, nonlinearity quantification for DPSs is calculated using the obtained stable linear time-invariant system. The complexity of the calculations for nonlinearity measures is greatly reduced after the model reduction using POD. This method easily estimates the extent to which the process behavior deviates from linearity, which aids in determining whether a linear system analysis and controller synthesis methods are adequate. The nonlinearity quantification indicates that DPSs with smaller values are better approximated by a linear model than DPSs with larger values in the target time/space domain. The effectiveness of the proposed method is illustrated using two numerical examples.

Improved control of distributed parameter systems using wireless sensor and actuator networks: An observer-based method**Project supported by the National Natural Science Foundation of China (Grant Nos. 61174021 and 61473136) and the 111 Project of China (Grant No. B12018).

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.

Pole assignment for a singular distributed parameter system coupled with a singular lumped parameter system}{Pole assignment for a singular distributed parameter system coupled with a singular lumped parameter system

The pole assignment for a first order singular distributed parameter control system coupled with a first order singular lumped parameter control system is discussed via functional analysis and operator theory in Hilbert space. The solutions of the problem and the constructive expressions of the solutions are given by the bounded inner inverse of the bounded linear operator. This research is theoretically important for studying the pole assignment and stabilizability of singular distributed parameter control systems.

Data-driven model reduction-based nonlinear MPC for large-scale distributed parameter systems

Model predictive control (MPC) has been effectively applied in process industries since the 1990s. Models in the form of closed equation sets are normally needed for MPC, but it is often difficult to obtain such formulations for large nonlinear systems. To extend nonlinear MPC (NMPC) application to nonlinear distributed parameter systems (DPS) with unknown dynamics, a data-driven model reduction-based approach is followed. The proper orthogonal decomposition (POD) method is first applied off-line to compute a set of basis functions. Then a series of artificial neural networks (ANNs) are trained to effectively compute POD time coefficients. NMPC, using sequential quadratic programming is then applied. The novelty of our methodology lies in the application of POD's highly efficient linear decomposition for the consequent conversion of any distributed multi-dimensional space-state model to a reduced 1-dimensional model, dependent only on time, which can be handled effectively as a black-box through ANNs. Hence we construct a paradigm, which allows the application of NMPC to complex nonlinear high-dimensional systems, even input/output systems, handled by black-box solvers, with significant computational efficiency. This paradigm combines elements of gain scheduling, NMPC, model reduction and ANN for effective control of nonlinear DPS. The stabilization/destabilization of a tubular reactor with recycle is used as an illustrative example to demonstrate the efficiency of our methodology. Case studies with inequality constraints are also presented.

Structural-parametric synthesis of time-optimal distributed parameter control systems with interval uncertainty of the plant characteristics

This work is devoted to a possible way to construct time-optimal closed systems for incompletely determined linear models of distributed-parameter control plants of parabolic type, which provides real-time identification of their parametric characteristics according to the results of monitoring the state of the plants. The structural-parametric synthesis of the proposed controllers is based on the alternance method of designing optimal software controls. The paper gives an example (of independent interest) of constructing a time-optimal system for the control of the process of induction heating under typical conditions of interval uncertainty of the initial temperature and heat losses.

Global controllability and stabilizability of Kawahara equation on a periodic domain

In this paper we study controllability and stabilizability of a class of distributed parameter control system described by the Kawahara equation posed on a periodic domain $\mathbb{T}$ with internal control acting on a sub-domain $\omega $ of $\mathbb{T}$. Earlier in [42], aided by Bourgain smoothing property of the system, we showed that the system is locally exactly controllable and exponentially stabilizable. In this paper, helped further by certain properties of propagation of compactness and regularity in Bourgain spaces for the solutions of the associated linear system, we show that the system is globally exactly controllable and globally exponentially stabilizable.

From conservation laws to wave propagation and back -dynamics and control in combined heat/electricity generation

Starting from some pioneering papers in distributed parameter control systems for steam turbines and their auxiliaries, a bilinear model for steam turbines with steam extraction and “long” steam pipes was elaborated and the feedback control synthesis has been performed using a suitable control Liapunov functional of quadratic type, both for distributed parameters systems and their lumped parameter approximation. The synthesized control ensures global stabilization of the steady state solution. It has been observed much later that the linearized steam wave propagation equations underlying the model were in fact a simplified linearized version of the conservation laws of the isentropic flow. Following this remark and bearing in mind the recent advances in the control of the systems described by conservation laws, the model of the combined heat electricity generation is re-written as a system which is linear in control; consequently the feedback stabilization also requires re-examination.

Geometric theory of special modes in the distributed-parameter control systems

The present paper is the first in the projected series of publications illustrating the application of the geometric theory of singular solutions of the nonlinear partial differential equations to the description of special modes in the distributed-parameter control systems. Consideration was given to the problem of biphase unidimensional filtering of fluids (oil and water) in the porous media of the natural oil pools. The paper is an extended version of the report presented at the International Conference PACO'2012 prepared for publication on recommendation of the Program Committee [1].

Modeling and Control of Temperature Field of the Secondary Cooling Zone in Continuous Casting of Steel as Distributed Parameter System

This paper presents some results on modeling and control of temperature field in a steel continuous casting, demonstrating the possibilities of using engineering methods for control of distributed parameter systems along with virtual engineering environments. A system to be controlled is considered as lumped-input and distributed-parameter-output system. Dynamics and control synthesis are decomposed into time and space components, respectively. Demonstrations of PID and adaptive model-based predictive control are being presented via cosimulation, utilizing virtual software environments for continuous casting simulation and distributed parameter control systems, respectively.

A New Type of Distributed Parameter Control Systems: Two-Point Boundary Value Problems for Infinite-Dimensional Dynamical Systems

This survey note describes a new type of distributed parameter control systems—the two-point boundary value problems for infinite-dimensional dynamical systems, particularly, for hyperbolic systems of partial differential equations of second order, some of the discoveries that have been done about it and some unresolved questions.

Finite-dimensional dual state feedback control of linear boundary control systems

In this article, the finite-dimensional control of distributed-parameter systems with boundary control and unbounded observation is considered. This problem is solved by extending the concept of dual observer-based compensators to infinite dimensions. These compensators have the advantage that, on the one hand, the separation principle can be used to directly determine a finite-dimensional compensator and, on the other hand they can be directly applied to boundary control systems with a time-derivative of the input. In order to achieve a low controller order as well as a desired control performance, a parametric approach is proposed to parameterise the degrees of freedom contained in the controller. Consequently, desired design specifications can be achieved by using a parameter optimisation. The proposed design of finite-dimensional dual observer-based compensators is demonstrated by means of a heat-conducting system with Neumann boundary control and boundary measurements.

Feedback stabilization of abstract neutral linear control systems

In this paper, the asymptotic stabilization of linear distributed parameter control systems of neutral type is considered. Specifically, we study control systems described by a special type of abstract neutral functional differential equation with finite delay. Assuming appropriate conditions, and using the spectral properties of quasi-compact semigroups, we show that the usual spectral controllability assumption implies the feedback stabilization of the system. We applied our results to the stabilization of several real systems of first and second order described by partial neutral functional differential equations.

Model of the optimal control of funds and competitiveness of the information-communication company

A two-level hierarchical organization system is used to consider a model for the optimal control of funds and competitive ability of an information---communication company. The model is based on a control problem for ordinary differential equations (that characterize the dynamics of funds) and on an initial---boundary-value problem for multidimensional quasilinear parabolic Lotka---Volterra equations (that describe the sales dynamics of competitive companies) and uses methods of optimal control for distributed-parameter systems. The sufficient existence conditions are established for the optimal control and a stable numerical algorithm is developed to search for optimal control functions.

Outils d’information/prévention sur les risques professionnels dans la filière Bois

In this work, dissipativity of Lur’e distributed parameter control systems has been addressed. Delay-dependent sufficient conditions for the dissipativity with respect to the infinite-dimensional version of energy supply rate (Q1,S1,R1) characterized exclusively by unbounded operator Q1 are established in terms of linear operator inequalities (LOIs). Finally, the heat equation illustrates our result.

Sensor Location Optimization for Distributed Parameter Systems Based on Wavelet Transforms

The sensor location optimization is the special problem of distributed parameter systems(DPS) for parameter identification. It has a great influence on the accuracy of parameter identification and it is important to optimal control of DPS. Therefore, it has a great significance to research the strategy of sensor optimal measurement locations for DPS. In this paper, based on the orthogonal function approximation method, Haar wavelet transforms method is applied to research the problem of sensor measurement locations of DPS. The method based on Fisher information matrix derived from the differential sensitivity equations is proposed to determine the sensor optimal measurement locations. The identification examples prove that the proposed method based on wavelet transforms is feasible and effective to locate the sensor in order to obtain the optimal measurement values. The algorithm makes the calculation simple, easy and accurate.

Variable Structure Control Based Wavelet Transforms for Linear Time-Invariant Distributed Parameter Systems

The distributed parameter systems(DPS) are usually described by the partial differential equations(PDEs). Compared the variable structure control problem of DPS with that of the lumped parameter systems(LPS) , it is more complicated because the problem of variable structure control for DPS is often closely related to the theory of the differential operator or integral operator. Based on Haar wavelets transform, the operational matrixes and their characteristics, this paper attempts to propose a new approach for the variable structure control problem of a class linear time-invariant DPS by converting it into that of lumped parameter systems(LPS) and then makes use of the mature research methods of LPS to design the variable structure control problem so as to solve the variable structure control problem of DPS. The proposed method in this paper has the advantages of the simpler algorithm, less computation and better control effect. The simulation results also prove that it is an efficient algorithm for DPS.