Distributed Parameter Systems Research Articles

Deep Extreme Learning Machines Based Two-Phase Spatiotemporal Modeling for Distributed Parameter Systems

Accurate and robust modeling of complex distributed parameter systems (DPSs) is a challenge for three reasons: 1) they have infinite-dimensional characteristics; 2) they are time/space coupled; and 3) there are model uncertainties. In this article, a two-phase spatiotemporal (S/T) modeling framework based on deep extreme learning machine (DELM) is proposed for DPSs. The modeling process consists of two S/T models in two phases: Phase I: a DELM model and Phase II: a Karhunen–Loève (KL) based ELM (KL-ELM) model. In phase I, the DELM model is constructed by combing the multilayer ELM (ML-ELM), ELM, and kernel-based ELM (K-ELM) to approximate the dominant S/T dynamics of DPSs. Since DPSs have an infinite-dimensional characteristic that can hardly be handled directly, ML-ELM is first employed to transform the infinite-dimensional systems into finite-dimensional systems. Then, the ELM model is adopted to further approximate the finite-dimensional systems to ensure the model can predict future dynamic behavior. Finally, the K-ELM is used to reconstruct the infinite-dimensional systems, which can be considered as the inverse process of ML-ELM. Thus, the final DELM model can be used for prediction in both space and time directions. In phase II, a KL-ELM model is constructed to compensate for modeling errors caused by reconstruction error or unknown nonlinear dynamics. By integrating the obtained DELM and KL-ELM models, the proposed two-phase S/T model can be constructed. Experiments on a typical industrial thermal process verified that the proposed method may work better in complex DPSs.

Data-Driven Real-Time Prediction of Pouch Cell Temperature Field Under Minimal Sensing

The monitoring of temperature distribution is crucial for advanced battery thermal management. This study proposes a data-driven temperature field prediction method for the pouch cell thermal process, a typical distributed parameter system (DPS). First, empirical spatial basis functions (SBFs) that represent underlying spatial modes of the thermal system are extracted from data snapshots collected offline. Then, we apply the obtained SBFs to the time/space (T/S) separation framework and perform online nonlinear modeling using the partial-node feedback data. On this basis, a dynamics reconstruction strategy is designed for full-node temperature prediction. Experimental studies indicate that the proposed method owns encouraging accuracy and allows minimal sensing configuration. In addition, the error source of the proposed method is systematically analyzed.

Fuzzy Boundary Control for Nonlinear Delayed DPSs Under Boundary Measurements.

For nonlinear delayed distributed parameter systems (DDPSs), this article considers a fuzzy boundary control (FBC) under boundary measurements (BMs). Initially, we accurately describe the nonlinear DDPS through a Takagi-Sugeno (T-S) fuzzy partial differential-difference equation (PDDE). Then, in accordance with the T-S fuzzy PDDE model, an FBC design under BMs ensuring the exponential stability for closed-loop DDPS is subsequently presented by spatial linear matrix inequalities (SLMIs) via using Wirtinger's inequality, Halanay's inequality, and the Lyapunov direct method, which respects the fast-varying and slow-varying delays. Moreover, we formulate SLMIs as LMIs for solving the fuzzy boundary controller design of nonlinear DDPSs under BMs. Finally, the effectiveness of the proposed FBC strategy is presented via simulation examples.

Latent-Variable-Modeling-Based Fault Diagnosis for Unknown Nonlinear Distributed Parameter Systems with Application to Snap Curing Oven

A novel fault detection method based on time/space separation and latent variable model is proposed for unknown nonlinear distributed parameter systems in sensor-constrained environments. By performing time/space separation, the augmented matrix formed by the spatio-temporal distribution data of the DPSs can be split into a spatial basis function (SBFs) and a time series model, and the dimensionality reduction capability of the SBF is further utilized to obtain a low-order temporal model. Then, the temporal model is further extracted by using a dynamic latent variable modeling method to obtain the dominant time components and establish the corresponding monitoring statistics. Utilizing the appropriate kernel density function, confidence bounds are selected for the monitoring statistics when the system is normal. As a data-based fault diagnosis method, it requires only the past data records of the system and no reliance on complex mathematical models. Two sets of experiments performed on a snap curing oven verified the effectiveness of the proposed method.

Neural network–based active control of a rigid–flexible spacecraft with bounded input

This paper investigates the simultaneous control of a spacecraft with a rigid central hub and two flexible appendages. Taking into account the coupling between the vibration of flexible appendages and the motion of the hub, the rigid–flexible spacecraft subjected to external disturbance is modeled as a hybrid lumped–distributed parameter system. To attenuate the vibrations of the hub and flexible appendages and simultaneously track the given attitude angle, two boundary control laws are developed based on the original dynamic equation, where all system modes are controlled and spillover instability can be avoided. Using the active disturbance rejection control technique, two extended state observers are designed to obtain the estimation of external disturbances, which can be canceled in the negative feedback loop. The radial basis function neural network with adaptive weight law is employed to deal with the impact of input saturation. The well-posedness of the closed-loop system is proved by applying the semigroup theory. Under the rigorous Lyapunov analysis, the proposed control strategy ensures the practical stability of the rigid–flexible spacecraft system. Simulation verifies the performance of the designed control scheme.

Distributed H ∞ Consensus Filtering for Parabolic Distributed Parameter Systems with Multiple Missing Measurements: A Mobile Sensing Approach

This paper investigates the distributed H ∞ consensus filtering issue for a class of distributed parameter systems with bounded disturbance. In a framework of optimizing performance, a new approach to improving filter performance is proposed by employing mobile sensor networks. Moreover, the information missing in mobile sensor networks is modeled as a conditional probability distribution. The aim of the filtering challenge is to construct a distributed consensus filter such that the filtering error system is globally asymptotically stable in the mean square, and what disturbances do to the estimation accuracy is attenuated at the H ∞ consensus performance level. Utilizing the Lyapunov direct approach and the spatial operator technique, several sufficient criteria are given for the proposed filter to satisfy the H ∞ consensus performance constraint. Finally, a numerical simulation is given to demonstrate the effectiveness of the design scheme of the proposed filter.

Regional Exponential Observation and error

The purpose of this paper is to provide original results related to the choice of the number of sensors and their supports for distributed parameter systems. We introduce the notion of exponential observation error. We show that, the number and location of sensor may be some interest in the existence of regional exponential observation state.

Vibration Control for an Active Mass Damper of a High-Rise Building With Input and Output Constraints

Aiming at the windproof and seismic problems of a high-rise building with large flexible structures, this article introduces a boundary control technology for a high-rise building with active mass damper (AMD) under input and output constraints. Hamilton's principle is used to establish an infinite-dimensional distributed parameter system model of a high-rise building with AMD. Based on the partial differential equations model, a boundary control law with input and output constraints is proposed, where the bounded input constraints are handled by a smooth hyperbolic tangent function and the output constraints are dealt with by a barrier Lyapunov function. It is proved that the vibration is well suppressed by the controller, and the input and output constraints are not violated. Numerical simulations and experiments are used to verify the effectiveness of the control performance.

Impact of the polarization control system on continuous-variable quantum key distribution system parameters

Subject of study. This study considers a polarization control method of optical radiation for a continuous-variable quantum key distribution system for correct polarization demultiplexing of the local oscillator and signal state necessary to ensure the correct performance of the presented system. Aim of study. This study aims to develop a system of active polarization control and experimentally evaluate the effect of this system on the continuous-variable quantum key distribution system parameters. Method. The polarization control system considered in this study is based on constant analysis of the local oscillator radiation and maximization of its intensity due to the stochastic gradient descent algorithm. Local oscillator fluctuations occur because of the principle of active polarization control operation. An experimental setup simulating the sender and receiver module of the continuous-variable quantum key distribution system is used to evaluate the introduced noise. This setup enables evaluation of the noise introduced by the controller operation. Main results. Excess noise caused by the polarization controller is comparable with the polarization noise generated in the quantum key distribution system. Practical significance. Correct operation of a continuous-variables quantum key distribution system can be implemented exclusively with the use of a polarization control device. Knowledge of the polarization control effect on the system gains an understanding of the possible future methods for designing and developing continuous-variables quantum key distribution systems.

Nonparametric identification based on Gaussian process regression for distributed parameter systems

This paper proposes a nonparametric identification method based on Gaussian process regression (GPR) for completely unknown nonlinear distributed parameter systems (DPSs). Inspired by linear parameter-varying (LPV) modelling approach, an interpolated spatio-temporal Volterra model is developed to represent the DPSs in nonparametric form, in which local Volterra models are interpreted as Gaussian processes. According to the empirical Bayesian approach, we design the third-order stable kernel structure used for embedding prior knowledge and derive the estimation of hyperparameters. The hyperparameters included in local weighting functions and kernel functions are determined by the maximum likelihood method. By utilising the nonparametric identification approach to avoid model structure selection, the proposed method can improve identification result for completely unknown distributed parameter systems. Finally, two case studies validate the effectiveness of the proposed identification method.

A novel approach to stability analysis of a wide class of irrational linear systems

This paper presents a general methodology for finding stability equivalence regions, of a wide class of linear time-invariant systems with irrational transfer functions, inside a parametric space. The proposed methodology can be applied to distributed-parameter, time-delay and fractional systems. Unlike rational transfer functions which have only a finite number of poles, irrational transfer functions may generally possess an infinite number of poles, branch points and even essential singularities. Due to this, stability of such systems is more difficult to analyze. Two variants of the new methodology are presented. The first one analyzes stability equivalence along a curve in the parametric space, starting from a given parametric point. The second one finds the maximal stability equivalence region in the parametric space around a given parametric point. Both methodologies are based on iterative application of Rouché’s theorem. They are illustrated on several examples, including heat diffusion equation and generalized time-fractional telegrapher’s equation, which exhibit special functions such as \(\sinh \) and \(\cosh \) of \(\sqrt{s}\), the Laplace variable of order 0.5.

Filter-Based Fault Detection and Isolation in Distributed Parameter Systems Modeled by Parabolic Partial Differential Equations

This paper covers model-based fault detection and isolation for linear and nonlinear distributed parameter systems (DPS). The first part mainly deals with actuator, sensor and state fault detection and isolation for a class of DPS represented by a set of coupled linear partial differential equations (PDE). A filter based observer is designed based on the linear PDE representation using which a detection residual is generated. A fault is detected when the magnitude of the detection residual exceeds a detection threshold. Upon detection, several isolation estimators are designed using filters whose output residuals are compared with predefined isolation thresholds. A fault on a linear DPS is declared to be of certain type if the corresponding isolation estimator output residual is below its isolation threshold while the other fault isolation estimator output residual is above its threshold. Next, the fault location is determined when a state fault is identified. The second part of this paper focuses on fault detection and isolation of nonlinear DPS by using a Luenberger type observer. Here fault isolation framework is introduced to isolate actuator, sensor and state faults with isolability condition by using additional boundary measurements and without filters. Finally, the effectiveness of the proposed fault detection and isolation schemes for both linear and nonlinear DPS are demonstrated through simulation.

Mutual Impedance-Based Force/Velocity Transmission Improvement for Bilateral Teleoperation

Tackling communication delays attracts interest in improving the stability and transparency of bilateral teleoperation. This study presents a novel concept; mutual impedance. Under the delays, this impedance is intrinsic in four-channel acceleration-based bilateral control (4ch ABC). In 4ch ABC, wave propagations can characterize the transmissions of force and velocity, which are described in distributed-parameter systems. The delays induce interference between applied force and velocity response and decrease transparency. The mutual relationship between force and position controllers can explain the interference. The proposed mutual impedance is the indicator of the impact of the relationship. This study notes that the impedance comprises a ratio of force and position controllers. Thus, a force proportional-integral (PI) controller with a gain constraint between the position controller is introduced. One-degree-of-freedom (1-DOF) motion experiments compare the proposed method with conventional methods in superiority. The applicability of the proposed approach to delay fluctuations and multi-DOF motion is verified through 3-DOF manipulators.

Model Identification and Control of Electromagnetic Actuation in Continuous Casting Process With Improved Quality

This paper presents an original theoretical frame-work to model steel material properties in continuous casting line process. Specific properties arising from non-Newtonian dynamics are herein used to indicate the natural convergence of distributed parameter systems to fractional order transfer function models. Data driven identification from a real continuous casting line is used to identify model of the electromagnetic actuator device to control flow velocity of liquid steel. To ensure product specifications, a fractional order control is designed and validated on the system. A projection of the closed loop performance onto the quality assessment at end production line is also given in this paper.

A Dual Adaptation-Based Spatial Model Predictive Control for Nonlinear Distributed Parameter Systems

A Dual Adaptation-Based Spatial Model Predictive Control for Nonlinear Distributed Parameter Systems

Globally linearising control of linear time-fractional diffusion-advection-reaction systems

The globally linearising control (GLC) structure is adopted to solve both the step tracking and disturbance rejection problems for distributed parameter system described by a time-fractional partial differential equation. The actuation is assumed to be distributed in the spatial domain while the controlled output is defined as a spatial weighted average of the state. First, following a similar reasoning to geometric control and based on the late lumping approach, an infinite dimensional state feedback that yields a fractional finite dimensional system in closed loop is developed. Then, the input of this resulting closed-loop system is defined by means of a robust controller to cope with step disturbances. Assuming that the output shaping function is non-vanishing, on the spatial domain, it is demonstrated that the GLC strategy is stable. Two applications examples are presented to show, through simulation runs, the stabilisation, step tracking and disturbance rejection capabilities of the GLC scheme.

Saturated Output Regulation of Distributed Parameter Systems with Collocated Actuators and Sensors⋆

This paper addresses the problem of output regulation of infinite-dimensional linear systems subject to input saturation. We focus on strongly stabilizable linear dissipative systems with collocated actuators and sensors. We generalize the output regulation theory for finite-dimensional linear systems subject to input saturation to the class of considered infinite-dimensional linear systems. The theoretic results are illustrated with an example where we consider the output regulation of a flexible satellite model that is composed of two identical flexible solar panels and a center rigid body.

Модернизация системы управления температуры теплоносителя в парогенераторных установках

In the article the device and operation of steam unit as an example of the core of a nuclear reactor. The description of the equipment included in the multiple forced circulation circuit forming the reactor. Considered in detail the process of controlling the flow of coolant in the reactor fuel channels and the necessity of automation of the process. Formulated and solved the problem of synthesis of automatic control system. The possibility of using the device, extended frequency response for frequency analysis of distributed parameter systems. Formulated and solved the problem by developing a method for calculating the settings PID-controller.

Iterative learning algorithms for boundary tracing problems of nonlinear fractional diffusion equations

<abstract><p>In this paper, the iterative learning control technique is extended to distributed parameter systems governed by nonlinear fractional diffusion equations. Based on $ P $-type and $ PI^{\theta} $-type iterative learning control methods, sufficient conditions for the convergences of systems are given. Finally, numerical examples are presented to illustrate the efficiency of the proposed iterative schemes. The numerical results show that the closed-loop iterative learning control scheme converges faster than the open-loop iterative learning control scheme and the $ PI^{\theta} $-type iterative learning control scheme converges faster than the $ P $-type and the $ PI $-type iterative learning control scheme.</p></abstract>

Trajectory planning and control of convection reaction models with storage effects

Distributed parameter systems consisting of several convection-reaction equations, which are distributed coupled with a reaction equation are considered. An alternative model description for this class of systems is obtained using the method of characteristics. The alternative description is constituted by a single partial differential equation of first order with respect to time. The proposed reformulation of the model allows for the efficient simulation of the system and for the straightforward calculation of inversion-based open-loop control laws. The stability of the original and the inverse models are discussed. The proposed method is illustrated by means of an example.