Distributed Parameter Systems Research Articles

Physics-Informed Graphical Representation-Enabled Deep Reinforcement Learning for Robust Distribution System Voltage Control

The anomalous measurements and inaccurate distribution system physical models cause huge challenges for distribution system optimization. This paper proposes a robust voltage control method that can deal with them by systematically integrating a representation network, the deep reinforcement learning (DRL) method, and the surrogate model. The partial observation of the distribution network is first represented as a graph with tree topology that is processed by a physics-informed global graph attention network (GGAT) and a deep auto-encoder (DAE) to achieve informative and robust representation of the real-time and pseudo-measurements. The extracted features are then fed into the soft actor-critic algorithm, during the training of which a graphical-learning-based power flow surrogate model is developed to provide a reward signal for the DRL algorithm. This allows the proposed method to reduce reliance on accurate distribution system parameters. The embedding of the structural information by the GGAT and the informative features extracted by the DAE further enhances the robustness of the proposed method against anomalous measurements. The proposed method is validated using IEEE 33-node and 119-node systems. Simulation results show the robustness of the proposed method against anomalous measurements.

Adaptive spatial-model-based predictive control for complex distributed parameter systems

Many industrial thermal processes can be classified as complex distributed parameter systems (DPS). The traditional control method has become ill-suited for complex DPS since it ignores the time-varying dynamics and spatially distributed behavior. Moreover, the controller incorporating a nonlinear model imposes substantial computational demands, hindering the timely acquisition of control strategies in practical scenarios. In this study, an adaptive spatial-model-based predictive controller with real-time linearization for complex DPS is proposed. Initially, an adaptive spatiotemporal modeling method is developed to characterize the time-varying dynamics of DPS more accurately. Based on this developed spatiotemporal model, a spatial model predictive control strategy with real-time linearization is further designed to reduce the computational burden of the controller. In addition, a weighted terminal cost is embedded to replace terminal constraints in the controller, ensuring stability while improving calculation efficiency. Theoretical analysis confirms the stability of the proposed controller. Finally, furnace simulation and oven experiments are performed to comprehensively evaluate the performance of the proposed controller. It shows that the proposed method significantly improves tracking performance and robustness while reducing computational load.

The Modeling and Control of (Renewable) Energy Systems by Partial Differential Equations—An Overview

Mathematical models of energy systems have been mostly represented by either linear or nonlinear ordinary differential equations. This is consistent with lumped-parameter dynamic system modeling, where dynamics of system state variables can be fully described only in the time domain. However, when dynamic processes of energy systems display both temporal and spatial evolutions (as is the case of distributed-parameter systems), the use of partial differential equations is necessary. Distributed-parameter systems, being described by partial differential equations, are mathematically (and computationally) much more difficult for modeling, analysis, simulation, and control. Despite these difficulties in recent years, quite a significant number of papers that use partial differential equations to model and control energy processes and systems have appeared in journal and conference publications and in some books. As a matter of fact, distributed-parameter systems are a modern trend in the areas of control systems engineering and some energy systems. In this overview, we will limit our attention mostly to renewable energy systems, particularly to partial differential equation modeling, simulation, analysis, and control papers published on fuel cells, wind turbines, solar energy, batteries, and wave energy. In addition, we will indicate the state of some papers published on tidal energy systems that can be modelled, analyzed, simulated, and controlled using either lumped or distributed-parameter models. This paper will first of all provide a review of several important research topics and results obtained for several classes of renewable energy systems using partial differential equations. Due to a substantial number of papers published on these topics in the past decade, the time has come for an overview paper that will help researchers in these areas to develop a systematic approach to modeling, analysis, simulation, and control of energy processes and systems whose time–space evolutions are described by partial differential equations. The presented overview was written after the authors surveyed more than five hundred publications available in well-known databases such as IEEE, ASME, Wiley, Google, Scopus, and Web of Science. To the authors’ best knowledge, no such overview on PDEs for energy systems is available in the scientific and engineering literature. Throughout the paper, the authors emphasize novelties, originalities, and new ideas, and identify open problems for future research. To achieve this goal, the authors reviewed more than five hundred journal articles and conference papers.

Including Shield Wires in the Analysis of Transient Processes Occurring in HVAC Transmission Lines

The article presents an analysis of electromagnetic transient processes in long ultra-high voltage transmission lines, taking into account shield wires. It was shown that EMTP and Matlab/Simulink software are currently widely used in the study of transient processes in power lines. The EMTP software package uses the finite element method when integrating the equation that mathematically models the distributed parameter transmission line. The Matlab/Simulink software uses the d’Alembert method. In both cases, it is not known how the boundary conditions for the partial differential equation that mathematically models the transmission line are determined. The power line is analyzed as a distributed parameter system, described by a second-order partial differential equation. The advantage of the proposed method of calculating the boundary conditions for the abovementioned equation is the use of boundary conditions of the second and third types of Neumann and Poincaré, which allowed us to take into account the mutual influence of shield wires and phase conductors of the line in one power system. On this basis, the methodology for obtaining time domain graphs, spatial distributions, and traveling wave distributions of voltages and currents for phase conductors and line shielding wires is presented. The results of a computer simulation of transient processes when switching on the power line, taking into account controlled phase commutation and under single-phase earth fault conditions, are presented. All calculation results of transient processes presented in the article were obtained exclusively using numerical methods.

Physics-reserved spatiotemporal modeling of battery thermal process: Temperature prediction, parameter identification, and heat generation rate estimation

The battery thermal process, as a typical distributed parameter system (DPS), is critical to battery management. In practice, the process information is often partially known. Data-driven spatiotemporal modeling is always used to approximate the battery thermal process. However, purely data-driven spatiotemporal modeling methods suffer from expensive costs for data acquirement, unsatisfactory accuracies for long-term prediction, and poor generalization performance. These inherent shortcomings significantly limit the applications of this kind of method in DPS modeling. To address these issues, we propose a novel physics-reserved spatiotemporal modeling method that embeds the partially known physics into deep learning architecture. Specifically, the proposed method constructs a composite network with the battery current and terminal voltage as extra control inputs to model the battery thermal process. By fully using the information conveyed by the partially known physics and the observed temperature data, it can predict the battery temperature accurately. Meanwhile, it can identify the unknown parameters and estimate the heat generation rate of the battery thermal process, which has not yet been achieved by data-driven spatiotemporal modeling methods. This paper makes an attempt to bridge the gap between physics and observed data for spatiotemporal modeling. The effectiveness of the proposed method has been demonstrated by extensive experiments.

Optimal Placement and Active Control Methods for Integrating Smart Material in Dynamic Suppression Structures

To simulate a lightweight structure with integrated actuators and sensors, two-dimensional finite elements are utilized. The study looks at the optimal location and active vibration control for a piezoelectric smart flexible structure. Intelligent applications are commonly used in engineering applications. In computational mechanics, selecting the ideal position for actuators to suppress oscillations is crucial. The structure oscillates due to dynamic disturbance, and active control is used to try to reduce the oscillation. Utilizing an LQR and Hinfinity controller, optimization is carried out to determine the best controller weights, which will dampen the oscillation. Challenging issues arise in the design of control techniques for piezoelectric smart structures. Piezoelectric materials have been investigated for use in distributed parameter systems (for example airplane wings, intelligent bridges, etc.) to provide active control efficiently and affordably. Still, no full suppression of the oscillation with this approach has been achieved so far. The controller’s order is then decreased using optimization techniques. Piezoelectric actuators are positioned optimally according to an enhanced optimization method. The outcomes demonstrate that the actuator optimization strategies used in the piezoelectric smart single flexible manipulator system have increased observability in addition to good vibration suppression results.

Time-space separation-based data driven method for monitoring distributed parameter process with sparse and noisy sensor data

In industrial applications, real-time monitoring of the distributed parameter processes is a difficult task, due to the infinite-dimensional nature and the nonlinear spatiotemporal dynamics of distributed parameter systems (DPSs). In addition, the limited number of sensors and the existence of measurement noise may result in failure for detecting DPS dynamics. In this study, a data-driven model is proposed to reconstruct the spatiotemporal states in DPSs using sparse and noisy sensor data based on the time/space separation theory. The proposed reconstruction model maps the high-dimensional DPS states into low-dimensional spatial features using an autoencoder-based spatial model, and then predicts temporal evolution of the spatial features based on the long short-term memory network (LSTM). In addition, in order to improve robustness of the model, a random noise layer is developed and is integrated with the reconstruction model to extract robust spatiotemporal features. The performance of the proposed model is illustrated through applications in two case studies including a thermal process of lithium-ion battery and a fluid process in oceanography. The effects of sensor number and noise intensity on the proposed spatiotemporal model for monitoring DPSs are quantitatively investigated. In addition, the proposed spatiotemporal model is compared with proper orthogonal decomposition-based model. Research results demonstrate that the proposed spatiotemporal model is able to produce accurate and robust reconstruction results for monitoring distributed parameter processes with sparse and noisy sensor data.

A Mixed Safety and Reliability Evaluation Method for the Spacecraft Power Supply System

A spacecraft power distribution system is a multi-parameter, strongly coupled complex system, and the safety of a spacecraft power distribution system directly affects the working status of the spacecraft. In order to achieve better research results in the safety analysis system of spacecraft energy systems, it is very necessary to establish an assessment method for the safety of spacecraft power distribution systems. Previous research mainly focuses on the safety assessment of power systems or aircraft power systems and has not formed a relatively complete assessment method for the safety of spacecraft power distribution systems. This paper proposes a comprehensive evaluation method for the safety of spacecraft power distribution systems. It combines objective and subjective evaluation methods to comprehensively evaluate the safety of spacecraft power distribution systems. The objective parameters of the spacecraft power distribution system are processed and objectively evaluated; Subjective evaluations are obtained using analytic hierarchy. The proposed method can reasonably evaluate the safety of spacecraft power distribution systems and assist in the selection of different spacecraft power distribution systems.

Modeling and consensus of flexible wings with bending deformation and torsion deformation based on partial differential equation model

Modeling and consensus control of flexible wings with bending deformation and torsion deformation are studied in this paper. Due to the physical properties of flexible materials, vibration suppression of the flexible wings is also considered in addition to consensus control. Different from most of the published work of multi-agent control theory, the agent system studied in this paper is a distributed parameter system. Considering the mutual coupling of the wing's bending deformation, torsion deformation and the rotation angle of the root joint, the dynamics model of each agent can be expressed by a set of partial differential equations (PDEs) and ordinary differential equations (ODEs). Boundary control algorithms are designed to achieve control objectives. It is proved that the states of all agents are consistent and the closed-loop system is asymptotically stable. Finally, numerical simulation is carried out to demonstrate the effectiveness of the proposed control scheme.

State estimation for linear time‐delay distributed parameter systems with mobile sensors

SummaryThis study deals with the state observer design for a class of linear time‐delay distributed parameter systems (DPSs) modeled by a parabolic partial differential equation (PDE) via mobile sensors. Initially, under the assumption that the spatial domain is decomposed into multiple subdomains according to the number of mobile sensors, the estimation scheme including a state observer and the guidance of mobile sensors is proposed for the linear time‐delay DPS. Then, by using Lyapunov direct technique and the projection modification algorithm, a design of the state observer plus mobile sensor guidance laws is developed, such that the resulting state estimation error system is exponentially stable and the mobile sensor guidance can improve the transient response of state estimation error. Finally, numerical simulations are presented to show the effectiveness of the proposed method.

Sparse structure preserving finite element model updating problem for gyroscopic systems

An important yet difficult aspect of the finite element model updating problem is to preserve the original inherent structures in the updated model. The analytical matrices resulting from the discretization of distributed parameter systems using finite element techniques are often symmetric and sparse. In this paper, an iterative method is proposed for solving the constrained optimization problem (COP) of gyroscopic systems, that is, finding the optimal updated matrices M̂,Ĝ and K̂ that satisfy the constraints of the characteristic equation, symmetry (or skew-symmetry) and sparsity. The proposed method is proved to be convergent and numerical examples verify the effectiveness of the method.

Confidence-Aware Multiscale Learning for Online Modeling of Distributed Parameter Systems With Application to Curing Process

In industrial applications, the modeling of distributed parameter systems (DPSs) is of significance for process control and monitoring. Due to infinite dimension, spatiotemporal coupled dynamics, nonlinearity and model uncertainties, however, modeling and online applications of DPSs are very difficult. To address these issues, an online spatiotemporal modeling method is proposed based on confidence-aware multiscale learning. From the spacial-scale perspective, an evolutionary learning-based spatial basis function is designed by learning from two dimensionality reduction methods, including Karhunen-Lo <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\grave{e}$</tex-math></inline-formula> ve and diffusion maps. From the temporal-scale perspective, an efficient broad learning system is developed as reduced-order model to online address temporal dynamics of DPSs. As for the spatiotemporal-scale learning, Gaussian process regression is proposed as confidence-aware estimator to compensate for model generalization errors caused by spatiotemporal coupled dynamics. Through integration with the three-scale learning, the proposed method enables online confidence-aware prediction for DPSs. Experiments based on the curing process in snap curing oven demonstrate the effectiveness of proposed method.

Fault-compensation-based boundary control for hyperbolic PDEs: An adaptive iterative learning scheme

In this paper, a fault-compensation-based boundary control strategy is developed for a class of distributed parameter systems expressed by second-order hyperbolic Partial Differential Equations (PDEs), in the case of actuator faults. Considering multiplicative actuator faults and additive actuator faults simultaneously, we put forward a hierarchical fault compensation scheme, i.e., an adaptive iterative learning boundary control technique. Lyapunov-Like analysis method and a variation of Wirtinger’s inequality are used to design a boundary control scheme with an adaptive law, guaranteeing the asymptotical stability of the closed-loop hyperbolic PDE system with multiplicative faults. An iterative learning term is proposed to boost the performance of the system under both multiplicative faults and additive faults, and a composite energy function is used in analysis. With the proposed fault-compensation-based adaptive iterative learning boundary control technique, multiplicative faults are redeemed towards the time horizon and additive faults are compensated towards the iteration horizon. An active acoustic noise reduction process is presented to illustrate the merit and effectiveness of the designed adaptive iterative learning boundary control technique.

The Method of Studying Cosmetic Creams Based on the Principles of Systems Theory and Mathematical Modeling Techniques

This paper reviews research on some cosmetic creams considered “distributed parameters systems” and on the experimental-computational mathematical models that have been determined for them. The determined models characterize the cosmetic creams in all stages of the manufacturing process, starting with the development of recipes, the description of raw materials, manufacturing technologies, and the determination of the physico-chemical and microbiological indicators that most strongly influence their quality. This approach suggests the possibility of performing optimization operations, specifically sensitivity analyses, which may lead to the identification of best quality indicators and to the amelioration of negative effects related to disturbance sizes (temperature, pressure, humidity etc.). Five emulsions with different compositions, prepared in vitro according to our own recipes, using raw materials and preparation methods approved for cosmetic products, were studied. Through specific physico-chemical and microbiological analyses, we obtained databases that were processed computationally. The resulting mathematical models, in the form of both graphs and equations, led to important conclusions regarding obtaining high quality in the studied creams and to the confirmation of the usefulness of applying the principles of Systems Theory to the study of cosmetic products.

A multi-kernel-based spatiotemporal modeling approach for energy transfer of complex thermal processes and its applications

Most of actual thermal processes work in a large-scale operation region. In each region, the processes are along with complex energy transfer and featured by nonlinear distributed parameter system (DPS). Also, the dynamics at different regions is different, and the energy transfer between neighboring regions is complex. All these factors increase the modeling difficulty of thermal processes. In this paper, a multi-kernel spatiotemporal modeling approach is proposed to reconstruct dynamics of this kind of processes. First, a multi-kernel global spatial function construction method is developed to extract the global spatial features of thermal dynamics. For each local region, it constructs the corresponding spatial kernel function to represent the energy exchange on space. In order to reflect the global spatial feature, these spatial kernel functions are integrated by using Gaussian mixture strategy to form a global spatial function. Then, the temporal dynamics can be obtained and modeled by projecting the spatiotemporal data on this global spatial function. Integrating the global spatial function and temporal model, the spatiotemporal model is constructed for this process with large-scale operation region. The performance of this method is verified by theoretical analysis. Using experiments, its modeling ability for thermal processes are demonstrated in comparison with two commonly used modeling methods.

Control of distributed-parameter systems using normal forms: an introduction

Abstract This paper gives an overview of the control of distributed-parameter systems using normal forms. Considering linear controllable PDE-ODE systems of hyperbolic type, two methods derive tracking controllers by mapping the system into a form that is advantageous for the control design, analogous to the finite-dimensional case. A flatness-based controller makes use of the hyperbolic controller canonical form that follows from a parametrization of the system’s solutions. A backstepping design exploits the strict-feedback form of the system to recursively stabilize and transform the subsystems.

Energy-Saving Control in Distributed Parameter Systems with Uniform Estimates of Target Sets

Energy-Saving Control in Distributed Parameter Systems with Uniform Estimates of Target Sets

IEEE Control Systems Society Technical Committee on Distributed Parameter Systems [Technical Activities]

IEEE Control Systems Society Technical Committee on Distributed Parameter Systems [Technical Activities]

Vibration Suppression of a High-Rise Building With Adaptive Iterative Learning Control.

This article considers the design of an adaptive iterative learning controller for high-rise buildings with active mass dampers (AMDs). High-rise buildings in this article are seen as distributed parameter systems, in which the characteristics of every point in buildings should be considered. Two partial differential equations (PDEs) and several ordinary differential equations are used to describe the model of buildings. To achieve the control target that is to suppress the vibration induced by high winds, an adaptive iterative learning controller is proposed for the flexible building system with boundary disturbance. The convergency of the adaptive iterative learning control (AILC) approach is proven by serious theory analysis. In simulations and experiments, this article uses both the analysis of figures and quantitative analysis (root-mean-square values) to illustrate the efficiency of the AILC scheme.

Robust Control for Semilinear Parabolic Distributed Parameter Systems With External Disturbances via Mobile Actuators and Sensors.

This article presents a robust feedback compensator design approach for semilinear parabolic distributed parameter systems (DPSs) with external disturbances via mobile actuators and sensors. An performance constraint is introduced to deal with the external disturbances from the model and measurement noise. Two types of feedback compensators are designed in terms of the collocated and noncollocated mobile actuators and sensors. By the Lyapunov direct technique, some sufficient conditions based on LMI constraints are proposed for the exponential stability under performance constraints in the L²-norm. Moreover, the open-loop and closed-loop well-posedness of the semilinear DPSs with external disturbances are analyzed via the C0 -semigroup theory approach. Finally, extensive numerical simulation results for semilinear DPSs with external disturbances via collocated and noncollocated mobile actuators and sensors are shown to verify the effectiveness of the proposed method.