Distributed Parameter Systems Research Articles

Robustly Linearized Model Predictive Control for Nonlinear Infinite-Dimensional Systems

This work presents a computationally efficient approach to robustly linearized model predictive control for nonlinear affine-in-control evolution equations on infinite-dimensional system state. In this setting, robust linearization refers to a need to account for the approximation errors in linearization and discretization in the model predictive control law, such that the original output constraints are not violated on the true system, a feature that present model predictive control frameworks lack. The main purpose of this work is to enable tractable model predictive control for nonlinear distributed parameter systems while accounting for these approximation errors by means of output constraints. These output constraints are derived using tight integral inequalities that rest on mild assumptions on the nonlinear system dynamics, and are easy to evaluate in real-time. Using our method, linearization and discretization errors are explicitly accounted for, producing for the first time a model predictive control law that is robust to approximation errors. This approach hence enables a trade-off between computational efficiency and strictness of output constraints, much akin to robust control methods. We demonstrate our method on a nonlinear distributed parameter system, namely a one-dimensional heat equation with a velocity-controlled moveable heat source, motivated by autonomous energy-based surgery.

Echo-state-network-based iterative learning control of distributed systems

The paper proposes an effective modeling and control procedure for the distributed-parameter systems using the echo-state network. The main idea is to reconstruct the spatiotemporal dynamics defined in a given multi-dimensional domain. In the investigated problem positions of both sensors and actuators are fixed allowing to delegate the complex system dynamics to echo-state network. Imposing a proper partitioning of the spatial domain, a specific topology of a neural network is used to form a reservoir capable to follow not only temporal but also spatial dynamics of the system. Based on available historical data, neural network model is initially trained and then used to derive the control law in the framework of iterative learning control. The echo-state network can be retrained after a particular control iterate in order to reduce model uncertainty and to fit it to the current operating conditions as much as possible. The performance of the proposed approach is tested and evaluated on the example of the squared clamped plate control.

Output regulation for general heterodirectional linear hyperbolic PDEs coupled with nonlinear ODEs

This paper considers general heterodirectional linear hyperbolic PDEs with boundary actuation and collocated measurement, that are bidirectionally coupled with nonlinear ODEs at the unactuated boundary. An output feedback regulator is designed to have the control output track a reference in the presence of disturbances, with a nonlinear signal model generating the reference and the disturbances. This leads to new challenges for both the observer and controller design. The regulator design makes use of results from output regulation theory for nonlinear lumped-parameter and distributed-parameter systems. The derivation of the state feedback regulator requires solving a new type of regulator equations, which consist of a Cauchy problem for linear and semilinear hyperbolic PDEs. A key component of the novel observer design is a nonlinear retarded observer for a finite-dimensional subsystem. Both the controller and the observer design are systematic in nature and derived in several successive steps, that include backstepping transformations and, most notably, predictions of PDE and ODE states. The latter are shown to be the unique solution of general nonlinear Volterra integro-differential equations. Combining the observer with the state feedback regulator is proven to achieve output regulation for the closed-loop system. A numerical example illustrates and confirms the theoretical results.

Dynamic DNR and Solar PV Smart Inverter Control Scheme Using Heterogeneous Multi-Agent Deep Reinforcement Learning

The conventional volt-VAR control (VVC) in distribution systems has limitations in solving the overvoltage problem caused by massive solar photovoltaic (PV) deployment. As an alternative method, VVC using solar PV smart inverters (PVSIs) has come into the limelight, which can respond quickly and effectively to solve the overvoltage problem by absorbing reactive power. However, the network power loss, that is, the sum of line losses in the distribution network, increases with reactive power. Dynamic distribution network reconfiguration (DNR), which hourly controls the network topology by controlling sectionalizing and tie switches, can also solve the overvoltage problem and reduce network loss by changing the power flow in the network. In this study, to improve the voltage profile and minimize the network power loss, we propose a control scheme that integrates the dynamic DNR with volt-VAR control of PVSIs. The proposed control scheme is practically usable for three reasons: Primarily, the proposed scheme is based on a deep reinforcement learning (DRL) algorithm, which does not require accurate distribution system parameters. Furthermore, we propose the use of a heterogeneous multiagent DRL algorithm to control the switches centrally and PVSIs locally. Finally, a practical communication network in the distribution system is assumed. PVSIs only send their status to the central control center, and there is no communication between the PVSIs. A modified 33-bus distribution test feeder reflecting the system conditions of South Korea is used for the case study. The results of this case study demonstrates that the proposed control scheme effectively improves the voltage profile of the distribution system. In addition, the proposed scheme reduces the total power loss in the distribution system, which is the sum of the network power loss and curtailed energy, owing to the voltage violation of the solar PV output.

Iterative learning based consensus control for distributed parameter type multi-agent differential inclusion systems with time-delay

This paper investigates consensus control problem for a class of distributed parameter type multi-agent differential inclusion systems with state time-delay by utilizing iterative learning control (ILC). Unlike most ILC literature of nonlinear distributed parameter systems that require an identical virtual leader, the virtual leader is iteratively varying in this work and can be described by any follower agent. Both P -type closed-loop and D -type open-loop ILC are proposed for the distributed parameter type multi-agent differential inclusion systems, which enable the output trajectories of each agent to achieve consensus in the sense of W 1 , 2 norm as the iteration number increases. Meanwhile, consensus control theorems for these protocols are established by using Steiner-type selector, Green's formulas and some technical inequalities. Finally, numerical simulations testify the validity of the proposed methods.

Subpredictor-Based Fuzzy Control Design for a Reaction–Diffusion Equation

This article addresses the stabilization of the nonlinear reaction–diffusion equation with an unknown but bounded delay. Based on Takagi–Sugeno (T–S) fuzzy rules, a T–S fuzzy partial differential equation (PDE) model is constructed to describe the nonlinear distributed parameter system. More importantly, we contribute to the large delay compensation and the future state prediction by introducing a chain of subpredictors for the T–S fuzzy PDE model, and the convergence of observation errors is guaranteed as well. Different from the conventional approaches, the proposed observer can compensate a larger delay. To stabilize the system, for the first time, a new subpredictor-based T–S fuzzy control law is suggested by using the proposed observer, which is composed of elementary observers connected in series. The implementation of the subpredictor feedback is simpler than the classical methods that only one of the elementary observers is employed. Via Lyapunov–Krasovskii approach, sufficient exponential stability conditions are established in the framework of linear matrix inequalities. A numerical example is provided to illustrate the effectiveness of theoretical results.

Collision prevention control method for production riser system in deep sea

In the deep-sea oil and gas exploitation process, the adjacent risers under the influence of environmental load and shielding effect will produce large amplitude vibration, which may lead to collision and damage to the riser structure. However, there is a lack of study on active collision-preventing control based on vessel flexible riser array system. This paper aims to better prevent the collision between vessel-risers and increase the motion spacing. Preliminarily, we model the vessel-risers system composed of top production vessel, riser array and environment load based on Hamilton's principle and the improved shielding effect model. In the next part, considering the control spillover problem, we design the collision-preventing boundary controllers directly for distributed parameter system (DPS) without discretization or simplification. And the uniform boundedness of the control system is strictly proved by the Lyapunov direct method. Eventually, we verify the effectiveness and feasibility of the collision-preventing controllers by simulating the system in different ocean currents. At the same time, the parameters of the collision-preventing controllers are independent of those of the riser array system, which ensures the robustness of the system.

Influence of lumped mass and rotary inertia on seismic isolated post equipment

This paper addresses a need to lessen the effects of seismic activity on heavy functional components installed on the top of post electrical equipment. A theoretical model was developed based on a distributed parameter system considering the lumped mass and the moment of inertia. Finite element analysis and shaking table tests were carried out on an ultra-high-voltage (UHV) bypass switch (BPS) with wire rope and viscous dampers to validate the theoretical model. Parameters analysis on seismic responses and isolation optimization based on rotational nonlinear constraints were conducted. Results show that the seismic responses of moment and displacement showed a strong linear law with the increase of lumped mass, but the acceleration response had a nonlinear decreasing trend. Notably, the moment of inertia effects shows a trend of increasing and then decreasing on moment responses. The composite isolation of stiffness and viscous damping can reduce the seismic response of equipment. For optimization analysis of seismic isolation, the ratio between variations of viscous damping and rotational stiffness along the steepest descent line are selected as a criteria, which can be used to identify the most influential parameter. Parametric analysis provides the optimal parameters for the seismic isolation, which are recommended for target-oriented control in engineering design.

Spatiotemporal kernel-local-embedding modeling approach for nonlinear distributed parameter systems

In actual distributed parameter systems (DPSs), each spatial point has nonlinear energy transfer with its local neighbor points. Also, this energy transfer is affected by the past states. However, these properties are often ignored by most of modeling methods, which causes these methods ineffective in modeling of DPSs. Aiming for this problem, a spatiotemporal kernel-local-embedding (STKLLE) Modeling approach is proposed here to reconstruct the nonlinear spatiotemporal dynamics of DPSs. First, in order to present the complex dynamics on space, a STKLLE strategy is developed to extract space basis functions (SBFs). On the one hand, this STKLLE method represents the energy transfer relation with its neighboring points and maintains this local relation in model. On the other hand, it considers the influence of the adjacent past states to the current state. Then, using T–S fuzzy algorithm, a temporal model is designed to represent the temporal dynamics of DPSs in each sampling period. Integrating these SBFs and the temporal fuzzy model, a spatiotemporal model is constructed to well present and predict the nonlinear spatiotemporal dynamics in DPSs. Through the actual experiment on Lithium-ion batteries and heating oven, the effectiveness of this proposed model is detailly verified, and quantitative comparisons with several data-driven modeling algorithms are further carried out to demonstrate the model efficiency.

Adaptive Event-Triggered [formula omitted] Control of Semi-Markov Jump Distributed Parameter Systems

This paper focuses on the problem of adaptive event-triggered L2−L∞ control for distributed parameter systems with semi-Markov jump parameters. An event-triggered transmission scheme, whose threshold function can be adaptively adjusted, is established to decrease the frequency of data transmission. Simultaneously, the utilization of limited network bandwidth resources is also improved due to plenty of “unnecessary” packets being discarded before accessing networks. Furthermore, the jumping of stochastic parameters in networks can be described by a semi-Markov jump model, in which the sojourn-time is considered subject to the Weibull distribution instead of the exponential distribution. Based on the aforesaid discussions, a mode-dependent controller is designed under an adaptive event-triggered scheme. Whereafter, some criteria are constructed based on the Lyapunov stability theory to guarantee stochastic stability and a prescribed L2−L∞ performance of the system. Ultimately, two simulation examples are provided to verify the feasibility of the proposed design approach.

State prediction of distributed parameter systems based on multi-source spatiotemporal information

To predict the process states of nonlinear distributed parameter systems (DPS) using various process variables, a novel multi-source spatiotemporal modeling method is proposed in this paper to improve conventional temporal modeling methods. To tackle the challenge of modeling industrial process data of DPS with multi-source spatiotemporal characteristics, a multi-source spatiotemporal network (MS-STN) model, which is the integration of a long short-term memory (LSTM) network to extract information containing temporal characteristics and a convolutional long short-term memory (ConvLSTM) network to extract information containing spatiotemporal characteristics, is constructed. The comprehensive use of various process information is beneficial to improving the fitting accuracy of the model, and the generalization ability of the model can be enhanced at the same time. To prevent the gradient vanishing or gradient explosion in presenting complex spatiotemporal data due to the increase of network layers, a model structure of the residual network based on ConvLSTM is proposed in performing model training. Finally, the industrial ethylene oxychlorination reaction process is taken as an example. The experimental results of predicting the temperature of the reaction tube well demonstrate the effectiveness of the proposed method.

Two-Dimensional Spatial Construction for Online Modeling of Distributed Parameter Systems

A 2-D spatial construction method is proposed for the online modeling of distributed parameter systems (DPSs), such as battery thermal process. The proposed method can combine the advantages of spectral method and Karhunen–Loève decomposition (KLD) method. First, the continuous spatial basis functions are designed by the 2-D spatial construction to keep the information between sensing locations. With the 2-D space-time separation and recursive learning, the derived model can preserve the couplings between spatial dimensions and update over time. The radial basis function network is utilized to identify the low-dimensional temporal dynamics. After the space-time synthesis, the constructed spatiotemporal model can provide continuous modeling of the DPS with satisfactory performance. Convergence analysis has been carried out, which proves that the proposed method can guarantee bounded errors. Finally, simulations and experiments on a pouch-type lithium-ion battery with unknown partial differential equations prove the effectiveness of the proposed method.

Trajectory Tracking Control for a Three-Dimensional Flexible Wing

This brief mainly considers trajectory tracking and vibration suppression for a 3-D flexible wing. The dynamical model of the flexible wing is regarded as a distributed parameter system, which is described by partial differential equations and ordinary differential equations. A control strategy regulates the flexible wing to track the desired trajectory by controlling two angles. Meanwhile, two active boundary controllers are proposed to restrain the vibrations both in bending and twisting. By using Lyapunov’s direct method, the stability of the flexible wing system can be ensured. Numerical simulations based on the finite-difference method demonstrate the effectiveness of the proposed control schemes.

Mobile Sensor Networks for Finite-Time Distributed H∞ Consensus Filtering of 3D Nonlinear Distributed Parameter Systems with Randomly Occurring Sensor Saturation

This paper is concerned with designing a distributed bounded H∞ consensus filter to estimate an array of three-dimensional (3D) nonlinear distributed parameter systems subject to bounded perturbation. An optimization framework based on mobile sensing is proposed to improve the performance of distributed filters. The measurement output is obtained from a mobile sensor network, where a phenomenon of randomly occurring sensor saturation is taken into account to reflect the reality in a mobile networked environment. A sufficient condition is established by utilizing operator-dependent Lyapunov functional for the filtering error system to be finite-time bounded. Note that the velocity law of each mobile sensor is included in this condition. The effect from the exogenous perturbation to the estimation accuracy is guaranteed at a given level by means of H∞ consensus performance constraint. Finally, simulation examples are presented to demonstrate the applicability of the theoretical results.

Iterative learning control for time-delay nonlinear hyperbolic distributed parameter systems

In this paper, we study the application of iterative learning control to a class of nonlinear varying time-delay equations. The handled procedure is the distributed parameter system, hyperbolic type. The selected plan is based on PD-type iterative learning control with initial state learning. Initially, we present the equation and the control law utilised. Subsequently, we presented some dilemmas. Then, sufficient conditions for monotone convergence of the error under the proper assumption are found. Also, a detailed convergence analysis is given based on the once-offered lemmas and Gronwall inequality. Finally, we show the usefulness of the method utilising a numerical model. Abbreviations DPS: distributed parameter system; ILC: iterative learning control; PDE:partial differential equation; DPS: partial difference system; PD: proportional derivative

Frequency response-based decoupling tuning for feedforward compensation ADRC of distributed parameter systems

A practical tuning method is proposed via frequency response or even cut-off frequency for active disturbance rejection control (ADRC) of distributed parameter systems (DPSs), whose models are hard to get but frequency characteristics are easy to measure. Moreover, a novel control structure, feedforward compensation ADRC (FC-ADRC), is presented to decouple the tuning of tracking and disturbance rejection (DR). The frequency response-based tuning method initializes the parameters and then iterates them to the optimal solution by following a simple rule. The basic idea of FC-ADRC is skillful. The closed-loop system is tuned to the desired dynamic via ADRC. Such a control system is a platform for a compensation block to be combined in cascade. ADRC only rejects disturbance while the feedforward compensation purely tracks. Simulation of six accepted irrational transfer functions (ITFs) shows the frequency response-based tuning for FC-ADRC performs better than compared control methods in robustness and performance of tracking and DR. The stability is proved based on the Nyquist criterion for DPSs. Two experiments verify the effectiveness of decoupling tuning and frequency response-based tuning. Therefore, frequency response-based tuning for FC-ADRC is not only a skillful and effective control structure but also a practical and compact method.

Spatial-Construction-Based Abnormality Detection and Localization for Distributed Parameter Systems

A spatial-construction-based fault diagnosis method is proposed to detect and locate the abnormality for unknown distributed parameter systems (DPSs). To accurately locate the abnormality, the continuous spatial basis functions (SBFs) are derived by the proposed spatial construction method from empirical data. Theoretical analysis proves that the B-spline curve is a proper solution to the spatial construction problem. Two new statistics are constructed based on the derived continuous SBFs and the improved independent component analysis algorithm. The abnormality can be timely detected according to the reference signals derived by the central limit theorem and hypothesis testing. With the continuous SBFs, the probability distribution of statistic contribution can be constructed to reveal the actual position of the abnormality. The proposed method can timely detect and locate the abnormality under fewer sensors without the knowledge of PDE and boundary conditions. The internal short circuit experiment on a lithium-ion battery demonstrates the effectiveness and superiority of the proposed method.

Optimal Operation of an Industrial Natural Gas Fired Natural Draft Heater

In this work, a custom dynamic mathematical model of an industrial vertical-cylindrical type natural gas fired natural draft heater is developed using gPROMS® ProcessBuilder®. The integrated model comprises sub-models for each of the distinct sections of the fired heater which are connected by mass and energy flows. The temperature profiles of the tubular coils and the process fluid, a heat transfer fluid (HTF) are modelled using the distributed parameter system (DPS) in the axial direction (1D). The flue gas temperature in each section is modelled using the lumped parameter approach. Published empirical methods and correlations are used for estimating some unknown model parameters. The resulting model is a system of partial differential-algebraic equations (PDAEs) and serves as a basis for conducting an optimisation study to aid decision-making and to identify the best operating conditions within the specified constraints that minimise the daily operational costs. Through process simulation studies, the model predictions are adjusted to closely approximate collected actual plant data. It is demonstrated through the optimisation study that significant reduction in fuel gas consumption can be achieved compared to the current operating consumption levels. The developed models can be extended for use by other hydrocarbon processing plant operators with slight modifications, by specifying geometric parameters, HTF thermophysical properties, fuel gas composition and properties, among others.

Adaptive vibration control of a flexible structure based on hybrid learning controlled active mass damping

Natural disasters such as earthquakes and strong winds will lead to vibrations in ultra-high or high-rise buildings and even the damages of the structures. The traditional approaches resist the destructive effects of natural disasters through enhancing the performance of the structure itself. However, due to the unpredictability of the disaster strength, the traditional approaches are no longer appropriate for earthquake mitigation in building structures. Therefore, designing an effective intelligent control method for suppressing vibrations of the flexible buildings is significant in practice. This paper focuses on a single-floor building-like structure with an active mass damper (AMD) and proposes a hybrid learning control strategy to suppress vibrations caused by unknown time-varying disturbances (earthquake, strong wind, etc.). As the flexible building structure is a distributed parameter system, a novel finite dimension dynamic model is firstly constructed by assumed mode method (AMM) to effectively analyze the complex dynamics of the flexible building stucture. Secondly, an adaptive hybrid learning control based on full-order state observer is designed through back-stepping method for dealing with system uncertainties, unknown disturbances and immeasurable states. Thirdly, semi-globally uniformly ultimate boundedness (SGUUB) of the closed-loop system is guaranteed via Lyapunov’s stability theory. Finally, the experimental investigation on Quanser Active Mass Damper demonstrates the effectiveness of the presented control approach in the field of vibration suppression. The research results will bring new ideas and methods to the field of disaster reduction for the engineering development.

Iterative learning control for hyperbolic distributed parameter systems based on sensor–actuator networks

AbstractThis paper proposes two kinds of iterative learning control (ILC) schemes for a class of the distributed parameter systems based on sensor–actuator networks which can be described by hyperbolic partial differential equations. A D‐type ILC algorithm is first considered and the convergent condition of the output error is obtained via the contraction mapping methodology. Then, the PD‐type ILC algorithm is considered in this hyperbolic distributed parameter systems based on sensor–actuator networks. Finally, a cable equation with air and structural damping is given to illustrate the effectiveness of the proposed methods.