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It is very difficult to control the distributed parameter system (DPS) for consistent spatial performance. In this paper, a dual scale spatio‐temporal control is designed for the DPS to achieve a consistent performance across the entire workspace under unknown exogenous disturbances. First, the generalized “spatial observer” should be designed under spectral decomposition/synthesis, to act as the nominal model of the DPS, through which the spatial mismatch between the model and the process could be estimated. Then a distributed disturbance compensator can be constructed to suppress all the undesirable spatial disturbance through the inner loop, and the compensated system will become closer to the nominal model and easier to control. Third, a dual controller will be designed in the outer loop for the final consistent spatial performance. Since the spatial performance is mainly affected by the dominant dynamics on the slow scale, a convex optimization algorithm can be effectively established in terms of nonlinear matrix inequalities for the dual controller. In this way, the nonlinear optimization problem is solved by converting it into the problem of a linear matrix inequalities with constraints. Besides, the spatio‐temporal state variable of the controlled plant is demonstrated to converge in Hilbert space. The feasibility and effectiveness of the proposed control method are verified by temperature control of a catalytic rod, a benchmark in chemical reactors. [ABSTRACT FROM AUTHOR]

This article investigates robust non-fragile event-triggered sampled-data fuzzy (ETSDF) control for uncertain nonlinear delayed distributed parameter systems. Initially, a T-S fuzzy delayed partial differential equation model is presented to exactly describe the uncertain nonlinear delayed distributed parameter systems (DPS). secondly, a robust non-fragile ETSDF control strategy is proposed to reduce the unnecessary SD and cope with the uncertainties in controller and system. Then, based on an appropriate Lyapunov functional, the exponential stability conditions of closed-loop nonlinear delayed DPS via linear matrix inequalities are presented. Lastly, one example is presented to illustrate the design method. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The distributed thermal processes are widely present in various industrial operations, but the presence of time delay effect and unknown model information make achieving fast and timely fault detection challenging. Furthermore, the involvement of spatiotemporal coupled data in measurement processes further exacerbates the situation. To solve these problems, this paper proposes a data-driven fault detection and location method for thermal processes described by distributed parameter systems (DPS). Firstly, a Time/Space separation is employed to decoupling the spatio-temporal data into spatial basis functions and temporal coefficients. Subsequently, dynamic partial least squares (DPLS) is employed to obtain the temporal information of the model with fault-free data. Monitoring statistics in both the temporal and spatial domains are then constructed, and their thresholds are estimated by kernel density function. Finally, an online strategy for fault detection and location is presented. The method was validated on the catalytic rod, and an experimental snap curing oven. • Dynamic partial least squares (DPLS) as a data-driven method for fault detection and location in distributed thermal processes. • The proposed method can fast complete the detection and solves the problem of time delay effect in fault diagnosis. • The proposed method does not require model information and can independently accomplish fault detection and location. • Compared to traditional methods, DPLS offers shorter response time and higher accuracy. [ABSTRACT FROM AUTHOR]

Modeling high-spatial dimensional (high-D) distributed parameter systems (DPSs) is very difficult because of the spatially distributed characteristic and complex spatiotemporal coupling. In this article, a new framework based on high-order singular vector decomposition (HOSVD) is proposed to model a high-D DPS. A modified HOSVD is designed for separation of time and multiple spatial variables. It can well preserve the spatially distributed nature of the high-D DPS. It also considers the interaction across different spatial modes, which is an important part of spatiotemporal coupling in the high-D DPS. Experiments of a two-spatial dimensional thermal curing process are used to verify the effectiveness of the proposed method. An average prediction error near 1% of the curing temperature can be achieved. [ABSTRACT FROM AUTHOR]

Compared to the fault detection problem, fault localization for spatially distributed processes is physically intuitive but was seldom studied. The main challenge lies in the contradiction between the spatially distributed nature of the processes and a limited number of sensors that can be placed in the space for applications. In this article, we make the first attempt to systematically study the fault localization problem for a class of nonlinear spatially distributed processes without knowing any prior information of the spatial distribution function of the spatio‐temporal fault. The main contribution is that a spatial mapping filter is first designed to generate a distributed residual signal which contains spatial information while using limited sensor measurements. The residual evaluation procedure is also conducted in a distributed manner. With these two parts, a systematic methodology framework is constructed and analyzed rigorously. Finally, the performance of the proposed method is evaluated on a faulty catalytic rod, which widely exists in chemical engineering. [ABSTRACT FROM AUTHOR]

Identification of abnormal source hidden in distributed parameter systems (DPSs) belongs to the category of inverse source problems. It is important in industrial applications but seldom studied. In this article, we make the first attempt to investigate the abnormal spatio-temporal (S-T) source identification for a class of DPSs. An inverse S-T model for abnormal source identification is developed for the first time. It consists of an adaptive state observer for source identification and an adaptive source estimation algorithm. One major advantage of the proposed inverse S-T model is that only the system output is utilized, without any state measurement. Theoretic analysis is conducted to guarantee the convergence of the estimation error. Finally, the performance of the proposed method is evaluated on a heat transfer rod with an abnormal S-T source. [ABSTRACT FROM AUTHOR]

For complex distributed parameter systems (DPSs) with strong nonlinearities and time-varying dynamics, the conventional spatiotemporal modeling methods become ill-suited since the elementary assumption that the process data follow a unimodal Gaussian distribution usually becomes invalid. In this paper, a multimode method is proposed for modeling of such systems. First, the original operating space is partitioned along the time dimension into several subspaces via modified dissimilarity analysis. Each subspace represents the local spatiotemporal characteristics of the original system. Second, the Karhunen–Loève decomposition (KLD)-based spatiotemporal modeling approach is applied to approximate the local dynamics of each subspace. Finally, an ensemble model is obtained using the soft weighting sum of the local ones, where the corresponding weights are calculated by principal component regression. By properly decomposing the original space into several local parts, the ensemble model is capable of handling the strong nonlinearities and time-varying dynamics of the system. The validity and efficiency of the proposed method are verified on two representative applications: 1) a one-dimensional parabolic catalytic rod and 2) a two-dimensional curing thermal process. The experimental results show that the proposed method provides a superior performance regarding modeling accuracy compared to several baselines. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper introduces a fuzzy control (FC) under spatially local averaged measurements (SLAMs) for nonlinear-delayed distributed parameter systems (DDPSs) represented by parabolic partial differential-difference equations (PDdEs), where the fast-varying time delay and slow-varying one are considered. A Takagi–Sugeno (T–S) fuzzy PDdE model is first derived to exactly describe the nonlinear DDPSs. Then, by virtue of the T–S fuzzy PDdE model and a Lyapunov–Krasovskii functional, an FC design under SLAMs, where the membership functions of the proposed FC law are determined by the measurement output and independent of the fuzzy PDdE plant model, is developed on basis of spatial linear matrix inequalities (SLMIs) to guarantee the exponential stability for the resulting closed-loop DDPSs. Lastly, a numerical example is offered to support the presented approach. [ABSTRACT FROM AUTHOR]

• Spatial multivariable SVR based 3-D fuzzy modeling methodology is proposed for distributed parameter systems. • Multivariable SVR with spatial kernel functions is proposed to cope with a set of spatiotemporal data. • Spatial multivariable SVR builds up a complete 3-D fuzzy rule-base. • 3-D fuzzy model is constructed in the form of data-driven design. Many industrial processes have significant spatiotemporal dynamics and they are usually called distributed parameter systems (DPSs). Modeling such system is challenging due to its nonlinearity, time-varying dynamics, and spatiotemporal coupling. Using model reduction techniques, traditional DPS modeling methods usually reduce an infinite-dimensional system to a finite-dimensional system, which leads to unknown nonlinearity and unmodeled dynamics. The modeling method and the established model are hard to understand. Here, we propose a spatial multivariable support vector regression (SVR) based three-domain (3-D) fuzzy modeling method for complex nonlinear DPSs. The proposed 3-D modeling method integrates the time-space separation and time-space synthesis into a 3-D fuzzy model. Therefore, it does not require model reduction and owns the capability of linguistic interpretability. A spatial multivariable SVR with spatial kernel functions is proposed to deal with spatiotemporal data. The spatial fuzzy basis functions from a 3-D fuzzy model are spatial kernel functions for a spatial multivariable SVR, which satisfy Mercy theorem. Hence, the spatial multivariable SVR can be directly employed to build up a complete 3-D fuzzy rule-base of the 3-D fuzzy model. The proposed modeling method integrates the merits of learning ability from a spatial multivariable SVR and fuzzy space processing and fuzzy linguistic expression from a 3-D fuzzy model. The proposed 3-D fuzzy modeling method is successful applied to a simulated rapid thermal processing system. In comparison with several newly developed modeling methods for DPSs, the simulation results validate the superiority of the proposed modeling method. [ABSTRACT FROM AUTHOR]

The aim of this article is to establish a novel boundary antidisturbance control to dampen the oscillation of a spatially nonlinear flexible string system influenced by unknown disturbances. To realize this, new disturbance rejection controllers are constructed to effectively suppress the external disturbances for vibration reduction with the help of a newly designed disturbance observer. Adopting Lyapunov direct method, we ensure that the derived control system is uniformly bounded stable. Simulations are also performed to demonstrate the feasibility and validity of the suggested strategy. [ABSTRACT FROM AUTHOR]

An incremental spatiotemporal learning scheme is proposed for online modeling of distributed parameter systems (DPSs). A novel incremental learning method is developed to recursively update the spatial basis functions and the corresponding temporal model based on the Karhunen–Loève decomposition for time-space separation. The time-space synthesis continually evolves by adding new increment data with more updated information and revising the existing parameters of the dynamic system. In this way, the spatiotemporal structure is inherited and updated efficiently as output data increases over time. The adaptive nature of this evolving structure makes it promising for online modeling of DPSs under streaming data environment. The proposed incremental modeling scheme is evaluated on the classical benchmark of a catalytic rod problem. The simulation results demonstrate the viability and efficiency of the proposed method for online modeling of DPSs. [ABSTRACT FROM AUTHOR]

In this paper, the exponential stabilization problem is addressed for a class of nonlinear parabolic partial differential equation (PDE) systems via sampled-data fuzzy control approach. Initially, the nonlinear PDE system is accurately represented by the Takagi–Sugeno (T–S) fuzzy PDE model. Then, based on the T–S fuzzy PDE model, a novel time-dependent Lyapunov functional is used to design a sampled-data fuzzy controller under spatially point measurements such that the closed-loop fuzzy PDE system is exponentially stable with a given decay rate. The stabilization conditions are presented in terms of a set of linear matrix inequalities (LMIs). Finally, simulation results on the control of the diffusion equation and the FitzHugh–Nagumo (FHN) equation to illustrate the effectiveness of the proposed design method. [ABSTRACT FROM AUTHOR]

In this paper, a novel method is developed to detect fault and identify its spatial location for a class of parabolic distributed parameter systems (DPSs) with limited sensors. The normal situation of the DPSs is first modeled under limited sensors. Then, the spatio–temporal dynamics of DPSs is decoupled under time/space separation. After the temporal coefficients are further decomposed using the independent component analysis method, the dominant temporal components are taken and then the spatial residual errors are used to form two monitoring statistics. Using the kernel density function, the confidence bounds of these two statistics (fault free) can be established as the reference signals. Unlike model-based fault detection methods that require explicit mathematical models of the processes, the proposed method is data driven and only utilizes the separable characteristic of parabolic DPSs. Experiments on a typical parabolic process and a snap curing oven are used to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Distributed parameter systems widely exist in many industrial thermal processes. Estimation of their temperature distribution in the entire operating area is not easy as the dynamics are time/space coupled, and there are only a few sensors available for measurement. In this paper, an effective spatiotemporal model is proposed for prediction of the temperature distribution. After the dominant spatial basis functions are obtained by the Karhunen–Loève method under the time/space separation, a kernel-based random vector functional-link network is developed for learning unknown temporal dynamics. After time/space synthesis, the spatiotemporal model can be constructed to effectively estimate the temperature distribution in high learning speed. The generalization performance of this model is discussed using Rademacher complexity. Simulations on two typical industrial thermal processes show that the proposed method has superior model performance than neural networks and least square support vector machine. [ABSTRACT FROM AUTHOR]

Summary: In this paper, an H∞ sampled‐data control problem is addressed for semilinear parabolic partial differential equation (PDE) systems. By using a time‐dependent Lyapunov functional and vector Poincare's inequality, a sampled‐data controller under spatially averaged measurements is developed to stabilize exponentially the PDE system with an H∞ control performance. The stabilization condition is presented in terms of a set of linear matrix inequalities. Finally, simulation results on the control of the diffusion equation and the FitzHugh‐Nagumo equation are given to illustrate the effectiveness of the proposed design method. [ABSTRACT FROM AUTHOR]

Data-based spatio-temporal modeling has rapidly developed over the past ten years. However, traditional spatio-temporal modeling methods will encounter some uncertainty caused by model reduction. In addition, the established model is complicated and short of linguistic interpretability. In this study, a novel three-dimensional (3-D) fuzzy modeling framework without model reduction is proposed and a new 3-D fuzzy modeling method based on clustering and support vector regression is developed. This method is based on a 3-D fuzzy system that naturally fuses time/space separation and time/space synthesis into a unified framework. Utilizing the machine learning algorithms (clustering and support vector regression), a 3-D fuzzy system is constructed for modeling an unknown nonlinear distributed parameter system. The advantages of the proposed modeling method over the traditional spatio-temporal modeling method are linguistic interpretability and no reliance on model reduction. The proposed modeling method consists of three steps. First, the nearest neighborhood clustering algorithm is used to learn initial structure model of antecedent sets of 3-D fuzzy rules. Then, similarity measure is used to simplify the initial structure via combining similar fuzzy sets and similar fuzzy rules. Finally, a support vector regression algorithm is applied to calculate spatial functions in the consequent sets of 3-D fuzzy rules. The simulation results demonstrate the effectiveness of the proposed modeling method. [ABSTRACT FROM AUTHOR]

The temperature distribution of a lithium-ion battery (LIB) belongs to a nonlinearly distributed parameter system (DPS), which is infinite dimensional in the space direction. Modeling of such systems often leads to the following challenges: time/space-coupled dynamics; time-varying dynamics; and spatial nonlinearity. For the first two challenges, Karhunen–Loève (KL) decomposition based data-driven spatiotemporal models have been widely researched and successfully applied to industrial thermal processes. However, this method is a global linear model reduction method that ignores the nonlinear properties of measurements. This will prohibit the model performance of a strong nonlinear DPS, which has strong spatial nonlinearity refers to the aforementioned third challenge. To address this problem, a local-properties-embedding-based modeling method is developed for the nonlinear DPS. First, the finite-dimensional nonlinear spatial basis functions that can be the representative of the nonlinear feature of the original space are learned by the local-properties-embedding-based method. Then, the low-dimensional representative can be derived using the time/space separation and the unknown temporal coefficients can be identified through the traditional neural learning algorithm. Finally, the spatiotemporal temperature distribution can be reconstructed by the time/space synthesis. Since the nonlinear structure feature of the spatiotemporal datasets has been considered, the proposed modeling method can be more effective than the traditional KL-based method for modeling the nonlinear DPS. Numerical simulations on the LIB showed that the proposed methods are more robust than the KL-based method in both the time direction and the space direction. [ABSTRACT FROM AUTHOR]

This paper presents a deep learning-based model reduction method for distributed parameter systems (DPSs). The proposed method includes three phases. In phase I, numerical or experimental data of the spatiotemporal distribution is reduced into low-dimensional representations using the deep auto-encoder (DAE). In phase II, the low-dimensional representations are used to establish the reduced-order model. In phase III, the reduced model is then used to reconstruct the high-dimensional DPS. Experimental studies are conducted to validate the proposed method. The proposed method is compared with the classical proper orthogonal decomposition method and demonstrates better modeling accuracy and efficiency in the experiments. [ABSTRACT FROM PUBLISHER]

Many industrial processes belong to nonlinear distributed parameter systems (DPS) with significant spatio-temporal dynamics. They often work at multiple operating points due to different production and working conditions. To obtain a global model, the direct modeling and experiments in a large operating range are often very difficult. Motivated by the multi-modeling, a fuzzy-based spatio-temporal multi-modeling approach is proposed for nonlinear DPS. To obtain a reasonable operating space division, a priori information and the fuzzy clustering are used to decompose the operating space from coarse scale to fine scale gradually. To reduce the dimension in the local spatio-temporal modeling, the Karhunen–Loève method is used for the space/time separation. Both multi-modeling and space/time separation can reduce the modeling complexity. Finally, to get a smooth global model, a three-domain (3D) fuzzy integration method is proposed. Using the proposed method, the model accuracy will be improved and the experiments become easier. The effectiveness is verified by simulations. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of fuzzy boundary control design for a class of nonlinear distributed parameter systems which are described by semilinear parabolic partial differential equations (PDEs). Both distributed measurement form and collocated boundary measurement form are considered. A Takagi–Sugeno (T–S) fuzzy PDE model is first applied to accurately represent the semilinear parabolic PDE system. Based on the T–S fuzzy PDE model, two types of fuzzy boundary controllers, which are easily implemented since only boundary actuators are used, are proposed to ensure the exponential stability of the resulting closed-loop system. Sufficient conditions of exponential stabilization are established by employing the Lyapunov direct method and the vector-valued Wirtinger's inequality and presented in terms of standard linear matrix inequalities. Finally, the advantages and effectiveness of the proposed control methodology are demonstrated by the simulation results of two examples. [ABSTRACT FROM PUBLISHER]

The guaranteed cost distributed fuzzy ( GCDF) observer-based control design is proposed for a class of nonlinear spatially distributed processes described by first-order hyperbolic partial differential equations ( PDEs). Initially, a T-S fuzzy hyperbolic PDE model is proposed to accurately represent the nonlinear PDE system. Then, based on the fuzzy PDE model, the GCDF observer-based control design is developed in terms of a set of space-dependent linear matrix inequalities. In the proposed control scheme, a distributed fuzzy observer is used to estimate the state of the PDE system. The designed fuzzy controller can not only ensure the exponential stability of the closed-loop PDE system but also provide an upper bound of quadratic cost function. Moreover, a suboptimal fuzzy control design is addressed in the sense of minimizing an upper bound of the cost function. The finite difference method in space and the existing linear matrix inequality optimization techniques are used to approximately solve the suboptimal control design problem. Finally, the proposed design method is applied to the control of a nonisothermal plug-flow reactor. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2366-2378, 2013 [ABSTRACT FROM AUTHOR]

Many industrial processes are nonlinear distributed parametersystems(DPSs). Data-based spatiotemporal modeling is required for analysisand control when the first-principles model is unknown. Because aDPS is infinite-dimensional and time–space coupled, a low-ordermodel is necessary for prediction and control in practice. For low-ordermodeling, traditional principal component analysis (PCA) is oftenused for dimension reduction and time–space separation. However,it is a linear method and leads to only one set of fixed spatial basisfunctions. Therefore, it might not be always effective for nonlinearsystems. In this study, a spatiotemporal multimodeling approach isproposed for unknown nonlinear DPSs. First, multimodel decompositionis performed, where probabilistic PCA (PPCA) is used to obtain multiplesets of spatial basis functions from the experimental data by maximizinga likelihood function. Using these multiple sets of PCA spatial basesfor time–space separation, the high-dimensionality spatiotemporaldata can be reduced to multiple sets of low-dimensionality temporalseries. Then, multiple low-order neural models can be easily establishedto model these local dynamics. Finally, the original spatiotemporaldynamics can be reconstructed by multimodel synthesis. Because theproposed spatiotemporal modeling approach involves a multimodelingmechanism, it can achieve better performance than the traditionalPCA-based single-modeling for nonlinear DPSs, which is demonstratedby numerical simulations. [ABSTRACT FROM AUTHOR]

Abstract: Many industrial processes belong to distributed parameter systems (DPS) that have strong spatial–temporal dynamics. Modeling of DPS is difficult but essential to simulation, control and optimization. The first-principle modeling for known DPS often leads to the partial differential equation (PDE). Because it is an infinite-dimensional system, the model reduction (MR) is very necessary for real implementation. The model reduction often works with selection of basis functions (BF). Combination of different BF and MR results in different approaches. For unknown DPS, system identification is usually used to figure out unknown structure and parameters. Using various methods, different approaches are developed. Finally, a novel kernel-based approach is proposed for the complex DPS. This paper provides a brief review of different DPS modeling methods and categorizes them from the view of time–space separation. [ABSTRACT FROM AUTHOR]

Abstract: It is difficult to model a distributed parameter system (DPS) due to the infinite-dimensional time/space nature and unknown nonlinear uncertainties. A low-dimensional and simple nonlinear model is often required for practical applications. In this paper, a spatio-temporal Volterra model is proposed with a series of spatio-temporal kernels for modeling unknown nonlinear DPS. To estimate these kernels, they are expanded onto spatial and temporal bases with unknown coefficients. To reduce the model dimension and parametric complexity in the spatial domain, the Karhunen–Loève (KL) method is used to find the dominant spatial bases. To reduce the parametric complexity in the temporal domain, the Laguerre polynomials are selected as temporal bases. Next, using the Galerkin method, this spatio-temporal modeling becomes a linear regression problem. Then unknown parameters can be easily estimated using the least-squares method in the temporal domain. After the time/space synthesis, the spatio-temporal Volterra model can be constructed. The convergence of parameter estimation can be guaranteed under certain conditions. This model has a low-dimensional and simple nonlinear structure, which is useful for the prediction and control of the DPS. The simulation and experiment demonstrate the effectiveness of the proposed modeling method. [Copyright &y& Elsevier]

An interval-valued fuzzy logic controller (I-V FLC) is presented to control a class of nonlinear distributed parameter systems. The proposed FLC is inspired by human operators' knowledge or expert experience to control a distributed parameter process from the point of view of overall space domain. Based on spatial fuzzy set, the I-V FLC employs a centralized rule base over the space domain. Using spatial membership degree fusion operation, the I-V FLC can compress spatial input information into interval-valued fuzzy sets and then execute an interval-valued rule inference mechanism; thereby the I-V FLC has the capability to process spatial information over the space domain. Compared with traditional FLCs, the I-V FLC can improve its control performance due to its increased ability to express and process spatial information. The I-V FLC is successfully applied to a catalytic packed-bed reactor and compared with the traditional FLCs. The results demonstrate its effectiveness to control the unknown nonlinear distributed parameter process. [ABSTRACT FROM AUTHOR]

Abstract: A multi-variable fuzzy logic controller (FLC) is proposed to control a class of distributed parameter systems (DPSs). When a DPS is transformed into finite-dimensional ordinary differential equations (ODEs) by using time/space separation, each ODE can be considered as a subsystem. According to design strategy of conventional FLC, one FLC should be designed for one subsystem. It will be very complex because there are many subsystems. In order to reduce design complexity, only a MF and a rule base are designed in the controller. For other subsystems or ODEs, their MFs can be designed equivalently by introducing scaling factors. Then, the proposed FLC has ability to control multi-variable processes. At last, the proposed FLC is applied to control a rod catalytic reaction process. The simulation results demonstrate the effectiveness of the proposed fuzzy control strategy. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the problem of robustly stochastically exponential stability and stabilization for a class of distributed parameter systems described by uncertain linear first-order hyperbolic partial differential equations (FOHPDEs) with Markov jumping parameters, for which the manipulated input is distributed in space. Based on an integral-type stochastic Lyapunov functional (ISLF), the sufficient condition of robustly stochastically exponential stability with a given decay rate is first derived in terms of spatial differential linear matrix inequalities (SDLMIs). Then, an SDLMI approach to the design of robust stabilizing controllers via state feedback is developed from the resulting stability condition. Furthermore, using the finite difference method and the standard linear matrix inequality (LMI) optimization techniques, recursive LMI algorithms for solving the SDLMIs in the analysis and synthesis are provided. Finally, a simulation example is given to demonstrate the effectiveness of the developed design method. [Copyright &y& Elsevier]

Abstract: Modeling of distributed parameter processes is a challenging problem because of their complex spatio-temporal nature, nonlinearities and uncertainties. In this study, a spatio-temporal Hammerstein modeling approach is proposed for nonlinear distributed parameter processes. Firstly, the static nonlinear and the distributed dynamical linear parts of the Hammerstein model are expanded onto a set of spatial and temporal basis functions. In order to reduce the parametric complexity, the Karhunen–Loève decomposition is used to find the dominant spatial bases with Laguerre polynomials selected as the temporal bases. Then, using the Galerkin method, the spatio-temporal modeling will be reduced to a traditional temporal modeling problem. Finally, the unknown parameters can be easily estimated using the least squares estimation and the singular value decomposition. In the presence of unmodeled dynamics, a multi-channel modeling framework is proposed to further improve the modeling performance. The convergence of the modeling can be guaranteed under certain conditions. The simulations are presented to show the effectiveness of this modeling method and its potential to a wide range of distributed processes. [Copyright &y& Elsevier]

Abnormality localization for industrial processes described by distributed parameter systems (DPSs) is vital but seldom studied to the best of our knowledge. In this paper, a systematic framework is proposed to address this problem for a class of linear parabolic DPSs using a limited number of in-domain measurements plus one boundary measurement rather than the full-state measurement. The proposed methodology consists of an abnormality detection filter (ADF) and an abnormality localization filter (ALF) design based on the backstepping techniques and eigenspectrum. For the detection purpose, the residual is evaluated in a lumped manner; For the localization purpose, a distributed residual is first constructed and then evaluated in a distributed manner. Numerical simulations on a heat transfer rod are conducted to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: An effective modeling method for nonlinear distributed parameter systems (DPSs) is critical for both physical system analysis and industrial engineering. In this paper, we propose a novel DPS modeling approach, in which a high-order nonlinear Volterra series is used to separate the time/space variables. With almost no additional computational complexity, the modeling accuracy is improved more than 20 times in average comparing with the traditional method. [Copyright &y& Elsevier]