Distributed Parameter Systems Research Articles

Event-triggered iterative learning control for discrete parabolic distributed parameter systems

Iterative learning control (ILC) is an intelligent control strategy which can achieve the desired trajectory tracking by continuously renewing the control signal based on the previous experience. In this article, an event-triggered condition that can save system resources by reducing the number of iterative updates is proposed. Moreover, an event-triggered ILC algorithm is designed for linear discrete parabolic distributed parameter systems, the system input is updated with the learning law only when the derived triggered condition is met. Through rigorous mathematical analysis, the tracking error can converge to zero when the iterative batch approaches infinity under the given sufficient condition. Then, we also extended the above ideas to nonlinear case. By simulation, the effectiveness of the designed algorithm are illustrated.

Event-triggered adaptive vibration control for a flexible satellite with time-varying actuator faults

In this study, vibration control is studied for the flexible satellite through wireless communication, and given the fact that the actuators are prone to unknown faults, the input signal event-triggering and time-varying actuator faults are considered for the flexible satellite simultaneously. The satellite system is composed of two symmetrical flexible panels attached to a centrebody, which is a distributed parameter system and the established model is represented by partial differential equations (PDEs). Based on the PDEs model of the flexible satellite, the input event-triggered mechanism using the relative threshold strategy is designed firstly to lower the communication burden, and then the event-triggered-based adaptive fault-tolerant control laws are developed with the aid of the designed auxiliary signals for the system with time-varying actuator faults. With the proposed control scheme, the vibration of the system is controlled to the small neighborhood of zero, and the angle of the panels is regulated to the desired position. Finally, numerical simulation results are given to further show the effectiveness of the designed control scheme.

Exponential Boundary Control for 2-D Spatial Distributed Parameter Systems Under Boundary Collocated and Planar Linear Measurements.

For a class of 2-D spatial distributed parameter systems (DPSs) with space-dependent diffusivity, this article aims to achieve exponential realization of their desired profiles. To reduce the number of required sensors and actuators, a planar output feedback boundary control strategy is proposed with combining two nonfull-domain measurement methods, boundary collocated measurement and planar linear measurement, in which only two boundaries of the considered 2-D spatial DPSs are controlled and a little output information is measured. Moreover, by employing the Poincaré-Wirtinger inequality and variable substitution dexterously, the final exponential convergence criteria of the error system can be obtained with method of "Diverse treatment for same term." Finally, we provide a general numerical example and an application example in 2-D heat conduction systems to illustrate the effectiveness and practicability of the proposed measurement and control schemes.

Development of a continuous reheating furnace state-space model based on the finite volume method

This study developed a modeling approach of a continuous steel slab reheating furnace process as a particular case of spatially distributed parameter systems involving radiative heat transfer. The aim of the resulting mathematical model, which is both detailed and computationally tractable, is to serve in prospective advanced process control (APC) and model-based optimization. The two-dimensional state-space model is introduced to accurately simulate the temperature distribution and dynamics, using the finite volume method (FVM) to incorporate essential heat transfer phenomena, including radiation, conduction, convection, advection, and simple combustion. The study presents a novel furnace measurement model that interprets temperature sensor readings (useful for state estimation), a benefit of the FVM treatment of radiative heat transfer. Strategies for linearization and model order reduction, such as balanced truncation, are proposed to facilitate real-time control. The simulation case study demonstrates the targeted capabilities of the model. The accuracy of the model is verified through comparisons with more complex computational fluid dynamics (CFD) software models. The study prioritizes theoretical modeling over empirical validation of a specific furnace unit, omitting experimental validation at this stage.

Boundary Optimal Control for Parabolic Distributed Parameter Systems With Value Iteration.

A reinforcement learning-based boundary optimal control algorithm for parabolic distributed parameter systems is developed in this article. First, a spatial Riccati-like equation and an integral optimal controller are derived in infinite-time horizon based on the principle of the variational method, which avoids the complex semigroups and operator theories. Using state data along the system trajectory, a value iteration algorithm via the Bellman optimality principle is proposed to obtain the solution of the spatial Riccati-like equation and the optimal control law. The convergence of the value iteration algorithm is proved. Subsequently, an approximation scheme based on weighted residuals is developed to implement the value iteration algorithm, where radial basis functions are chosen as the basic functions to approximate the solution of the spatial Riccati-like equation. Simulations on the diffusion-reaction process demonstrate the effectiveness of the developed method.

Sampling-based event-triggered iterative learning control in nonlinear hyperbolic distributed parameter systems

This article explores a sampling-based event-triggered iterative learning control (SETILC) method for achieving precise control in nonlinear hyperbolic distributed parameter systems. Firstly, by designing a Lyapunov function regarding the system output error, reasonable triggering conditions are derived to selectively update the system control input. Subsequently, a sampling-based event-triggered iterative learning control algorithm is proposed to further enhance the control performance of the system while avoiding the occurrence of Zeno phenomena. A condition sufficient for ensuring the convergence of the system’s tracking error to zero is presented, and its convergence is proven. Finally, the proposed method’s effectiveness is verified through numerical simulations.

Modeling and vibration suppression based on Nussbaum function for beam bridge with unknown control directions and unknown nonlinear time-varying actuator faults

In this paper, the modeling of the beam bridge system with in-domain control and the vibration suppression under unknown control directions, unknown nonlinear time-varying actuator faults and external disturbances are studied. The beam bridge with fixed ends can be regarded as Euler Bernoulli beam, which is a typical distributed parameter system. Firstly, the partial differential equation (PDE) model of the beam bridge is established according to Hamilton principle. Then, an adaptive in-domain control scheme based on Nussbaum function is designed on the PDE model to eliminate the vibration of the beam bridge. It is proved theoretically that all closed-loop signals are uniformly bounded under this control law, and the vibration of the system asymptotically converges to zero. The simulation results also prove the effectiveness of the proposed control scheme. What’ more, the modeling and control scheme presented in this paper can be applied to a class of systems similar to beam bridges, such as vibration suppression of the main beam of an overhead crane bridge.

An iterative method for updating finite element models with connectivity constraints

It is well known that the analytical matrices arising from the discretization of distributed parameter systems using the finite element technique are usually symmetric and banded. How to preserve the coefficient matrices of the updated model being of the same band structure is an important yet difficult challenge for model updating in structural dynamics. In this paper, an iterative method for updating mass, damping and stiffness matrices simultaneously based on partial modal measured data is provided. By the method, the optimal updated matrices can be obtained within finite iteration steps by choosing a special kind of initial matrix triplet. The proposed approach not only preserves the physical connectivity of the original model, but also the updated model reproduces the measured modal data, which can be utilized for various finite element model updating problems. Numerical examples confirm the effectiveness of the introduced method.

Adaptive resilient control for a class of nonlinear distributed parameter systems with actuator faults

This paper presents a new model-based fault resilient control scheme for a class of nonlinear distributed parameter systems (DPS) represented by parabolic partial differential equations (PDE) in the presence of actuator faults. A Luenberger-like observer on the basis of nonlinear PDE representation of DPS is developed with boundary measurements. A detection residual is generated by taking the difference between the measured output of the DPS and the estimated one given by the observer. Once a fault is detected, an unknown actuator fault parameter vector together with a known basis function is utilized to adaptively estimate the fault dynamics. A novel tuning algorithm is derived to estimate the unknown actuator fault parameter vector. Next, in order to achieve resilience, the controller from the healthy scenario is adjusted to mitigate the faults by using both estimated fault dynamics and a secondary measurement. Subsequently, an explicit formula is developed to estimate the time-to-resilience (TTR). Finally, a nonlinear example is utilized to illustrate the effectiveness of the proposed scheme.

Observer-based dynamic event-triggered control for distributed parameter systems over mobile sensor-plus-actuator networks

Abstract The objective of this paper is to develop a policy of observer-based dynamic event-triggered state feedback control for distributed parameter systems over a mobile sensor-plus-actuator network. It is assumed that the mobile sensing devices that provide spatially averaged state measurements can be used to improve state estimation in the network. For the purpose of decreasing the update frequency of controller and unnecessary sampled data transmission, an efficient dynamic event-triggered control policy is constructed. In an event-triggered system, when an error signal exceeding a specified time-varying threshold it indicates the occurrence of a typical event. The global asymptotic stability of the event-triggered closed-loop system and the boundedness of the minimum inter-event time can be guaranteed. Based on the linear quadratic optimal regulator, the actuator selects the optimal displacement only when an event occurs. A simulation example is finally used to verify the effectiveness of such a control strategy can enhance the system performance.

Reduced order in domain control of distributed parameter port-Hamiltonian systems via energy shaping

An in-domain finite dimensional controller for a class of distributed parameter systems on a one-dimensional spatial domain formulated under the port-Hamiltonian framework is presented. Based on (Trenchant et al. 2017) where positive feedback and a late lumping approach is used, we extend the Control by Interconnection method and propose a new energy shaping methodology with an early lumping approach on the distributed spatial domain of the system. Our two main control objectives are to stabilize the closed-loop system, as well as to improve the closed-loop dynamic performances. With the early lumping approach, we investigate two cases of the controller design, the ideal case where each distributed controller acts independently on the spatial domain (fully-actuated), and the more realistic case where the control action is piecewise constant over certain intervals (under-actuated). We then analyze the asymptotic stability of the closed-loop system when the infinite dimensional plant system is connected with the finite dimensional controller. Furthermore we provide simulation results comparing the performance of the fully-actuated case and the under-actuated case with an example of an elastic vibrating string.

Multilayer Online Sequential Reduced Kernel Extreme Learning Machine-Based Modeling for Time-Varying Distributed Parameter Systems.

A significant number of industrial dynamic processes belong to time-varying distributed parameter systems (DPSs). To develop an accurate approximation model for these systems, it is critical to capture their time-varying behavior and strong nonlinearity. In this article, a multilayer online sequential reduced kernel extreme learning machine (ML-OSRKELM)-based online spatiotemporal modeling approach is developed for such DPSs. First, ML-OSRKELM stacks multiple online sequential reduced kernel extreme learning machine autoencoders (OSRKELM-AEs) to create a deep network, which can translate the spatiotemporal domain into a low-dimensional time domain. Then, an online sequential reduced kernel extreme learning machine (OS-RKELM) is employed to construct a dynamic temporal model. Finally, after obtaining time coefficients from the time domain, OS-RKELM is also used to reconstruct the original spatiotemporal domain. By using the kernel trick and the support vector selection strategy, the proposed method can remove redundant information while maintaining satisfactory nonlinear learning performance. Furthermore, the designed sequential update scheme can update the model parameters with real-time data, which makes it a promising method for capturing time-varying dynamics. Experiments and simulations on a lithium-ion battery's thermal process confirm the excellent performance and validity of the proposed model.

Fuzzy Boundary Sampled-Data Control for Nonlinear Parabolic DPSs.

For a nonlinear parabolic distributed parameter system (DPS), a fuzzy boundary sampled-data (SD) control method is introduced in this article, where distributed SD measurement and boundary SD measurement are respected. Initially, this nonlinear parabolic DPS is represented precisely by a Takagi-Sugeno (T-S) fuzzy parabolic partial differential equation (PDE) model. Subsequently, under distributed SD measurement and boundary SD measurement, a fuzzy boundary SD control design is obtained via linear matrix inequalities (LMIs) on the basis of the T-S fuzzy parabolic PDE model to guarantee exponential stability for closed-loop parabolic DPS by using inequality techniques and a LF. Furthermore, respecting the property of membership functions, we present some LMI-based fuzzy boundary SD control design conditions. Finally, the effectiveness of the designed fuzzy boundary SD controller is demonstrated via two simulation examples.

Concurrent Learning Robust Adaptive Fault Tolerant Boundary Regulation of Hyperbolic Distributed Parameter Systems.

This article develops a robust adaptive boundary output regulation approach for a class of complex anticollocated hyperbolic partial differential equations subjected to multiplicative unknown faults in both the boundary sensor and actuator. The regulator design is based on the internal model principle, which amounts to stabilize a coupled cascade system, which consists of a finite-dimensional internal model driven by a hyperbolic distributed parameter system (DPS). To this end, a systematic sliding mode equipped with a backstepping approach is developed such that the robust state feedback control can be realized. Moreover, since the available information is a faulty boundary measurement at the right side point, state estimation is required. However, due to the presence of boundary unknown faults, we need to solve an issue of joint fault-state estimation. Restrictive persistent excitation conditions are usually required to guarantee the exact estimation of faults but are unrealistic in practice. To this end, a novel concurrent learning (CL) adaptive observer is proposed so that exponential convergence is obtained. It is the first time that the spirit of CL is introduced to the field of DPSs. Consequently, the observer-based adaptive boundary fault tolerant control scheme is developed, and rigorous theoretical analysis is given such that the exponential output regulation can be achieved. Finally, the effectiveness of the proposed methodology is demonstrated via comparative simulations.

Computation-Efficient Fault Detection Framework for Partially Known Nonlinear Distributed Parameter Systems.

Fault detection for distributed parameter systems (DPSs) generally requires the complete model information to be known so far. However, for numerous industrial applications, it is common that accurate first-principles physical models are extremely difficult to obtain. Hence, the applicability of traditional model-based methods is being restricted. To pave the way, an adaptive neural network (AdNN) is constructed to simultaneously estimate the state variable and the unknown nonlinearity for a class of partially known nonlinear DPSs. Moreover, considering that full-state measurement is unrealistic in applications, the proposed adaptive neural observer is based on a reduced-order model, which also increases the computation efficiency. Then, the residual generation and evaluation are conducted using the output estimation error of the proposed adaptive neural observer. Bearing the effects of the neglected fast dynamics in mind, a data-driven threshold generation scheme is proposed. Extensive experimental results are presented and analyzed to validate the effectiveness of the proposed method.

Adaptive prescribed performance control for wave equations with dynamic boundary and multiple parametric uncertainties

<abstract><p>In modern engineering, the dynamics of many practical problems can be described by hyperbolic distributed parameter systems. This paper is devoted to the adaptive prescribed performance control for a class of typical uncertain hyperbolic distributed parameter systems, since uncertainties are inevitable in practice. The systems in question simultaneously have unknown in-domain spatially varying damping coefficient and unknown boundary constant damping coefficient. Moreover, dynamic boundary condition is considered in the present paper. These characteristics make the control problem in the paper essentially different from those in the related works. To solve the problem, using adaptive technique based projection operator, backstepping method developed for ODEs and Lyapunov stability theories, a powerful adaptive prescribed performance control scheme is proposed to successfully guarantee that all states of the resulting closed-loop system are bounded, furthermore, the original system state converges to an arbitrary prescribed small neighborhood of the origin. Compared with the existing results, the developed control schemes can not only effectively handle the serious uncertainties, but also overcome the technical difficulties in the infinite-dimensional backstepping control design method caused by the dynamic boundary condition and guarantee prescribed performance.</p></abstract>

Self-Correcting Iterative Learning-Based Fault Estimation for Parabolic Distributed Parameter Systems

Self-Correcting Iterative Learning-Based Fault Estimation for Parabolic Distributed Parameter Systems

Physical Informed Sparse Learning for Robust Modeling of Distributed Parameter System and Its Industrial Applications

Physical Informed Sparse Learning for Robust Modeling of Distributed Parameter System and Its Industrial Applications

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.