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The assessment and diagnosis of controller performance for model‐based closed‐loop control systems has received considerable attention in recent years. A recognized factor dilapidating the controller performance is mismatching the true dynamical model of the plant and the mathematic model employed in the controller. In order to reduce the heavy effort to re‐identify the entire model, a large amount of recent works have been focusing on locating the mismatch. To further improve the mathematic model as well as controller performance, in this article, we provide a novel prediction‐based plant‐model mismatch quantification approach, which belongs to the class of moment match methodology. In particular, two cases of output prediction are considered: one‐step ahead prediction and multistep ahead prediction. Compared with existing efforts along the same line of mismatch quantification, when using the one‐step ahead prediction, our method shows an advantage of light computational complexity. On the other hand, when utilizing multistep predictions, it shows better convergence and robustness than the former, especially in the case of structural mismatches, and the long‐term prediction capability of the model is employed. With both predictions and consideration of the existence of unknown noise models in practice, we show that the plant‐model mismatch and unknown parameters of noise models can be quantified as the solution of a minimization issue that penalizes the discrepancy between the sample of plant outputs and the predictions calculated by considering the plant‐model mismatch and noise model parameters. Several examples are provided to demonstrate the effectiveness of the proposed methods, respectively. [ABSTRACT FROM AUTHOR]

This article studies the problem of prescribed‐time constrained tracking control for a class of 2×2$$ 2\times 2 $$ hyperbolic partial differential equation (PDE) systems with actuator dynamics, which are described by a set of nonlinear ordinary differential equations (ODEs). Since the control input only appears in the ODE subsystem rather than directly on the boundary of PDE subsystem, the control task becomes quite challenging. The most important is that for the control of such ODE controlled PDE systems we mainly make the following two contributions: (1) the controlled output of the PDE system tracks the reference signal within the prescribed time; (2) the controlled output and all the actuator states are constrained. It is the first time that such a prescribed‐time constrained tracking control problem is addressed for the PDE‐ODE coupled system considered in this article. Through rigorous theoretical proof, it is demonstrated that all the system states and control signals are bounded and sufficiently continuous by configuring appropriate design parameters. Finally, the performance is investigated via numerical simulation. [ABSTRACT FROM AUTHOR]

This work develops a network of adaptive boundary observers and studies the agreement between state and parameter estimates for a single target parabolic partial differential equation (PDE) system in the presence of structured and unstructured uncertainties. It is assumed that the unknown parameters take the form of either a structured uncertainty with unknown constant parameters or an unstructured uncertainty that can be neutralized by a radial basis function neural networks with unknown weights. The proposed adaptive observers consisting of m$$ m $$ agents in the network follow the structure of adaptive identifiers for the considered target PDE systems with the insertion of a penalty term in both the state and parameter estimates. Different from earlier efforts, the proposed adaptive laws include a penalty term of the mismatch between the parameter and state estimates generated by the other adjacent agents, which helps to accelerate the estimation of uncertainties. Additionally, the effects of these modifications on the agreement amongst the state and parameter estimates are investigated. Theoretical proofs are provided to show that the proposed approach guarantees the exponential convergence of estimation errors in the case of structured uncertainties and the ultimate boundedness of estimation errors in the case of unstructured uncertainties. Finally, numerical simulations are carried out to verify the effectiveness of the design methods. [ABSTRACT FROM AUTHOR]

The state estimation and sensor placement for a continuous pulp digester with delayed measurements are investigated. The underlying model of interest is heat transfer in a pulp digester modeled by two coupled hyperbolic partial differential equations and an ordinary differential equation. Output measurements are considered with delay due to the possible low sampling rate. The Cayley–Tustin transformation is utilized to realize model time discretization in a late lumping manner which does not account for any type of spatial approximation or model reduction. The discrete Kalman filter is applied to estimate the system states using the delayed measurements. The selection of sensor location is addressed along with estimator design accounting for the delayed measurements and investigated by minimizing the variance of estimation error. The performance of the state estimator is evaluated, and the sensor placement is analyzed through simulation studies, which offers a planning view of sensor location in industrial applications. [ABSTRACT FROM AUTHOR]

The model predictive controller (MPC) design is developed for a tubular chemical reactor, considering a second‐order hyperbolic partial differential equation as the model of the transport‐reaction process with boundary actuation. Without loss of generality, closed–closed boundary conditions and relaxed total flux are assumed. At the same time, the model is discretized in time by the Cayley–Tustin method, and, under the assumption that only the reactor's output is measurable, the observer design for the state reconstruction is addressed and integrated with the MPC design. The Luenberger observer gain is obtained by solving the operator Ricatti equation in the discrete‐time setting, while the MPC accounts for constrained and optimal control. The simulations show that the output‐based MPC design stabilizes the system under the input and output constraints satisfaction. In addition, to address the models' disparities, the results for both parabolic and hyperbolic equations are presented and discussed. [ABSTRACT FROM AUTHOR]

This work explores the design of a model predictive controller of the continuous pulp digester process consisting of the co‐current zone and counter‐current zone modeled by a set of nonlinear coupled hyperbolic partial differential equations (PDEs). The distributed parameter system of interest is not spectral, and slow–fast dynamic separation does not hold. To address this challenge, the nonlinear continuous‐time model is linearized and discretized in time utilizing the Cayley–Tustin discretization framework, which ensures system theoretic properties and structure preservation without spatial discretization or model reduction. The discrete model is used in the full state model predictive controller design, which is augmented by the Luenberger observer design to achieve the output constrained regulation. Finally, a numerical example is provided to demonstrate the feasibility and applicability of the proposed controller designs. [ABSTRACT FROM AUTHOR]

This manuscript develops a robust output regulator for the column froth flotation process in the presence of unknown disturbance. In particular, motivated by relevant physical modeling setting, all information (including magnitude, phase, bias, and frequency) of the disturbance is unavailable. The system considered is consisting of froth and collection zones and is governed by a set of conservative heterodirectional transport hyperbolic partial differential equations (PDEs). Moreover, the transport related time delay between the froth and the collection region is considered, and is associated with the boundary conditions of the PDEs. The velocity of the feed is considered the input and the concentration of the solid particle with air phase at the top of froth region as the output. We propose a disturbance frequency identifier and formulate a robust controller according to the internal model principle such that the output tracks the desired concentration despite the model uncertainties and unknown disturbance. [ABSTRACT FROM AUTHOR]

In this manuscript, common chemical engineering transport‐reaction systems are modeled by taking into consideration the inertia in the transport phenomena, leading to hyperbolic partial differential equations (PDEs), which have finite speed of propagation. The findings provide the derivation of the hyperbolic transport‐reaction PDEs and a direct comparison with their corresponding dissipative parabolic PDEs. The stability analysis of the dynamical systems is considered and complemented by numerical simulations for typical processes, such as the heat diffusion in a slab, transport‐reaction inside a chemical reactor, and a phase change problem. The results demonstrate the effects associated with the modeling and/or limits of the approximation used in the derivation and application of the hyperbolic PDE for transport‐reaction systems, and the difference between the dynamics of this type of equation and the generally used parabolic PDEs. [ABSTRACT FROM AUTHOR]

This study proposes a new method based on sensitivity analysis to solve a series of sequential parametric linear programmings (LPs) such as that those arise in l1 model predictive control l1 (MPC). The main idea is to find a relationship between each of the two successive parametric LPs by using sensitivity analysis strategy. Tolerance analysis-based MPC (TA-l1 MPC) and sensitivity analysis-based MPC (SA-l1 MPC) are introduced for reducing computational complexity and runtime. TA-l1 MPC takes O(Nn²) operations per step time, where N and n are the prediction horizon and the number of states, respectively. This approach is very faster than generic optimisation methods but it can be applied only for initial conditions that are near to steady-state values. SA-l1 MPC has not any limitation in usage and it reduces the runtime significantly compared with common solvers. Finally, numerical results indicate the potential of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This study proposes a new method based on sensitivity analysis to solve a series of sequential parametric linear programmings (LPs) such as that those arise in l1 model predictive control l1 (MPC). The main idea is to find a relationship between each of the two successive parametric LPs by using sensitivity analysis strategy. Tolerance analysis‐based MPC (TA‐ l1 MPC) and sensitivity analysis‐based MPC (SA‐ l1 MPC) are introduced for reducing computational complexity and runtime. TA‐ l1 MPC takes O(Nn2) operations per step time, where N and n are the prediction horizon and the number of states, respectively. This approach is very faster than generic optimisation methods but it can be applied only for initial conditions that are near to steady‐state values. SA‐ l1 MPC has not any limitation in usage and it reduces the runtime significantly compared with common solvers. Finally, numerical results indicate the potential of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Summary: In this paper, we propose a simultaneous state estimation and fault estimation approach for a class of first‐order hyperbolic partial integral differential equation systems. Specifically, we consider the multiplicative boundary actuator and sensor faults, ie, unknown fault parameters multiplying by the boundary input or boundary state (ie, output). As a consequence, two difficulties arise immediately: (1) simultaneous estimation of both plant state and faults is a nonlinear problem due to the multiplication between fault parameters and plant signals; (2) no prior information is available to determine the type (actuator or sensor) of faults. To overcome these difficulties, this paper develops adaptive fault parameter update laws and embeds the resulting laws into the plant state observer design. First, we propose new approaches to estimate actuator fault and sensor fault, respectively. Next, we develop a novel method to simultaneously estimate actuator and sensor faults. The proposed observer and update laws, designed using only one boundary measurement, ensure both state estimation and fault parameter estimation. By choosing appropriate Lyapunov functions, we prove that the estimates of state and fault parameters converge to an arbitrarily small neighborhood of their true values. Numerical simulations are used to demonstrate the effectiveness of the proposed estimation approaches. [ABSTRACT FROM AUTHOR]

This work focuses on the receding horizon optimal control for a solar‐thermal district heating (STDH) system containing lumped parameter and distributed parameter subsystems. A common STDH system includes solar collector system, a short‐term energy storage tank and a district heating loop system with a secondary gas boiler system. The inclusion or exclusion of these components leads to different operational and working modes. Detailed system description and mathematical models are provided, and three working modes are introduced and in each mode several operations are demonstrated and addressed. Single‐objective and multiobjective problems are formulated. Moreover, in the mode where gas boiler system is included to help addressing the district heating demand, the internal model based boundary servo‐control approach is proposed and applied to obtain desired boiler water temperatures such that the expected district heating demand can be satisfied. Moreover, a boundary state observer is designed for the considered solar collector system. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1217–1233, 2018 [ABSTRACT FROM AUTHOR]

The article deals with systematic development of linear model predictive control algorithms for linear transport-reaction models emerging from chemical engineering practice. The finite-horizon constrained optimal control problems are addressed for the systems varying from the convection dominated models described by hyperbolic partial differential equations (PDEs) to the diffusion models described by parabolic PDEs. The novelty of the design procedure lies in the fact that spatial discretization and/or any other type of spatial approximation of the process model plant is not considered and the system is completely captured with the proposed Cayley-Tustin transformation, which maps a plant model from a continuous to a discrete state space setting. The issues of optimality and constrained stabilization are addressed within the controller design setting leading to the finite constrained quadratic regulator problem, which is easily realized and is no more computationally intensive than the existing algorithms. The methodology is demonstrated for examples of hyperbolic/parabolic PDEs. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2644-2659, 2017 [ABSTRACT FROM AUTHOR]

Observer and optimal boundary control design for the objective of output tracking of a linear distributed parameter system given by a two-dimensional (2-D) parabolic partial differential equation with time-varying domain is realized in this work. The transformation of boundary actuation to distributed control setting allows to represent the system's model in a standard evolutionary form. By exploring dynamical model evolution and generating data, a set of time-varying empirical eigenfunctions that capture the dominant dynamics of the distributed system is found. This basis is used in Galerkin's method to accurately represent the distributed system as a finite-dimensional plant in terms of a linear time-varying system. This reduced-order model enables synthesis of a linear optimal output tracking controller, as well as design of a state observer. Finally, numerical results are prepared for the optimal output tracking of a 2-D model of the temperature distribution in Czochralski crystal growth process which has nontrivial geometry. © 2014 American Institute of Chemical Engineers AIChE J, 61: 494-502, 2015 [ABSTRACT FROM AUTHOR]

A mechanical geometric crystal growth model is developed to describe the crystal length and radius evolution. The crystal radius regulation is achieved by feedback linearization and accounts for parametric uncertainty in the crystal growth rate. The associated parabolic partial differential equation (PDE) model of heat conduction is considered over the time-varying crystal domain and coupled with crystal growth dynamics. An appropriately defined infinite-dimensional representation of the thermal evolution is derived considering slow time-varying process effects. The computational framework of the Galerkin's method is used for parabolic PDE order reduction and observer synthesis for temperature distribution reconstruction over the entire crystal domain. It is shown that the proposed observer can be utilized to reconstruct temperature distribution from boundary temperature measurements. The developed observer is implemented on the finite-element model of the process and demonstrates that despite parametric and geometric uncertainties present in the model, the temperature distribution is reconstructed with the high accuracy. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2839-2852, 2014 [ABSTRACT FROM AUTHOR]

A novel methodology for the order-reduction of parabolic partial differential equation (PDE) systems with time-varying domain is explored. In this method, a mapping functional is obtained, which relates the time-evolution of the solution of a parabolic PDE with time-varying domain to a fixed reference domain, while preserving space invariant properties of the initial solution ensemble. Subsequently, the Karhunen-Loève decomposition is applied to the solution ensemble on fixed spatial domain resulting in a set of optimal eigenfunctions. Further, the low dimensional set of empirical eigenfunctions is mapped on the original time-varying domain by an appropriate mapping, resulting in the basis for the construction of the reduced-order model of the parabolic PDE system with time-varying domain. This methodology is used in three representative cases, one- and two-dimensional (1-D and 2-D) models of nonlinear reaction-diffusion systems with analytically defined domain evolutions, and the 2-D model of the Czochralski crystal growth process with nontrivial geometry. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4142-4150, 2013 [ABSTRACT FROM AUTHOR]

The thermal regulation problem for a lithium ion (Li-ion) battery with boundary control actuation is considered. The model of the transient temperature dynamics of the battery is given by a nonhomogeneous parabolic partial differential equation (PDE) on a two-dimensional spatial domain which accounts for the time-varying heat generation during the battery discharge cycle. The spatial domain is given as a disk with radial and angular coordinates which captures the nonradially symmetric heat-transfer phenomena due to the application of the control input along a portion of the spatial domain boundary. The Li-ion battery model is formulated within an appropriately defined infinite-dimensional function space setting which is suitable for spectral controller synthesis. The key challenges in the output feedback model-based controller design addressed in this work are: the dependence of the state on time-varying system parameters, the restriction of the input along a portion of the battery domain boundary, the observer-based optimal boundary control design where the separation principle is utilized to demonstrate the stability of the closed loop system, and the realization of the outback feedback control problem based on state measurement and interpolation of the temperature field. Numerical results for simulation case studies are presented. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3782-3796, 2013 [ABSTRACT FROM AUTHOR]

The boundary feedback regulator design for heat exchangers with delayed feedback is developed. Counter‐flow/parallel‐flow heat exchanger systems described by a pair of coupled transport hyperbolic partial differential equations (PDEs) with delayed boundary feedback loop modeled by the boundary time lag are considered. The coupled transport hyperbolic PDEs and boundary delay by application of boundary transformation are transformed in the corresponding linear infinite‐dimensional system utilized in the regulator design. The regulator design initially addresses a full state feedback controller realization augmented by the observer design to achieve simultaneously output exponential stabilization as well as tracking and disturbance rejection of polynomial and/or harmonic type of reference signals. The simulations studies demonstrate the proposed design for counter‐flow and parallel‐flow heat exchangers, two common configurations present in industrial practice. [ABSTRACT FROM AUTHOR]

A realistic pipeline modeled by a nonlinear coupled first‐order hyperbolic partial differential equations (PDEs) system is studied for the long transportation pipeline leak detection and localization. Based on the so‐called water hammer equation, a linear distributed parameter system is obtained by linearization. The structure and energy preserving time discretization scheme (Cayley–Tustin) is used to realize a discrete infinite‐dimensional hyperbolic PDEs system without spatial approximation or model order reduction. In order to reconstruct pressure and mass flow velocity evolution with limited measurements, a discrete‐time Luenberger observer is designed by solving the operator Riccati equation. Based on this distributed observer system, data on different normal and leakage conditions (various leak amounts and positions) are generated and fed to train a support vector machine model for leak detection, amount, and position estimation. Finally, the leak detection, amount estimation, and localization effectiveness of the developed method are proved by a set of simulations. © 2019 American Institute of Chemical Engineers AIChE J, 65: e16532 2019 [ABSTRACT FROM AUTHOR]