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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 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]

Highlights: [•] Boundary model predictive control of thin film thickness. [•] Kuramoto–Sivashinsky (K–S) equation. [•] Model modal predictive controller (MPC). [•] Input and PDE states constraints satisfaction. [Copyright &y& Elsevier]

Abstract: Interior point optimization and model predictive control along with moving horizon estimator are used to maximize and regulate lipid production in a fed-batch heterotrophic microalgae cultivation of Auxenochlorella protothecoides. Motivation for microalgae bioreactor optimal control arises from the need to increase lipid production rate, which results in economic feasibility of microalgae bio-fuel production process. A complex time-varying microalgae fed-batch growth and lipid production model (De la Hoz Siegler et al., 2011) is used and a large-scale nonlinear programming optimization along with moving horizon estimator and model predictive control are applied to maximize the lipid concentration in the bioreactor. An optimal feeding strategy for lipid production is determined using the state-of-the-art interior point optimizer (IPOPT) solver. Moving horizon estimator (MHE) and model predictive controller (MPC) are used to estimate unmeasurable state (nitrogen concentration) and provide regulation of a highly nonlinear and time-varying microalgae growth process as a realizable real-time control strategy. In addition to the constrained large-scale optimization, naturally present input constraints (lower and upper bound on feed rates) and state constraints (lower bound on all concentration related states and upper bound on glucose concentration) are accounted for in an explicit manner with moving horizon estimator and model predictive controller. The estimator and controller design is based on a set of linearized models in microalgae growth fed-batch process. The paper provides a reliable and computationally efficient optimization, estimation and regulation procedure suitable for the real-time microalgae bioreactor operation. The procedure takes into account present constraints on inputs and states, and measurement noises present in the realistic operation conditions and is computationally efficient, along with the improvement in results with respect to previous methods. [Copyright &y& Elsevier]

Abstract: In this work an asymptotic stabilization of highly dissipative Kuramoto–Sivashinsky equation (KSE) by means of boundary model modal predictive control (MMPC) in the presence of input and state constraints is demonstrated. The KS equation is initially defined in an appropriate functional space setting and an exact transformation is used to reformulate the original boundary control problem as an abstract boundary control problem of the KSE partial differential equation (PDE). An appropriate discrete infinite-dimensional representation of the abstract boundary control problem is used for synthesis of low dimensional model modal predictive controller (MMPC) incorporating both the pointwise enforced KSE state constraints and input constraints. The proposed control problem formulation and the performance of the closed-loop system in the full state feedback controller realization have been evaluated through simulations. [ABSTRACT FROM AUTHOR]

Abstract: This work focuses on the model predictive control design methodology that successfully accounts for the state and input constraints applied in the context of highly dissipative Kuramoto–Sivashinsky (KS) partial differential equation (PDE) describing stability of a thin film thickness in the two-phase annular flow in vertical pipes. The evolution of a linear dissipative KSE PDE state is given by an abstract evolution equation in an appropriate functional space. The proposed constrained predictive control law utilizes a low order modal representation in the optimization functional, while higher modes are included only in the PDE state constraints. Simulation results demonstrate a successful application of the proposed predictive control technique that achieves optimal stabilization of a spatially-uniform unstable steady state of Kuramoto–Sivashinsky equation in the presence of input and state constraints. [Copyright &y& Elsevier]

Abstract: This work focuses on predictive control of linear parabolic partial differential equations (PDEs) with boundary control actuation subject to input and state constraints. Under the assumption that measurements of the PDE state are available, various finite-dimensional and infinite-dimensional predictive control formulations are presented and their ability to enforce stability and constraint satisfaction in the infinite-dimensional closed-loop system is analyzed. A numerical example of a linear parabolic PDE with unstable steady state and flux boundary control subject to state and control constraints is used to demonstrate the implementation and effectiveness of the predictive controllers. [Copyright &y& Elsevier]

For transport-reaction processes with certain general cost functions indicating comprehensive profit, the existing linear–quadratic optimal control or model predictive control (MPC) methods may be conservative. Due to their spatial characteristics, dynamic evolutions and final target static spatial distributions under different control strategies may result in remarkable variation of operation performance. This article presents a novel economic model predictive control (EMPC) synthesis for systems described by hyperbolic/parabolic partial differential equations (PDEs) with pre-optimized static spatially distributed profile, from both convergence and performance points of view. Instead of deriving approximate ordinary differential equations (ODEs) and applying finite-dimensional control strategies, this work addresses the optimization and stabilization problem on the basis of infinite dimensional model itself, which is realized by Cayley–Tustin (CT) transformation without any type of spatial approximation. The accumulated economic cost, input/output constraints are explicitly considered in the finite horizon optimal control problem (FHOCP), with an additional energy-like contractive constraint accounting for closed-loop convergence toward the target optimal steady-state profile. By directly solving Lyapunov functions associated with PDEs models, the parameters in the FHOCP are suitably defined such that the composite EMPC system admits algorithm feasibility and closed-loop stability. Finally, the proposed method is applied to typical examples; numerical results indicates the effectiveness and remarkable performance improvement of the EMPC method compared to standard MPC results. • Transport-reaction processes (TRP) that being described by hyperbolic/parabolic PDEs. • Economic MPC for TRP from both convergence and performance point of view. • The economic optimizations are carried out without any type of spatial approximation. • Typical examples illustrate the effectiveness with emphasis on enhanced performance. [ABSTRACT FROM AUTHOR]

Column flotation is an efficient method commonly used in the mineral industry to separate useful minerals from ores of low grade and complex mineral composition. Its main purpose is to achieve maximum recovery while ensuring desired product grade. This work addresses a model predictive control design for a mineral column flotation process modeled by a set of nonlinear coupled heterodirectional hyperbolic partial differential equations (PDEs) and ordinary differential equations (ODEs), which accounts for the interconnection of well-stirred regions represented by continuous stirred tank reactors (CSTRs) and transport systems given by heterodirectional hyperbolic PDEs, with these two regions combined through the PDEs’ boundaries. The model predictive control considers both optimality of the process operations and naturally present input and state/output constraints. For the discrete controller design, spatially varying steady-state profiles are obtained by linearizing the coupled ODE–PDE model, and then the discrete system is obtained by using the Cayley–Tustin time discretization transformation without any spatial discretization and/or without model reduction. The model predictive controller is designed by solving an optimization problem with input and state/output constraints as well as input disturbance to minimize the objective function, which leads to an online-solvable finite constrained quadratic regulator problem. Finally, the controller performance to keep the output at the steady state within the constraint range is demonstrated by simulation studies, and it is concluded that the optimal control scheme presented in this work makes this flotation process more efficient. [ABSTRACT FROM AUTHOR]

The temperature gradients and distribution evolution within the crystal domain in Czochralski crystal growth process have important role in produced crystal's quality. Precise and tight regulation of temperature distribution and gradients is the most promising approach to ensure the crystal quality. In this work, the coupled crystal pulling dynamics and heat transfer models in Czochralski crystal growth with a time-varying boundary is considered. The moving boundary finite element method is used to obtain the optimal reference temperature trajectory associated with the reference crystal shape taking into account constraints on input and the temperature gradients. The obtained reference trajectory is used to implement a model predictive control strategy to track the reference temperature despite uncertainties in crystal domain geometry evolution and disturbances. Finally, the proposed method is implemented on a high fidelity finite element process model with non-planar interface and results are presented to validate the success of the proposed methodology. [ABSTRACT FROM AUTHOR]

This paper discusses the development of model predictive control algorithm which accounts for the input and state constraints applied to the parabolic partial differential equations (PDEs) system describing the axial dispersion chemical reactor. Spatially varying terms arising from the nonlinear PDEs model are accounted for in model development. Finite-dimensional modal representation capturing the dominant dynamics of the PDEs system is derived for controller design through Galerkin's method and modal decomposition technique. Tustin's discretization and Cayley transform are used to obtain infinite-dimensional discrete-time dynamic modal representations which are used in subsequent constrained controller design. The proposed discrete-time constrained model predictive control synthesis is constructed in a way that the objective function is only based on the low-order modal representation of the PDEs system, while higher-order modes are utilized only in the constraints of the PDEs state. Finally, the MPC formulations are successfully applied, via simulation results, to the PDEs system with input and state constraints. [ABSTRACT FROM AUTHOR]