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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 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]

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]

This work addresses the model predictive controller design for a complex solar boreal thermal storage system which models a real Drake Landing Solar Commercial Community. The overall discrete system is obtained from a coupled finite and infinite dimensional subsystems of solar collector, heat exchanger, hot tank and gas boilers without any spatial approximation or model reduction. The novel model predictive control addresses a house heat regulation by constrained optimization problem with the manipulation constraints, and accounts for possible unstable system dynamics and disturbances arising from solar and geothermal radiations. The realistic output regulation is considered by the inclusion of an observer which constructs finite and infinite dimensional states. The proposed model development and control regulation can successfully account for the long range variability in environmental and/or economic conditions associated with the overall operational costs of the large scale solar energy community. Finally, the controller performance is assessed by numerical simulations. [ABSTRACT FROM AUTHOR]

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: 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]

Abstract: This work focuses on the development of computationally efficient predictive control algorithms for nonlinear parabolic and hyperbolic PDEs with state and control constraints arising in the context of transport-reaction processes. We first consider a diffusion-reaction process described by a nonlinear parabolic PDE and address the problem of stabilization of an unstable steady-state subject to input and state constraints. Galerkin’s method is used to derive finite-dimensional systems that capture the dominant dynamics of the parabolic PDE, which are subsequently used for controller design. Various model predictive control (MPC) formulations are constructed on the basis of the finite dimensional approximations and are demonstrated, through simulation, to achieve the control objectives. We then consider a convection-reaction process example described by a set of hyperbolic PDEs and address the problem of stabilization of the desired steady-state subject to input and state constraints, in the presence of disturbances. An easily implementable predictive controller based on a finite dimensional approximation of the PDE obtained by the finite difference method is derived and demonstrated, via simulation, to achieve the control objective. [Copyright &y& Elsevier]

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]

This manuscript proposes moving horizon control and state/parameter estimation designs for pipeline networks modelled by partial differential equations (PDEs) with boundary actuation. The spatial–temporal pressure and velocity dynamics within the pipelines are described by a system of six coupled one-dimensional first-order nonlinear hyperbolic PDEs. To address the discrete-time modelling challenge and preserve the infinite-dimensional nature of the pipeline system, the Cayley–Tustin transformation is deployed for model time discretization without any spatial discretization or model reduction. Considering the lack of full state information across the entire pipeline manifold, unknown states and uncertain parameters are estimated using moving horizon estimation (MHE). Based on the estimated states and parameters, a tracking model predictive control (MPC) strategy for the discrete-time infinite-dimensional pipeline system is proposed, which enables specific operation while ensuring physical constraint satisfaction. The effectiveness of the proposed controller and estimator designs is demonstrated via numerical examples. • A branched distributed parameter pipeline system modelled by PDEs is proposed. • A moving horizon estimator for state and parameter estimation is developed. • A tracking MPC is proposed to steer the controlled output to the desired set-points. [ABSTRACT FROM AUTHOR]

Energy process system positively contributes to the energy utilization efficiency, the energy complement, and the construction of a low-carbon sustainable energy system. The multiple energy subsystems are deep interdependent, therefore, significant operational risks exist in the energy process system. To avoid system risk and fulfill operation requirement, we propose the Safety-Index based model predictive control that coordinates the controller design and system safety in this work. The innovation of the method is to integrate the state-space model of process system with advanced controller design while accounting for system safety. Since the state-space model of the energy process system is described by coupled partial differential equations and ordinary differential equations, which leads to difficulties in modeling and solving, the main contribution of this work is to simplify the constrained optimization problem formed by model predictive controller. The paper addresses the compressed air energy storage system as case study. From the numerical simulations of the safety controller performance, it shows that the system safety can be guaranteed by control strategy which realizes the system operation target and reject the system external disturbances, which caused by environmental or operation change. • The paper addresses the modeling and dynamic safety control of compressed air energy storage system. • A control loop for safety operation that consists of controllers, system models, system constraints, and safety index is proposed. [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]

• Model predictive control of a non-isothermal axial dispersion tubular reactor with recycle. • The proposed controller is designed to manipulate the system to operate at an unstable condition despite physical limitations and input disturbance. • The design of the controller accounts for different mass and energy Peclet numbers in the axial dispersion tubular reactor. • The discrete version of the model is based on the application of energy-preserving Cayley-Tustin time discretization scheme. This paper addresses the model predictive output controller design for a non-isothermal axial dispersion tubular reactor accounting for energy and mass transport in a recycle stream. The underlying transport-reaction process is characterized by different mass and energy Peclet numbers. Open-loop analysis reveals unstable operating conditions based on the reactor's parameters. The discrete model of the system is obtained by considering a Crank-Nicolson type of discretization method without any model reduction and/or spatial approximation for the system of coupled parabolic PDEs. The proposed predictive controller accounts for asymptotic close-loop system stabilization and/or naturally present input and state constraints with the rejection of possible disturbances arising from reactor operations. To account for the output controller design, a discrete observer is developed to reconstruct the infinite dimensional states in the predictive control realization. Finally, the controller's performance is assessed via simulation studies, implying proper state stabilization and constraints satisfaction with input disturbance rejection. [ABSTRACT FROM AUTHOR]