arXiv subjects

John Bagterp Jørgensen

Publications and source records attributed to John Bagterp Jørgensen.

At least 19 recordsLinked to original sources

arXiv2026

Hierarchical 2-degree-of-freedom control combining Youla-Kucera parameterization and model predictive control

A hierarchical 2DOF (2-degree-of-freedom) structure combining Youla-Kucera (YK) parameterization and model predictive control (MPC) is presented in this paper. The YK parameterization employs the coprime factorization of the nominal system and controller, thereby introducing an auxiliary feedforward channel dedicated to system optimization and a controller parameterization channel. The feedforward channel is utilized to implement cascaded MPC for system optimization. The controller parameterization channel is utilized to achieve offset-free MPC by designing an appropriate YK parameter through the H2 optimal controller design.

eess.SY↗

arXiv2026

A simulation- and model-based approach to PI control pairing and tuning for the pyro process in a cement plant

The operation of the pyro process in cement production significantly affects the energy efficiency and sustainability of the cement plant, especially for reductions in carbon dioxide emissions. Hence, pyro process control is essential to obtain efficient and sustainable operation of cement plants. In this paper, we demonstrate how simulations and models can be utilized to evaluate and design control strategies for the pyro section in cement plants. We apply a novel differential algebraic equation (DAE) model for dynamic simulation of the pyro-section in cement plants to design decentralized PI controllers for the pyro-section. We utilize the pyro-process model to evaluate the control structure design. Through linearization of the pyro-process model, we apply the Relative Gain Array (RGA) method to choose and evaluate the pairings of the manipulated variables (MVs) and the controlled variables (CVs). Using simulations of the pyro-section, we generate step responses to estimate transfer models and apply Internal Model Control (IMC) for the tuning of the individual decentralized single-input single-output (SISO) PI controllers. Closed-loop simulations of the PI controllers demonstrate that PI controllers with IMC parameters provide smoother and faster responses compared with manually tuned PI parameters.

eess.SY↗

arXiv2026

A Systematic Modeling Framework for Dynamic Simulation of Fixed-Bed Reactors

We present a modular and thermodynamically consistent modeling framework for simulating steady-state and transient behavior in fixed-bed reactors. Accurate simulation of dynamic reactor behavior is essential for enabling flexible operation in Power-to-X (P2X) applications, such as Power-to-Ammonia and Power-to-Methanol, where fluctuating renewable energy inputs demand robust and responsive process control. The proposed models integrate non-ideal thermodynamics through cubic equations of state and account for both advective and dispersive transport phenomena. We derive consistent mass and energy balances using internal energy as the energy state variable, and obtain temperature and pressure from thermodynamic constraints. Our simulation methodology provides the necessary model functions for steady-state and dynamic simulations, as well as parametric sensitivity analysis. It is applied to two fundamental fixed-bed reactor units, the fixed-bed reactor (FBR) and the direct-cooled reactor (DCR). In the context of ammonia synthesis, we simulate representative reactor variants, the adiabatic fixed-bed reactor (AFBR) and the isothermal direct-cooled reactor (IDCR). Simulations assess the impact of real and ideal thermodynamic models, transport assumptions, and steady-state approximations. Results show that real-fluid effects at elevated pressures significantly influence steady-state outlet temperatures and conversions for the IDCR, while common literature model assumptions generally provide accurate dynamic predictions. Altogether, the framework supports systematic reactor model development and analysis under variable operating conditions and model assumptions relevant to Power-to-X applications.

math.DS↗

arXiv2025

Dynamic modeling and simulation of an electric flash clay calcination plant for green cement production

We present a novel dynamic model of an electric flash clay calcination plant. Calcined kaolinite-rich clay has been identified as one of the most effective candidates for supplementary cementitious material (SCM), because of its large availability. Calcination of clay is achieved via the dehydroxylation reaction, which does not release CO2 (unlike limestone), but has a considerable energy requirement. The required high temperature can be met by electric resistive heating of the working gas in the plant, that can be powered by renewable energy. Therefore, CO2-free calcination of clay can be achieved. Up to 50\% of the limestone-based clinker can be substituted by calcined clay (CC), making the cement more sustainable. We consider a plant that consists of gas-material cyclones that pre-heat the clay, a calciner, and a gas-recirculation system with electric heating of the gas. The model is formulated as a system of differential-algebraic equations (DAE). The model consists of thermophysical properties, reaction kinetics and stoichiometry, transport, mass and energy balances, and algebraic constraints. The model can be used to perform dynamic simulations with changing inputs, process design, and optimization. Moreover, it can be used to develop model-based control, which is relevant for flexible operation of a clay calcination plant for green cement production.

math.DS↗

arXiv2025

Comparing Model-based Control Strategies for a Quadruple Tank System: Decentralized PID, LMPC, and NMPC

This paper compares the performance of a decentralized proportional-integral-derivative (PID) controller, a linear model predictive controller (LMPC), and a nonlinear model predictive controller (NMPC) applied to a quadruple tank system (QTS). We present experimental data from a physical setup of the QTS as well as simulation results. The QTS is modeled as a stochastic nonlinear continuous-discrete-time system, with parameters estimated using a maximum-likelihood prediction-error-method (ML-PEM). The NMPC applies the stochastic nonlinear continuous-discrete-time model, while the LMPC uses a linearized version of the same model. We tune the decentralized PID controller using the simple internal model control (SIMC) rules. The SIMC rules require transfer functions of the process, and we obtain these from the linearized model. We compare the controller performances based on systematic tests using both the physical setup and the simulated QTS. We measure the performance in terms of tracking errors and rate of movement in the manipulated variables. The LMPC and the NMPC perform better than the decentralized PID control system for tracking pre-announced time-varying setpoints. For disturbance rejection, the MPCs perform only slightly better than the decentralized PID controller. The primary advantage of the MPCs is their ability to use the information of future setpoints. We demonstrate this by providing simulation results of the MPCs with and without such information. Finally, the NMPC achieves slightly improved tracking errors compared to the LMPC but at the expense of having a higher input rate of movement.

math.OC↗

arXiv2025

Dynamical Simulation Model of the Pyro-Process in Cement Clinker Production

This study presents a dynamic simulation model for the pyro-process of clinker production in cement plants. The study aims to construct a simulation model capable of replicating the real-world dynamics of the pyro-process to facilitate research into the improvements of operation, i.e., the development of alternative strategies for reducing CO2 emissions and ensuring clinker quality, production, and lowering fuel consumption. The presented model is an index-1 differential-algebraic equation (DAE) model based on first engineering principles and modular approaches. Using a systematic approach, the model is described on a detailed level that integrates geometric aspects, thermo-physical properties, transport phenomena, stoichiometry and kinetics, mass and energy balances, and algebraic volume and energy conservations. By manually calibrating the model to a steady-state reference, we provide dynamic simulation results that match the expected reference performance and the expected dynamic behavior from the industrial practices.

eess.SY↗

arXiv2025

Hybrid Optimization Methods for Parameter Estimation of Reactive Transport Systems

This paper presents a hybrid optimization methodology for parameter estimation of reactive transport systems. Using reduced-order advection-diffusion-reaction (ADR) models, the computational requirements of global optimization with dynamic PDE constraints are addressed by combining metaheuristics with gradient-based optimizers. A case study in preparative liquid chromatography shows that the method achieves superior computational efficiency compared to traditional multi-start methods, demonstrating the potential of hybrid strategies to advance parameter estimation in large-scale, dynamic chemical engineering applications.

math.OC↗

arXiv2025

Numerical Discrete-Time Implementation of Continuous-Time Linear-Quadratic Model Predictive Control

This study presents the design, discretization and implementation of the continuous-time linear-quadratic model predictive control (CT-LMPC). The control model of the CT-LMPC is parameterized as transfer functions with time delays, and they are separated into deterministic and stochastic parts for relevant control and filtering algorithms. We formulate time-delay, finite-horizon CT linear-quadratic optimal control problems (LQ-OCPs) for the CT-LMPC. By assuming piece-wise constant inputs and constraints, we present the numerical discretization of the proposed LQ-OCPs and show how to convert the discrete-time (DT) equivalent into a standard quadratic program. The performance of the CT-LMPC is compared with the conventional DT-LMPC algorithm. Our numerical experiments show that, under fixed tunning parameters, the CT-LMPC shows better closed-loop performance as the sampling time increases than the conventional DT-LMPC.

math.OC↗

arXiv2024

A first engineering principles model for dynamical simulation of cement pyro-process cyclones

We provide a cyclone model for dynamical simulations in the pyro-process of cement production. The model is given as an index-1 differential-algebraic equation (DAE) model based on first engineering principle. Using a systematic approach, the model integrates cyclone geometry, thermo-physical aspects, stoichiometry and kinetics, mass and energy balances, and algebraic equations for volume and internal energy. The paper provides simulation results that fit expected dynamics. The cyclone model is part of an overall model for dynamical simulations of the pyro-process in a cement plant. This model can be used in the design of control and optimization systems to improve energy efficiency and reduce CO2 emission.

math.DS↗

arXiv2024

A Dynamic Cooler Model for Cement Clinker Production

We present a 2D model for a grate belt cooler in the pyro-section of a cement plant. The model is formulated as an index-1 differential-algebraic equation (DAE) model based on first engineering principles. The model systematically integrates thermo-physical aspects, transport phenomena, reaction kinetics, mass and energy balances, and algebraic volume and energy relations. The model is used for dynamic simulation of the cooler and the paper provides dynamic and steady-state simulation results matching the expected behavior. The cooler model is one part of a full pyro-section model for dynamical simulations. The model can serve as a basis for the design of optimization and control systems towards improving energy efficiency and CO2 emission.

eess.SY↗

arXiv2024

Differential algebraic modeling of an alkaline electrolyzer plant

We develop a mathematical model for dynamic simulation of an alkaline electrolyzer plant. The plant includes the stack, a water recirculation system and hydrogen storage with compressor. We model each component of the system with mass and energy balances. Our modeling strategy consists of a rigorous and systematic formulation using differential algebraic equations (DAE), along with a thermodynamic library that evaluates thermophysical properties. We perform a simulation with step power input. Dynamic modeling enables simulation and model-based optimization and control for optimal hydrogen production under varying operating conditions.

eess.SY↗

arXiv2024

Numerical Discretization Methods for the Discounted Linear Quadratic Control Problem

This study focuses on the numerical discretization methods for the continuous-time discounted linear-quadratic optimal control problem (LQ-OCP) with time delays. By assuming piecewise constant inputs, we formulate the discrete system matrices of the discounted LQ-OCPs into systems of differential equations. Subsequently, we derive the discrete-time equivalent of the discounted LQ-OCP by solving these systems. This paper presents three numerical methods for solving the proposed differential equations systems: the fixed-time-step ordinary differential equation (ODE) method, the step-doubling method, and the matrix exponential method. Our numerical experiment demonstrates that all three methods accurately solve the differential equation systems. Interestingly, the step-doubling method emerges as the fastest among them while maintaining the same level of accuracy as the fixed-time-step ODE method.

math.OC↗

arXiv2024

ESDIRK-based nonlinear model predictive control for stochastic differential-algebraic equations

In this paper, we present a nonlinear model predictive control (NMPC) algorithm for systems modeled by semi-explicit stochastic differential-algebraic equations (DAEs) of index 1. The NMPC combines a continuous-discrete extended Kalman filter (CD-EKF) with an optimal control problem (OCP) for setpoint tracking. We discretize the OCP using direct multiple shooting. We apply an explicit singly diagonal implicit Runge-Kutta (ESDIRK) integration scheme to solve systems of DAEs, both for the one-step prediction in the CD-EKF and in each shooting interval of the discretized OCP. The ESDIRK methods use an iterated internal numerical differentiation approach for precise sensitivity computations. These sensitivities are used to provide accurate gradient information in the OCP and to efficiently integrate the covariance information in the CD-EKF. Subsequently, we present a simulation case study where we apply the NMPC to a simple alkaline electrolyzer stack model. We use the NMPC to track a time-varying setpoint for the stack temperature subject to input bound constraints.

math.OC↗

arXiv2024

Identification of PK-PD Insulin Models using Experimental GIR Data

We present a method to estimate parameters in pharmacokinetic (PK) and pharmacodynamic (PD) models for glucose insulin dynamics in humans. The method combines 1) experimental glucose infusion rate (GIR) data from glucose clamp studies and 2) a PK-PD model to estimate parameters such that the model fits the data. Assuming that the glucose clamp is perfect, we do not need to know the details of the controller in the clamp, and the GIR can be computed directly from the PK-PD model. To illustrate the procedure, we use the glucoregulatory model developed by Hovorka and modify it to have a smooth non-negative endogeneous glucose production (EGP) term. We estimate PK-PD parameters for rapid-acting insulin analogs (Fiasp and NovoRapid). We use these PK-PD parameters to illustrate GIR for insulin analogs with 30% and 50% faster absorption time than currently available rapid-acting insulin analogs. We discuss the role of system identification using GIR data from glucose clamp studies and how such identified models can be used in automated insulin dosing (AID) systems with ultra rapid-acting insulin.

q-bio.QM↗

arXiv2024

A Dynamical Simulation Model of a Cement Clinker Rotary Kiln

This study provides a systematic description and results of a dynamical simulation model of a rotary kiln for clinker, based on first engineering principles. The model is built upon thermophysical, chemical, and transportation models for both the formation of clinker phases and fuel combustion in the kiln. The model is presented as a 1D model with counter-flow between gas and clinker phases and is demonstrated by a simulation using industrially relevant input. An advantage of the proposed model is that it provides the evolution of the individual compounds for both the fuel and clinker. As such, the model comprises a stepping stone for evaluating the development of process control systems for existing cement plants.

math.DS↗

arXiv2024

A First-Engineering Principles Model for Dynamical Simulation of a Calciner in Cement Production

We present an index-1 differential-algebraic equation (DAE) model for dynamic simulation of a calciner in the pyro-section of a cement plant. The model is based on first engineering principles and integrates reactor geometry, thermo-physical properties, transport phenomena, stoichiometry and kinetics, mass and energy balances, and algebraic volume and internal energy equations in a systematic manner. The model can be used for dynamic simulation of the calciner. We also provide simulation results that are qualitatively correct. The calciner model is part of an overall model for dynamical simulation of the pyro-section in a cement plant. This model can be used in design of control and optimization systems to improve the energy efficiency and \ce{CO2} emission from cement plants.

math.DS↗

arXiv2024

A whole-body mathematical model of cholesterol metabolism and transport

Cardiovascular diseases are the leading cause of death. Increased levels of plasma cholesterol are consistently associated with an increased risk of cardiovascular disease. As a result, it is imperative that studies are conducted to determine the best course of action to reduce whole-body cholesterol levels. A whole-body mathematical model for cholesterol metabolism and transport is proposed. The model can simulate the effects of lipid-lowering drugs like statins and anti-PCSK9. The model is based on ordinary differential equations and kinetic functions. It has been validated against literature data. It offers a versatile platform for designing personalized interventions for cardiovascular health management.

q-bio.QM↗

arXiv2024

Modeling principles for a physiology-based whole-body model of human metabolism

Physiological whole-body models are valuable tools for the development of novel drugs where understanding the system aspects is important. This paper presents a generalized model that encapsulates the structure and flow of whole-body human physiology. The model contains vascular, interstitial, and cellular subcompartments for each organ. Scaling of volumes and blood flows is described to allow for investigation across populations or specific patient groups. The model equations and the corresponding parameters are presented along with a catalog of functions that can be used to define the organ transport model and the biochemical reaction model. A simple example illustrates the procedure.

q-bio.QM↗