Tobias Kasper Skovborg Ritschel

Technical University of Denmark | DTU · Department of Applied Mathematics and Computer Science

We present and critically discuss five commonly used mathematical models of the meal glucose rate of appearance in humans. Such models are key to simulation of the metabolism in healthy people, people with diabetes, and obese people, and they are central to developing effective treatments and prevention strategies. Furthermore, we discuss important...

We present a whole-body model of human metabolism that utilizes a system of organs and blood vessels to simulate the enzymatic reactions. The model focuses on key organs, including the brain, heart and lungs, liver, gut, and kidney, as well as muscle and adipose tissue. The model equations are formulated using stoichiometry and Michaelis-Menten kin...

In this chapter, we discuss how residential batteries within microgrids (MGs) can be used to provide flexibility to the DSO. On this lowest level of the grid hierarchy we only consider active power demand. In particular, we manipulate the aggregated power demand by charging and discharging residential batteries while neglecting the grid topology.

In this chapter, we present a numerical example of the approach presented in the previous chapters based on modifications of small-scale standard test systems. We emphasise that the sizes of these grids are very small and the power demands very low when compared to real-world grids. For example, active power transmission demand in real-world TSO gr...

In this chapter, we discuss how flexibilities from microgrids conveyed through the distribution level can be utilized in the operation of transmission systems. To this end, we consider both nonlinear (2.2)–(2.7) and semidefinite (2.8)–(2.13) OPF formulations and introduce flexible demand nodes (representing the connections to the DSO level) to anal...

In this chapter, we describe the implementation of the optimal amount of power delivered by the transmission grid in the distribution grid and the microgrids.

In this chapter, we describe how to determine the flexibility of a distribution grid given the flexibility of a set of microgrids (see Chap. 3). Specifically, we compute the minimum, maximum, and optimal active power demand of the entire distribution grid, i.e., the amount of power which must be supplied by the transmission grid.

In this chapter, we present the power-flow equations [5, 9], the optimal power-flow problem, the semidefinite approach for solving optimal power-flow problems [7], and the dynamic structure-preserving power grid model [8] which are relevant to several of the sections in the remainder of the book.

In this paper, we present a Newton-like method based on model reduction techniques, which can be used in implicit numerical methods for approximating the solution to ordinary differential equations. In each iteration, the Newton-like method solves a reduced order linear system in order to compute the Newton step. This reduced system is derived usin...

This paper validates a glucoregulatory model including glucagon receptors dynamics in the description of endogenous glucose production (EGP). A set of models from literature are selected for a head-to-head comparison in order to evaluate the role of glucagon receptors. Each EGP model is incorporated into an existing glucoregulatory model and valida...

Cyber-physical systems (CPSs) for real-time advanced process control (RT-APC) are a class of control systems using network communication to control industrial processes. In this paper, we use simple examples to describe the software principles and concepts used in the implementation of such systems. The key software principles are 1) shared data in...

Objective To assess the efficacy and safety of a dual-hormone (DH [insulin and glucagon]) closed-loop system compared to a single-hormone (SH [insulin only]) closed-loop system in adolescents with type 1 diabetes.Methods This was a 26-hour, two-period, randomized, crossover, inpatient study involving 11 adolescents with type 1 diabetes (nine males...

This paper presents models for renewable energy systems with storage, and considers its optimal operation. We model and simulate wind and solar power production using stochastic differential equations as well as storage of the produced power using batteries, thermal storage, and water electrolysis. We formulate an economic optimal control problem,...

We compare the performance of proportional-integral-derivative (PID) control, linear model predictive control (LMPC), and nonlinear model predictive control (NMPC) for a physical setup of the quadruple tank system (QTS). We estimate the parameters in a continuous-discrete time stochastic nonlinear model for the QTS using a prediction-error-method b...

State estimation incorporates the feedback in optimization based advanced process control systems and is very important for the performance of model predictive control. We describe the extended Kalman filter, the unscented Kalman filter, the ensemble Kalman filter, and a particle filter for continuous-discrete time nonlinear systems involving stoch...

In type 2 diabetes (T2D) treatment, finding a safe and effective basal insulin dose is a challenge. The dose-response is highly individual and to ensure safety, people with T2D titrate by slowly increasing the daily insulin dose to meet treatment targets. This titration can take months. To ease and accelerate the process, we use short-term artifici...

In this work, a novel insulin-glucagon-glucose model is proposed, where the glucagon effect on the endogenous glucose production (EGP) is described by the dynamics of the glucagon receptors. In order to assess the quality of the model, its parameters are fitted in such a way that the influence of glucagon on EGP is isolated. Experimental data is us...

In this work, a novel insulin-glucagon-glucose model is proposed, where the glucagon effect on the endogenous glucose production (EGP) is described by the dynamics of the glucagon receptors. In order to assess the quality of the model, its parameters are fitted in such a way that the influence of glucagon on EGP is isolated. Experimental data is us...

In this work, we present methods for state estimation in continuous-discrete nonlinear systems involving stochastic differential equations. We present the extended Kalman filter, the unscented Kalman filter, the ensemble Kalman filter, and a particle filter. We implement the state estimation methods in Matlab. We evaluate the performance of the met...

We propose a whole-body model of the metabolism in man as well as a generalized approach for modeling metabolic networks. Using this approach, we are able to write a large metabolic network in a systematic and compact way. We demonstrate the approach using a whole-body model of the metabolism of the three macronutrients, carbohydrates, proteins and...

We propose a virtual clinical trial for assessing the safety and efficacy of closed-loop diabetes treatments prior to an actual clinical trial. Such virtual trials enable rapid and risk-free pretrial testing of algorithms, and they can be used to compare different treatment variations for large and diverse populations. The participants are represen...

In this paper, we propose a virtual clinical trial for assessing the performance and identifying risks in closed-loop diabetes treatments. Virtual clinical trials enable fast and risk-free tests of many treatment variations for large populations of fictive patients (represented by mathematical models). We use closed-loop Monte Carlo simulation, imp...

In this work, we present a switching nonlinear model predictive control (NMPC) algorithm for a dual-hormone artificial pancreas (AP), and we use maximum likelihood estimation (MLE) to identify model parameters. A dual-hormone AP consists of a continuous glucose monitor (CGM), a control algorithm, an insulin pump, and a glucagon pump. The AP is desi...

We propose a model-free artificial pancreas (AP) for people with type 1 diabetes. The algorithmic parameters are tuned to a virtual population of 1,000,000 individuals, and the AP repeatedly estimates the basal and bolus insulin requirements necessary for maintaining normal blood glucose levels. Therefore, the AP can be used without healthcare pers...

We present a numerical case study for modeling and simulation of upstream and downstream processes for monoclonal antibody (mAb) production. We apply a systematic and intuitive modeling methodology for an existing upstream process and downstream process. The resulting models are based on differential mass balances and kinetic expressions for the re...

In this work, we present a switching nonlinear model predictive control (NMPC) algorithm for a dual-hormone artificial pancreas (AP), and we use maximum likelihood estimation (MLE) to identify the model parameters. A dual-hormone AP consists of a continuous glucose monitor (CGM), a control algorithm, an insulin pump, and a glucagon pump. The AP is...

We propose a model predictive control (MPC) approach for minimising the social distancing and quarantine measures during a pandemic while maintaining a hard infection cap. To this end, we study the admissible and the maximal robust positively invariant set (MRPI) of the standard SEIR compartmental model with control inputs. Exploiting the fact that...

Most countries have started vaccinating people against COVID-19. However, due to limited production capacities and logistical challenges it will take months/years until herd immunity is achieved. Therefore, vaccination and social distancing have to be coordinated. In this paper, we provide some insight on this topic using optimization-based control...

Triggered by the increasing number of renewable energy sources, the German electricity grid is undergoing a fundamental change from mono to bidirectional power flow. This paradigm shift confronts grid operators with new problems but also new opportunities. In this chapter we point out some of these problems arising on different layers of the grid h...

For people with type 1 diabetes and some with type 2 diabetes, the problem of insulin titration, i.e. finding an adequate basal rate of insulin, is a complex and time-consuming task. This paper proposes a simple model-free algorithm and a procedure for fast initial titration in people with type 1 diabetes (T1D). A modified proportional-integral-der...

The world is waiting for a vaccine to mitigate the spread of SARS-CoV-2. However, once it becomes available, there will not be enough to vaccinate everybody at once. Therefore, vaccination and social distancing has to be coordinated. In this paper, we provide some insight on this topic using optimization-based control on an age-differentiated compa...

In this work, we present a nonlinear model reduction approach for reducing two commonly used nonlinear dynamical models of power grids: the effective network (EN) model and the synchronous motor (SM) model. Such models are essential in real-time security assessments of power grids. However, as power grids are often large-scale, it is necessary to r...

In this paper, we provide insights on how much testing and social distancing is required to control COVID-19. To this end, we develop a compartmental model that accounts for key aspects of the disease: 1) incubation time, 2) age-dependent symptom severity, and 3) testing and hospitalization delays; the model's parameters are chosen based on medical...

In this work, we present a nonlinear model reduction approach for reducing two commonly used nonlinear dynamical models of power grids: the effective network (EN) model and the synchronous motor (SM) model. Such models are essential in real-time security assessments of power grids. However, as power grids are often large-scale, it is necessary to r...

We model and simulate an exothermic reaction conducted in an adiabatic continuous stirred tank reactor (CSTR). The system has multiple steady states in part of its operating window. We demonstrate that the three-state model representing the mass and energy balances of the system can be well approximated with a two-state as well as a one-state model...

In this paper we numerically assess the performance of Java linear algebra libraries for the implementation of nonlinear filters in an Android smart phone (Samsung A5 2017). We implemented a linear Kalman filter (KF), an extended Kalman filter (EKF), and an unscented Kalman filter (UKF). These filters are used for state and parameter estimation, as...

In this paper, we consider dynamic optimization of thermal and isothermal oil recovery processes which involve multicomponent three-phase flow in porous media. We present thermodynamically rigorous models of these processes based on 1) conservation of mass and energy, and 2) phase equilibrium. The conservation equations are partial differential equ...

Oil remains the world’s leading fuel, and it accounted for a third of the global energy consumption in 2016. Oil is mainly used as a source of energy, but it is also used for non-energy purposes, e.g. for road surfaces, lubricants, and in the chemical industry. Furthermore, the global demand for oil is expected to increase towards 2040 where it is...

We present a nonlinear model predictive control (NMPC) algorithm for semi-explicit index-1 stochastic differential-algebraic equations. It is natural to model isoenergetic-isochoric (constant energy-constant volume) flash processes with such equations. The algorithm uses the continuous-discrete extended Kalman filter (EKF) for state estimation, and...

In this work, we consider algorithms for solving production optimization problems that involve isothermal (constant temperature) and compositional oil production processes. The purpose of production optimization is to compute a long-term production strategy that is economically optimal. We present a thermodynamically rigorous model of isothermal oi...

In this paper, we consider dynamic optimization of thermal and isothermal oil recovery processes which involve multicomponent three-phase flow in porous media. We present thermodynamically rigorous models of these processes based on 1) conservation of mass and energy, and 2) phase equilibrium. The conservation equations are partial differential equ...

In this paper, we discuss mathematical models and computational methods for computation of vapor-liquid equilibrium in systems relevant to reservoir simulation and optimization. We formulate the phase equilibrium problem as an optimization problem and discuss the UV-flash, the TV-flash, and the PT-flash. The UV-flash occurs for thermal and composit...

We model thermal and compositional reservoir production as mass and energy balances combined with a phase equilibrium constraint. The phase equilibrium constraint is modeled as a thermodynamically rigorous UV flash process. The UV flash problem is a mathematical statement of the second law of thermodynamics, and it replaces the condition of equalit...

We present an extended Kalman filter for state estimation of semi-explicit index-1 differential-algebraic equations. It is natural to model dynamic UV flash processes with such differential-algebraic equations. The UV flash is a mathematical statement of the second law of thermodynamics. It is therefore important to thermodynamically rigorous model...

In this technical report, we describe the computation of phase equilibrium and phase envelopes based on expressions for the fugacity coefficients. We derive those expressions from the residual Gibbs energy. We consider 1) ideal gases and liquids modeled with correlations from the DIPPR database and 2) nonideal gases and liquids modeled with cubic e...

This paper presents a novel single-shooting algorithm for gradient-based solution of optimal control problems with vapor-liquid equilibrium constraints. Such optimal control problems are important in several engineering applications, for instance in control of distillation columns, in certain two-phase flow problems, and in operation of oil reservo...

Process system tools, such as simulation and optimization of dynamic systems, are widely used in the process industries for development of operational strategies and control for process systems. These tools rely on thermodynamic models and many thermodynamic models have been developed for different compounds and mixtures. However, rigorous thermody...

The production of single-cell protein (SCP) in a U-loop reactor by a methanotroph is a cost efficient sustainable alternative to protein from fish meal obtained by over-fishing the oceans. SCP serves as animal feed. In this paper, we present a mathematical model that describes the dynamics of SCP production in a U-loop reactor. We use this model to...

Cryogenic air separation (CAS) is the leading technology for large scale production of pure N2, O2 and Ar. This process is very electric-energy intensive; thus it is a likely candidate for load balancing of power stations in a smart grid. This type of intermittent operation of CAS, requires a non-linear model based control to achieve optimal techno...

This paper presents a novel single-shooting algorithm for gradient-based solution of optimal control problems with vapor-liquid equilibrium constraints. Dynamic optimization of UV flash processes is relevant in nonlinear model predictive control of distillation columns, certain two-phase flow problems, and oil reservoir production with significant...

This is a technical report which accompanies the article ”An open-source thermodynamic software library” which describes an efficient Matlab and C implementation for evaluation of thermodynamic properties. In this technical report we present the model equations, that are also presented in the paper, together with a full set of first and second orde...