Tobias Kasper Skovborg Ritschel

Tobias Kasper Skovborg Ritschel
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Tobias verified their affiliation via an institutional email.
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Tobias verified their affiliation via an institutional email.
  • PhD in Applied Mathematics
  • Professor (Assistant) at Technical University of Denmark

About

90
Publications
6,805
Reads
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306
Citations
Introduction
I develop computationally efficient numerical methods and software for (nonlinear) simulation, state/parameter estimation, optimal control, and model predictive control as well as model order reduction.
Current institution
Technical University of Denmark
Current position
  • Professor (Assistant)
Additional affiliations
January 2019 - December 2020
2-control ApS
Position
  • Developer
February 2016 - May 2016
Technical University of Denmark
Position
  • Research Assistant
Description
  • 02612 Constrained Optimization (http://kurser.dtu.dk/course/02612)
February 2014 - May 2014
Technical University of Denmark
Position
  • Research Assistant
Description
  • 01907 Calculus and Algebra 2 (http://kurser.dtu.dk/course/01907)
Education
August 2015 - August 2018
Technical University of Denmark
Field of study
  • Applied Mathematics
September 2013 - July 2015
Technical University of Denmark
Field of study
  • Mathematical Modelling and Computations
September 2010 - July 2013
Technical University of Denmark
Field of study
  • Mathematics and Technology

Publications

Publications (90)
Preprint
Full-text available
In this paper, we propose a general approach for approximate simulation and analysis of delay differential equations (DDEs) with distributed time delays based on methods for ordinary differential equations (ODEs). The key innovation is that we 1) approximate the kernel by the probability density function of an Erlang mixture and 2) use the linear c...
Preprint
Time delays are ubiquitous in industrial processes, and they must be accounted for when designing control algorithms because they have a significant effect on the process dynamics. Therefore, in this work, we propose a simultaneous approach for numerical optimal control of delay differential equations with distributed time delays. Specifically, we...
Preprint
Time delays are ubiquitous in industry, and they must be accounted for when designing control strategies. However, numerical optimal control (NOC) of delay differential equations (DDEs) is challenging because it requires specialized discretization methods and the time delays may depend on the manipulated inputs or state variables. Therefore, in thi...
Presentation
Proton exchange membrane water electrolyzer (PEMWE) takes a central place in the hydrogen economy as a crucial technology for green hydrogen production. However, this technology still faces challenges, such as the cost of the materials, performance losses at high current densities, and durability. To overcome these obstacles, better comprehension o...
Preprint
Full-text available
Renewable Energy Sources play a key role in smart energy systems. To achieve 100% renewable energy, utilizing the flexibility potential on the demand side becomes the cost-efficient option to balance the grid. However, it is not trivial to exploit these available capacities and flexibility options profitably. The amount of available flexibility is...
Preprint
Full-text available
This paper proposes an adaptive mechanism for price signal generation using a piecewise linear approximation of a flexibility function with unknown parameters. In this adaptive approach, the price signal is parameterized and the parameters are changed adaptively such that the output of the flexibility function follows the reference demand signal pr...
Article
Objective: To evaluate the impact of missed or late meal boluses (MLBs) on glycemic outcomes in children and adolescents with type 1 diabetes using automated insulin delivery (AID) systems. Research Design and Methods: AID-treated (Tandem Control-IQ or Medtronic MiniMed 780G) children and adolescents (aged 6-21 years) from Stanford Medical Center a...
Preprint
Full-text available
Demand-side management provides a great potential for improving the efficiency and reliability of energy systems. This requires a mechanism to connect the market level and the demand side. The flexibility function is a novel approach that bridges the gap between the markets and the dynamics of physical assets at the lower levels of the energy syste...
Preprint
Full-text available
Time delays are ubiquitous in industry and nature, and they significantly affect both transient dynamics and stability properties. Consequently, it is often necessary to identify and account for the delays when, e.g., designing a model-based control strategy. However, identifying delays in differential equations is not straightforward and requires...
Preprint
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...
Preprint
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...
Chapter
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.
Chapter
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...
Chapter
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...
Chapter
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.
Chapter
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.
Chapter
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.
Preprint
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...
Article
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...
Preprint
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...
Article
Full-text available
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 male...
Preprint
Full-text available
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,...
Preprint
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...
Preprint
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...
Preprint
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...
Article
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...
Conference Paper
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...
Preprint
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...
Preprint
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...
Preprint
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...
Preprint
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...
Preprint
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...
Preprint
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...
Article
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...
Article
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...
Preprint
Full-text available
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...
Article
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...
Chapter
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...
Article
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...
Preprint
Full-text available
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...
Article
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...
Preprint
Full-text available
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...
Preprint
Full-text available
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...
Article
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...
Preprint
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...
Article
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...
Thesis
Full-text available
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...
Article
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...
Conference Paper
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...
Preprint
Full-text available
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...
Article
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...
Article
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...
Article
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...
Technical Report
Full-text available
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...
Article
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...
Article
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...
Chapter
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...
Chapter
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...
Chapter
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...
Technical Report
Full-text available
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...

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