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Control and Process Engineering


Recent engineering problems become more and more complex, nonlinear and high-dimensional. We develop together with students systems to analyze, simulate and control these technological processes. Control algorithms like Model Predictive Control and fresh high-level programming languages like Julia or MATLAB are associated with artificial intelligence, embedded computing or process engineering to span a wide range of research. These fields of research are explained in detail below.

Scheme of a heating plate with three heat sources and five sensors

Thermal Process Engineering

Thermal problems play an important role in many technological processes. Many examples like building air conditioning, cooling of engines or server clusters, and optimal tempering for the production of synthetic material unveil the significance of the right heat supply. Our team develops simulations and control algorithms for thermal problems in the case of multiple heat sources. In these scenarios the controller has to decide how much heat shall be supplied and at which position. Common applications can be found in the field of bake processes for the semiconductor industry.

Scientific Machine Learning

Recent machine learning approaches have a huge impact on IT services like search engines and social networks. Though, the research of complex systems bases as well on data-driven modeling. In many cases it is too complicated to describe these complex systems in detail. Therefore, systems with partly known properties are modeled as so called grey box models to approach the real system with the computation on large data sets. For example the driving dynamics of vehicles cannot be described in detail because every component has some certain influence. Instead a grey box model is considered which is improved with data from experiments and test drives. Chemical reactions with a huge amount of particles or reactants state another example. It is very hard to state a model in closed form for these reactions because every component could interact with each other. Thus, these chemical reactions are modeled as grey box models and optimized with data from experiments.

See also: SciML

Embedded Systems

Embedded systems can be found in almost every technological application ranging from consumer electronics to industrial robotics. They are used for measuring and processing data, for example light management in buildings. In many cases, commercial controllers are less flexible and more expensive than single-board computer. Thus, we use single-board computers as controlling units in scientific projects and small scale industrial processes in the areas of process technology, electrical and mechanical engineering to examine their field of application.

Thermal Processes

We develop three-dimensional numerical models of heating plates with multiple sources. The operating heat conduction is assumed as a quasi-linear process to enable the analysis of high temperature processes on a very precise level. We model actuators and sensors with characteristics (e.g. imperfections) which are situated on the plate’s boundaries.

Heatmap of a two-dimensional heat conduction simulation
Heatmap of a two-dimensional heat conduction simulation with imperfect actuators.
Stephan Scholz

Stage 1: Prototype of model

In the first part of this project a two-dimensional prototype of a quasi-linear heat conduction model was created to highlight the main problems and goals of this project.

  • Analytical modeling of quasi-linear heat conduction
  • Description of measuring and actuation along boundaries
  • Numerical modeling with Finite Volumes
  • Simulation, evaluation and discussion of resulting heat conduction

Article and Source Code


Stage 2: A digital twin

In the second stage a software library shall be developed to simulate quasi-linear heat conduction in one, two and three dimensions. Furthermore, the basic control and machine learning concepts shall be sketched. This is still work in progress!

  • Development of a software library to simulate quasi-linear heat conduction

  • Documentation and introducing tutorials

  • Design of the open-loop and closed-loop control

  • Design of scientific machine learning methods

Source Code


Theses and Projects

We offer theses and projects in the domain of modeling, simulation and control. A selection of finished projects and theses can be found here.

In-Domain Control of a 1-Dimensional Heat Equation


Accurate control of heating processes remains an ongoing topic of research due to the wide variety of applications in the process, semiconductor and manufacturing industries. This report investigates the in-domain control of the average temperature in a one dimensional, insulated rod using multiple heat sources.

To this end, the heat diffusion in the rod is modelled by the heat equation which is a partial differential equation. The report introduces a method to spatially discretize the system to obtain a finite dimensional state-space representation in the form of a linear system of ODEs. This model is used to design an LQR feedback controller and a feedforward controller.

The control algorithm is implemented in C-Code and incorporated into a simulation environment by compiling it to a MATLAB executable file in order to increase the computational efficiency and to perform Software-in-the-Loop tests.

Simulations are performed to investigate the open- and closed-loop behavior of the system. The controller is able to track a variety of different reference inputs as long as the bandwidth of the reference is limited and a tracking error is acceptable. Future research directions include the use of output feedback to improve tracking and disturbance rejection as well as methods from optimal control like Model Predictive Control to take constraints of the heat sources into account.

Report (Embedded Control 2023 / 2024) in English

Optimization Based Control of Cascaded Electrical Circuits


In this thesis, the challenges of optimizing higher-order circuits are addressed, with a focus on various methods to align system performance with desired reference outputs. The primary question under consideration pertains to the feasibility of optimization techniques in managing the complexities of higher-order system dynamics and, if so, which optimization approach—global or local—minimizes output errors.

Three optimization techniques - Flatness-Based Control (FBC), Optimization-Based Control (OBC), and Model Predictive Control (MPC) - are applied and analyzed. Notably, FBC faced challenges when dealing
with higher-order systems, primarily due to its reliance on the steepness of the reference signal. In contrast, OBC and MPC proved effective in handling such systems.

Within the OBC framework, the Polyopt optimizer demonstrated exceptional performance, effectively managing parameter variations. In the context of MPC, the interplay of prediction horizon and control horizon underscored the importance of an extended prediction horizon and a shorter control horizon.

Furthermore, the behavior of global optimizers revealed their ability to closely follow reference signals, albeit with increased jitter. Local optimization, on the other hand, yielded input signals that led to lower errors and smoother output responses.

The findings presented here hold substantial promise for applications in power electronics and motor control, offering the potential for smoother responses and improved control methods, particularly in systems such as, power converters, clippers and clampers.

Master thesis in English

Solution of Maxwell’s Equation - A Numerical Approximation

The objective of this thesis is to provide a comprehensive understanding of Maxwell’s equations and their numerical approximation using the finite-difference time-domain (FDTD) method.

Bachelor Thesis in English

Evaluation of Dynamic Mode Decomposition for Cascaded Electrical Oscillators

In this report the author presents the modeling, implementation and simulation of dynamic mode decomposition for cascaded electrical circuits in open-loop and closed-loop scenarios with full-state feedback.

Report (Scientific Project) in English

Sliding-Mode Control for Nonlinear RC and RLC Circuits

In this report the authors present the design, implementation and simulation of sliding-mode control for small linear and nonlinear electrical circuits.

Report (Embedded Control 2022 / 2023) in English

Simulation of two-dimensional heat conduction in Julia programming language using CUDA


Heat is vital when work and energy are involved in phase transitions, according to this fact, heat conduction qualities as well as the properties of molecules inside the bodies needed to be analyzed. Computation of heat transfer has been a considerable challenge during the last decade, especially when time is considered as a component with an unaffordable price.

The heat equation is a parabolic partial differential equation that represents how temperature varies in space over time. It may also be described as the process which reflects how heat is transferring from a higher temperature median to a lower temperature one. In some complex occasions it is nearly impossible to calculate the heat diffusion manually, that is why Julia programming language is utilized to solve one and two-dimensional heat equation problems by using CUDA, which is configured to accelerate the calculation through the graphics processing unit (GPU).

Bachelor thesis in English

High-order electrical RLC oscillators - PID and LQR control


The interest of this work is to design a PID and LQR controller for a high-order electrical RLC oscillator. For this purpose, state space equations are first formed for the cases n = 1, n = 2, n = 3 and n = n. After that, the general stability behaviour is checked and simulated. Finally, the PID and LQR controls are created.

Report (Embedded Control 2021 / 2022) in English

Regelungsentwurf mittels maschinellen Lernens für ein Wärmeleitermodell


This thesis deals with a one dimensional heat conduction problem: the end of a rod is heated to a given temperature. This process is controlled by a PI controller. Different boundary conditions for the end of the rod are considered. Requirements for the control as well as the parametrization for the different boundary conditions are discussed.

Afterwards the process is simulated numerically using the Julia programming language. Therefore the instationary heat conduction equation is firstly solved manually using the numerical finite difference method FTCS (Forward-Time Central-Space) and after that the vertical line method in connection with generic solvers is used.

The previously used explicit Euler-method is compared with selected Julia solvers. A data set is created that contains the temperature distribution of the different sections of the rod during heating. After that the collected temperature distributions are used to identify through the application of machine learning the control parameters that the PI controller has used during heating. Different optimization algorithms are compared. In addition it is examined how much information, i.e. the temperature distribution of how many location points is needed to reliably identify the parameters.

Bachelor thesis in German

Optimal Control of the heat equation in Julia


Optimal control of systems described using partial differential equations is a field of interest in research and industry. The heat equation, a partial differential equation, describes various heating and cooling processes. It is usually accompanied by constraints on the input signals, temperature through the body or both, which motivates applying optimal control in such processes.

In this thesis, a solution to the optimal boundary control of the heat equation is presented. The heat equation is numerically approximated using Finite difference method. The optimal control problem is formulated using a direct method into a non linear program. JuMP, a mathematical modelling language built on Julia is used to solve the problem. Simulation results are presented for a one dimensional rod and a two dimensional plate.

Bachelor thesis in English




  • S. Scholz, L. Berger: Optimization-based Trajectory Planning for Heat Conduction. Proceedings of the 2024 25th International Carpathian Control Conference (ICCC), Krynica-Zdrój, Poland, 2024. (accepted, pending for publication)
  • S. Scholz, L. Berger: Fast Computation of Function Composition Derivatives for Flatness-based Control of Diffusion Problems. (accepted, pending for publication)
  • D. Peters, S. Scholz, L. Berger: Dynamic Mode Decomposition for Cascaded Electrical Circuits. Proceedings of the 2023 6th International Conference on Mathematics and Statistics.
  • S. Scholz, L. Berger, D. Lebiedz: Benchmarking of flatness-based controlof the heat equation. arxiv:2307.16764
  • S. Scholz, L. Berger: Hestia.jl: A Julia library for heat conduction modeling with boundary actuation.
  • S. Scholz, L. Berger: Modeling of a multiple source heating plate. arxiv:2011.14939



  • Stephan Scholz: Optimization-based Trajectory Planning for Heat Conduction. 25th International Carpathian Control Conference (ICCC), Krynica-Zdrój, Poland, 2024.
  • Stephan Scholz: Electrical Circuit Models for Courses on Simulation and Control of Differential Equations - From Transfer Functions to PDEs. DMV Jahrestagung 2023, Ilmenau.
  • Stephan Scholz: Fast Computation of Function Composition Derivatives for Flatness-based Control of Diffusion Problems. ECMI 2023, Wroclaw.
  • Stephan Scholz: Hestia.jl: A Julia library for heat conduction modeling with boundary actuation. ASIM 2022, Vienna.


  • Stephan Scholz: Control the Heat: Flatness vs. Optimization. Tag der Promotion 2023, RWU, Weingarten.
  • Stephan Scholz: Scientific Machine Learning. Erasmus+ stay 2022, University of Zielona Góra.
  • Stephan Scholz: Heating a cuboid is the future of thermal process engineering. Tag der Promotion 2022, RWU, Weingarten.
  • Stephan Scholz: Scientific Machine Learning. Kolloquium 2022, RWU, Weingarten.

Scientific Machine Learning

Date 30.06.2022
Place   RWU


Kontakt & Personen

Allgemeine Kontaktinformationen

Postadresse RWU Hochschule Ravensburg-Weingarten
University of Applied Sciences
Control and Process Engineering
Postfach 30 22
D 88216 Weingarten

Research Group

Prof. Dr.-Ing. Lothar Berger

Leiter des Labors Regelungs- und Prozesstechnik
Regelungstechnik, Prozesstechnik, Mathematische Methoden
Lothar Berger

Stephan Scholz M.Sc.

Akademischer Mitarbeiter, Doktorand
Modellbildung, Numerische Simulation, Regelungstechnik
Stephan Scholz

Ralf Albrecht