In many industrial applications a workpiece is continuously fed through a heating zone in order to reach a desired temperature to obtain specific material properties. Many examples of such distributed parameter systems exist in heavy industry and also in furniture production such processes can be found. In this paper, a real-time capable model for a heating process with application to industrial furniture production is modeled. As the model is intended to be used in a Model Predictive Control (MPC) application, the main focus is to achieve minimum computational runtime while maintaining a sufficient amount of accuracy. Thus, the governing Partial Differential Equation (PDE) is discretized using finite differences on a grid, specifically tailored to this application. The grid is optimized to yield acceptable accuracy with a minimum number of grid nodes such that a relatively low order model is obtained. Subsequently, an explicit Runge-Kutta ODE (Ordinary Differential Equation) solver of fourth order is compared to the Crank-Nicolson integration scheme presented in Weiss et al. (2022) in terms of runtime and accuracy. Finally, the unknown thermal parameters of the process are estimated using real-world measurement data that was obtained from an experimental setup. The final model yields acceptable accuracy while at the same time shows promising computation time, which enables its use in an MPC controller.
This paper presents a modeling approach of an industrial heating process where a stripe-shaped workpiece is heated up to a specific temperature by applying hot air through a nozzle. The workpiece is moving through the heating zone and is considered to be of infinite length. The speed of the substrate is varying over time. The derived model is supposed to be computationally cheap to enable its use in a model-based control setting. We start by formulating the governing PDE and the corresponding boundary conditions. The PDE is then discretized on a spatial grid using finite differences and two different integration schemes, explicit and implicit, are derived. The two models are evaluated in terms of computational effort and accuracy. It turns out that the implicit approach is favorable for the regarded process. We optimize the grid of the model to achieve a low number of grid nodes while maintaining a sufficient amount of accuracy. Finally, the thermodynamical parameters are optimized in order to fit the model's output to real-world data that was obtained by experiments.
This paper describes the development of a control system for an industrial heating application. In this process a moving substrate is passing through a heating zone with variable speed. Heat is applied by hot air to the substrate with the air flow rate being the manipulated variable. The aim is to control the substrate’s temperature at a specific location after passing the heating zone. First, a model is derived for a point attached to the moving substrate. This is modified to reflect the temperature of the moving substrate at the specified location. In order to regulate the temperature a nonlinear model predictive control approach is applied using an implicit Euler scheme to integrate the model and an augmented gradient based optimization approach. The performance of the controller has been validated both by simulations and experiments on the physical plant. The respective results are presented in this paper.
Feature-Based Proposal Density Optimization for Nonlinear Model Predictive Path Integral Control
(2022)
This paper presents a novel feature-based sampling strategy for nonlinear Model Predictive Path Integral (MPPI) control. In MPPI control, the optimal control is calculated by solving a stochastic optimal control problem online using the weighted inference of stochastic trajectories. While the algorithm can be excellently parallelized the closed- loop performance is dependent on the information quality of the drawn samples. Because these samples are drawn using a proposal density, its quality is crucial for the solver and thus the controller performance. In classical MPPI control, the explored state-space is strongly constrained by assumptions that refer to the control value variance, which are necessary for transforming the Hamilton-Jacobi-Bellman (HJB) equation into a linear second-order partial differential equation. To achieve excellent performance even with discontinuous cost-functions, in this novel approach, knowledge-based features are used to determine the proposal density and thus, the region of state- space for exploration. This paper addresses the question of how the performance of the MPPI algorithm can be improved using a feature-based mixture of base densities. Further, the developed algorithm is applied on an autonomous vessel that follows a track and concurrently avoids collisions using an emergency braking feature.
This paper presents a systematic comparison of different advanced approaches for motion prediction of vessels for docking scenarios. Therefore, a conventional nonlinear gray-box-model, its extension to a hybrid model using an additional regression neural network (RNN) and a black-box-model only based on a RNN are compared. The optimal hyperparameters are found by grid search. The training and validation data for the different models is collected in full-scale experiments using the solar research vessel Solgenia. The performances of the different prediction models are compared in full-scale scenarios. %To use the investigated approaches for controller design, a general optimal control problem containing the advanced models is described. These can improve advanced control strategies e.g., nonlinear model predictive control (NMPC) or reinforcement learning (RL). This paper explores the question of what the advantages and disadvantages of the different presented prediction approaches are and how they can be used to improve the docking behavior of a vessel.
In this paper, a novel feature-based sampling strategy for nonlinear Model Predictive Path Integral (MPPI) control is presented. Using the MPPI approach, the optimal feedback control is calculated by solving a stochastic optimal control (OCP) problem online by evaluating the weighted inference of sampled stochastic trajectories. While the MPPI algorithm can be excellently parallelized, the closed-loop performance strongly depends on the information quality of the sampled trajectories. To draw samples, a proposal density is used. The solver’s and thus, the controller’s performance is of high quality if the sampled trajectories drawn from this proposal density are located in low-cost regions of state-space. In classical MPPI control, the explored state-space is strongly constrained by assumptions that refer to the control value’s covariance matrix, which are necessary for transforming the stochastic Hamilton–Jacobi–Bellman (HJB) equation into a linear second-order partial differential equation. To achieve excellent performance even with discontinuous cost functions, in this novel approach, knowledge-based features are introduced to constitute the proposal density and thus the low-cost region of state-space for exploration. This paper addresses the question of how the performance of the MPPI algorithm can be improved using a feature-based mixture of base densities. Furthermore, the developed algorithm is applied to an autonomous vessel that follows a track and concurrently avoids collisions using an emergency braking feature. Therefore, the presented feature-based MPPI algorithm is applied and analyzed in both simulation and full-scale experiments.
Analysing observability is an important step in the
process of designing state feedback controllers. While for linear
systems observability has been widely studied and easy-to-check
necessary and sufficient conditions are available, for nonlinear
systems, such a general recipe does not exist and different classes
of systems require different techniques. In this paper, we analyse
observability for an industrial heating process where a stripe-
shaped plastic workpiece is moving through a heating zone where
it is heated up to a specific temperature by applying hot air to its
surface through a nozzle. A modeling approach for this process
is briefly presented, yielding a nonlinear Ordinary Differential
Equation model. Sensitivity-based observability analysis is used
to identify unobservable states and make suggestions for addi-
tional sensor locations. In practice, however, it is not possible
to place additional sensors, so the available measurements are
used to implement a simple open-loop state estimator with
offset compensation and numerical and experimental results are
presented.
Comparison of Data-Driven Modeling and Identification Approaches for a Self-Balancing Vehicle
(2023)
This paper gives a systematic comparison of different state–of–the–art modeling approaches and the corresponding parameter identification processes for a self–balancing vehicle. In detail, a nonlinear grey box model, its extension to consider friction effects, a parametric black box model based on regression neural networks, and a hybrid approach are presented. The parameters of the models are identified by solving a nonlinear least squares problem. The training, validation, and test datasets are collected in full–scale experiments using a self–balancing vehicle. The performance of the different models used for ego–motion prediction are compared in full–scale scenarios, as well. The investigated model architectures can be used to improve both, simulation environments and model–based controller design. This paper shows the upsides and downsides arising from using the different modeling approaches. Videos showing the self–balancing vehicle in action are available at: https://tinyurl.com/mvn8j7vf22nd
The problem of controlling autonomous surface vessels in an energy-optimal way is important for the electrification of maritime systems and is currently being investigated by many researchers. In this paper, we use numerical optimal control to plan an energy-optimal docking trajectory in river currents and show that it can save energy compared to other widespread planning approaches. An optimal control problem including a detailed vessel model is defined, transcribed into a nonlinear optimization problem via direct multiple shooting, and solved using a homotopy procedure. The optimal solution is compared to a geometrical path planning approach with path-velocity decomposition. The results of this comparison show that prescribing a path with fixed vessel orientation leads to very suboptimal results. Further, we demonstrate how shrinking horizon MPC can control the vessel in an energy-optimal way even under severe disturbances, by replanning the energy-optimal trajectories in real-time. We believe that energy-optimal MPC could become a key technology for the electrification of maritime systems.
