Age-structured population models are an intuitive way to model competing bacteria populations in bioreactors, and are of interest for biotechnology processes, wastewater treatment, or epidemics. Such multi-population models with competition terms result in coupled partial differential equations with integral terms and non-local boundary conditions. They represent the population density of each species at a specific time and age. In this work, a model to represent two intra-and interspecific competing populations in a bioreactor is introduced. It has two system inputs, namely the dilution rate with nutrient solution and a recycling rate which introduces biomass in a steady-state from a second bioreactor. Adding a recycling rate to the multi-population models allows for influencing not only the entire biomass in the bioreactor but also the age distribution of the bacteria. In order to use population models to develop improved control concepts for such a cascaded bioreactor experiment, an extensive steady-state analysis is carried out. There exists an infinite number of steady-states of the system in dependence of the initial condition. Each choice of that initial condition lead to uniquely determined steady-state profiles, inputs and outputs. In a next step, a stabilization around these steady-states is necessary.

The design of thermal management strategies for electric vehicle powertrains is an important task, since these strategies influence performance, energy consumption, safety and durability of the powertrain operation. In the present paper, a predictive thermal management strategy for the powertrain cooling system is developed. The aims are to minimize the energy consumption of the cooling system, to increase the efficiency of the electric motors and to operate them in a temperature area of safety and durability. The thermal management strategy is realized by a real-time capable nonlinear model predictive controller, incorporating a dynamical model for the powertrain of the battery electric vehicle under consideration. The usage of this model-based approach ensures a fast adaption of the control strategy to different vehicle architectures. Since predictions of the disturbances acting on the system are uncertain in general, the control strategy is extended by a stochastic model predictive control approach to handle uncertainties in the disturbance prediction. The effectiveness of the resulting strategies is demonstrated using an accurate simulation model. Special attention is given to the possible energy savings, the robustness with respect to uncertainties, as well as the computational effort of the algorithms.

Modern production requires shorter measuring cycles of measuring machines, which can be achieved with highly dynamic references causing dynamic deviations of the actual tool-center-point (TCP) position. To minimize the TCP tracking error, the considered measuring machine is extended with a redundant axis and a modular control concept is proposed. For this dual-stage actuation setting, a higher-level reference allocation module exploits the resulting redundancy and yields suitable position references for the lower-level controlled subsystems. On the higher-level, two dual-stage control concepts are presented, yielding both significantly reduced tracking errors in experiments compared to using only the main axis. Furthermore, to deal with strongly spatially varying friction of the main axis of the considered measuring machine, its lower-level control system is improved.

The dynamics of microorganisms in a bioreactor are described by population systems. The tracking of the biomass of a desired trajectory is ensured by means of a nonlinear control law, as long as the reference trajectory complies with certain naturally given inequality constraints. To generate such a reference trajectory, an optimal control problem based on a double integrator with nonlinear state inequality constraints is solved. The necessary optimality criteria are extracted and the differential equations are solved. Using these solutions and parameter assumptions, which are shown to be non-limiting, it is proven that at most one constraint at a time is active. In addition, it is shown that the intervals in which no constraint is active and those in which one constraint is active alternate.

The dynamics of measuring machines are typically limited and do not suffice to fully exploit state-of-the-art metrology concepts. Therefore, dual-stage approaches become increasingly popular in this field. This paper uses a modeling approach including the lumped dynamic deviations and couplings between the actuators based on which optimal design paradigms are derived. Furthermore, the model is used to exploit the degree-of-freedom in the reference allocation considering the dynamic characteristics and limitations of each stage in a model predictive control fashion. A simulation study shows the benefits of the dual-stage approach as well as the proposed two-degree-of-freedom optimal reference allocation control structure.

In model predictive direct switching control (MPDSC) approaches, the finite set of inverter switch positions for the control of electrical drives is taken as control variables within the MPC underlying optimization problem. The cost function can be designed to track a torque or current reference while also considering additional control goals like minimizing switching and conduction losses, as well as physical constraints. The challenge is to solve the resulting integer quadratically constrained quadratic program (IQCQP) with high sampling frequencies online in order to obtain the optimal switch positions at each fixed time step. This paper presents two new MPDSC algorithms, namely relaxed barrier functions iteration scheme (RBF) and alternating direction method of multipliers heuristic (ADMM) and compares them with two state-of-the-art algorithms, namely full enumeration (FE) and multistep with sphere decoding (MSD) for the example of a multi-phase permanent-magnet synchronous motor (PMSM) in simulations.

Along the German and Luxembourgian part of the Moselle River, eleven distributed local water level and discharge controllers ensure safe navigation by guaranteeing a water level within a specified tolerance and by reducing variations in the river discharge. The current control scheme is based on gain scheduled PI control with a feed forward disturbance compensation element. Both were parametrized using a 1D Saint- Venant model. Due to advancements in control strategies and processing power, the current scheme will be upgraded by adding a model predictive feed forward component (MPFFC) which improves local control and links the isolated local controllers to coordinate their efforts. The authors want to report on this process from an operator’s point of view and share their insights from the ongoing testing procedure prior to actual service. A prototype implementation was deployed on the target hardware and linked to the data acquisition system to verify real time operation. The logged results are then verified using a simulation model.

Modern industries demand the production of smaller and yet more complex parts requiring the machine tool itself to fulfill increasing precision standards. Thermal stability is crucial to satisfy the producer's and the client's expectations regarding the product's quality and reliability. Using high-tech materials with very low coefficients of expansion, integrating water cooling or insulation can improve the thermal stability but is not always possible due to geometric constraints. In this paper, a systematic approach is suggested to compensate the thermally induced deformations by controlling a small number of additional cooling elements. The analytic description of the thermal-mechanical behavior is derived from a Finite Element system that allows the modeling of very complex machine geometries. The Balanced Truncation method is then applied to determine a reduced order model that is used for an optimization based feed-forward controller design. It will be shown that this controller not only significantly reduces the deformations but can also be successfully applied to the original high-order model. As perfect knowledge of both the model and the disturbances can rarely be guaranteed, a feedback controller is finally introduced to improve the compensation of thermally induced deformations.

The considered transport systems, which possess an actuator with a spatial influence characteristic along the transport path, are used for the transport of material between different process stages and for the conditioning of the conveyed goods at the same time. The spatially acting input results in complex input/output behaviour of a Single-Input Single-Output (SISO) system with distributed delays. The feedforward control task under consideration is defined by a setpoint change of the subsequent process stage. For the feedforward controller design, an inversion-based approach in the frequency domain is investigated to steer the output of the transport system towards a predefined constant value. In order to compensate model uncertainties and reject unknown disturbances, the results of the inversion-based feedforward control are used to design a feedback controller.

Model predictive control applications have broadened from industrial plants with slow system dynamics to the implementation of control algorithms on low-cost hardware. Ip2go has been developed with the aim of making model predictive control readily accessible on embedded systems. It generates efficient, problem-tailored solvers for optimal control problems. The code generator implements Mehrotra’s predictor-corrector interior-point method with Riccati recursions. It can be applied to quadratic programming problems with linear discrete-time system dynamics and polytopic inequality constraints. Both hard and soft constraints can be implemented. In this paper the features of ip2go, the underlying algorithm, the benefits of code generation and the generation process are set out. The comparison of ip2go-generated solvers to state-of-the-art solvers shows that ip2go can compete in terms of efficiency and code-size. The open and modular design allows all users to amend the generator. The Matlab and based and LGPL licensed C-code generator ip2go is available under https://github.com/fabiankrank/ip2go.

This paper presents a new method for parametric model order reduction based on balanced truncation. Parametric model order reduction seeks to generate low-order models from larger models without losing the dependence on a parameter. Using a Taylor expansion of the original system, a Taylor expansion of the balanced system can be obtained. In contrast to interpolation-based approaches for the solution of the parametric model order reduction problem, the proposed approach permits calculation of the reduced system as well as the corresponding projection matrix for different parameter values with reduced computation power. This bypasses the problem of incompatible subspaces from different snapshot points potentially occurring in interpolation based approaches that can lead to unexpected behavior up to instability. The presented method can handle multidimensional parameter spaces. Sufficient conditions for the convergence of the Taylor series of the balanced system based on holomorphic functions are derived. The truncation step as well as error bounds are discussed. A Bernoulli beam model is used as an example to demonstrate the performance of the technique.

The automatic management of impounded rivers ensures easy and safe navigation implying the realization of two contradicting control goals. These are a steady water level at the ship locks and under bridges as well as the attenuation of discharge transients. The operational local gain scheduled PI based control solution used in Moselle river barrages can only guarantee a steady water level at the cost of propagating and amplifying discharge disturbances from reach to reach. To remedy this behavior, a linear model predictive feedforward control method for constant discharge setpoints is available. This paper analyzes the changing dynamics of the Moselle reaches at different setpoints and proposes an online scheduled linear model predictive feedforward approach to cover all practically relevant discharge setpoints. To maintain real time capability, simple control models based on linearized and discretized Saint-Venant equations are conveniently identified using existing high precision models. Together with few intuitive parameters, a global control solution for all relevant setpoints is presented. The performance of the presented control solution is asserted by simulation experiments on verified high precision models.

The present paper addresses the problem of control reconfiguration in the case of actuator failures in the context of active vibration control of the reference system Stuttgart SmartShell. Due to the use of hydraulically actuated tripods, the failure of single actuators introduces nonlinear input constraints in the nominal optimal control problem. The suggested control reconfiguration is based on the lineariziation of the input constraints, leading to a time-varying optimal control problem, which is solved using a Riccati approach. The controller is then implemented in a model-predictive control scheme. The suggested approach is evaluated in simulation. The results indicate that the approach is able to at least partially recover control performance and is well-suited for real-time implementation.

The article deals with the design of a feedforward controller for a transport system with spatially distributed control input considering input constraints. The feedforward controller is used to compensate transport delays in the input-/output (I/O) behavior of the transport system by realizing exact trajectory tracking of the nominal output along desired trajectories. The proposed method is based on the inversion of the linear I/O-model of the considered transport system. The input constraints are considered by optimizing parameters of the planned output trajectories. The presented method is compared to an early lumping approach discretizing the model equations and solving an optimization problem of the discretized system. Finally simulation results are presented and discussed.

The automatic management of barrage controlled river segments tries to ensure easy and safe navigation and at the same time suppress large water discharge variations. The predominant local PI based control solution used in Moselle river barrages can only guarantee a steady water level at the cost of possibly amplifying inflow disturbances. To balance these contradicting goals, a model predictive controller (MPC) based feed-forward control method is proposed to retrofit the already established local PI-control. The propsed method does not require feedback from the plant, eliminating unwanted interactions with already installed controllers. To achieve real time operation on industrial control hardware, the MPC utilizes simplified river models. Two approaches are compared in this paper: Fully linearized and discretized Saint-Venant equations and an analytical approximate solution of the Hayami equations are used as discharge prediction models for the MPC. The satisfying performance of the proposed approaches is demonstrated using a verified numerical simulation model and is compared to the performance of the existing PI control solution.

Active Heave Compensation (AHC) systems need an active control of the heaving winch in order to decouple the offshore crane's lift operation from the vertical motion of the vessel. Two-degree-of-freedom control (2DOF) can give good tracking control performance for such applications. However, every 2DOF control system requires a reference trajectory which has to fulfill requirements regarding continuity and differentiability. In case of AHC applications, the drive system of the winch is usually limited by velocity and acceleration constraints. Thus, the trajectory planning needs to take these constraints into account. Furthermore, the trajectory needs to be generated in real-time which narrows down the number of possible algorithms. In this work, a real-time model predictive trajectory planner is presented. By means of predictions of the vertical position and velocity of the crane tip, an optimal control problem is formulated and solved online for every time step. Furthermore, state constraints are taken into account. For the case when no optimal control solution can be found within the available time, a repetitive polynomial-based trajectory planner is used as fallback-strategy. The proposed approach is validated with simulations as well as experiments on the Liebherr AHC test bench.

In small and midsize harbors, boom cranes are used for multiple applications. These include bulk cargo handling and container transloading. For container handling, a spreader is attached to the crane hook. While grabbing a container with the spreader, both the position and the orientation of the spreader and the container must match. The spreader orientation is usually referred-to as skew angle. Other synonyms are yaw angle or spreader heading. The skew angle is controlled using a hook-mounted rotator motor. Since wind, impact, and uneven load distribution can cause skew vibrations, active skew control is desirable for facilitating crane operation, improving positioning accuracy, and increasing turnover. Different skewing device designs are used for different types of cranes. This contribution presents the skew dynamics on a boom crane along with an actuator model and a sensor configuration. Subsequently a two-degrees of freedom control concept (2-DOF) is derived which comprises a state observer for the skew dynamics, a reference trajectory generator, and a feedback control law. The control system is implemented on a Liebherr mobile harbor crane and its effectiveness is validated with multiple test drives.

The automatic management of barrage controlled river segments tries to combine several contradicting goals. To facilitate ship traffic and at the same time prevent large water discharge surges, the two competing goals of a steady water level and a homogenized water discharge into the next river section have to be harmonized with each other. As local water level control is already state of the art, an approach to homogenize the resulting water discharge by utilizing water level tolerances is proposed in this work. To achieve this goal, a model predictive water level coordinator is proposed that uses an inverted distributed parameter river section model. The use of this coordinator on standard industrial control hardware with limited computational capabilities requires the simplification of the existing nonlinear Saint-Venant river models. A reduced linear Hayami model is therefor deducted and identified, making a power series based analytical solution possible which reduces the computational cost significantly. The effectiveness of this method will be illustrated and evaluated on a verified and precise model of an impounded river section of the lower Mosel river with a fully automated barrage system. It is shown that the water discharge can be homogenized while keeping the the water level within given bounds.