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The modular open-source framework GRAMPC-D for model predictive control of distributed systems is presented in this paper. The modular concept allows to solve optimal control problems (OCP) in a centralized and distributed fashion using the same problem description. It is tailored to computational efficiency with the focus on embedded hardware. The distributed solution is based on the Alternating Direction Method of Multipliers (ADMM) and uses the concept of neighbor approximation to enhance convergence speed. The presented framework can be accessed through Cpp and Python and also supports plug-and-play and data exchange between agents over a network., Submitted to Optimization and Engineering

Zusammenfassung Der Beitrag stellt ein Verfahren zur Bewegungsplanung von dynamischen Fahrsimulatoren basierend auf der modellprädiktiven Regelung vor. Das Ziel dabei ist es, einen möglichst realitätsnahen Bewegungseindruck bei einer Testperson unter Berücksichtigung des beschränkten Arbeitsraums des Simulators zu erzeugen. Zusätzlich wird eine Methode zur Schätzung des zukünftigen Fahrerverhaltens auf Basis der optimalen Regelung vorgestellt, mit der die zukünftigen Referenzwerte für die modellprädiktive Regelung geschätzt werden, um so den prädiktiven Charakter des Verfahrens auch in der Online-Anwendung voll ausnutzen zu können.

Industry 4.0 is associated with numerous technologies, which offer great potential for optimizing linear winding processes as used in electric motor manufacturing. To further increase flexibility and quality in the production of mass products like coils, data-driven techniques such as machine learning (ML) are increasingly moving into focus. To generate the required data, however, linear winding machines must be equipped with suitable sensors. Accordingly, this paper will first present all known influencing and quality parameters in linear winding based on earlier research work. Based on this, suitable data sources and sensor systems are identified and a concept for applying ML techniques is derived.

Zusammenfassung Dieser Beitrag stellt eine modellprädiktive Pfadfolgeregelung für die Kombination mit einer kollisionsfreien Bewegungsplanung für Roboter vor. Zwei Besonderheiten sind mit diesem Anwendungsfall verbunden. Zum einen wird keine hochgenaue Pfadfolge benötigt, solange die Bewegung kollisionsfrei ist. Somit kann die Pfadfolgeregelung vom geplanten Pfad abweichen, um die Zielkonfiguration effizienter zu erreichen. Zum anderen ist eine exakte Bewegung entlang des Pfades prinzipiell möglich, so dass mit Hilfe einer Referenztrajektorie rekursive Lösbarkeit und Stabilität garantiert werden kann. Die Vorteile zeigen sich vor allem bei graphbasierten Planungsverfahren, wo die berechneten Pfade typischerweise stückweise linear sind und eine exakte Pfadfolge sehr aufwändig ist. Die Anwendung der Methodik wird in Simulationen für einen Manipulator und einen mobilen Roboter gezeigt.

This paper discusses the use of model predictive control (MPC) for industrial robot applications with physical robot-environmental interaction. A model predictive interaction control (MPIC) scheme is introduced that deals both with the prediction of the robot motion and the forces between robot and environment. With regard to the robot motion, either the rigid body dynamics, a simplified model, or a cascaded control structure can be employed. The external forces or torques are treated as additional state variables whose dynamics are based on the elastic behavior of the contact surface. Since the force prediction depends on the knowledge of the environmental stiffness, a method for online estimation is discussed. The approach allows to realize different tasks as motion control, compliance control, direct force control as well as hybrid force/motion control by adjusting the weighting factors in the cost function. The implementation is based on the nonlinear MPC software Grampc and the library Pinocchio for computation of rigid body dynamics. Besides comparing the different robot dynamics models, the approach is demonstrated for a hand-guiding and a table wiping task.

In this paper an optimal control approach based on a combination of inversion-based control and internal model control (IMC) is designed to keep the controlled states of a minimum-phase input-affine MIMO system within predefined tubes while respecting input constraints. This contribution extends recently presented results for the SISO case to nonlinear input-affine MIMO systems. The developed approach uses ideas developed in the design of inversion-based IMC controllers for setpoint tracking and extends them to ‘tube tracking’. It shows the interesting result that for input-affine systems the control task of maintaining each controlled state within a tube while minimizing energy consumption and respecting input constraints can be expressed as a convex quadratic optimization problem. This concept allows to handle dynamic systems where the number of control inputs differs from the number of controlled outputs are not equal. The control approach is illustrated by three simulation examples.

This letter proposes a predictive path-following controller for efficient time parameterization during continuous replanning with dynamic roadmaps (DRMs). DRMs are an approach for fast global path planning in changing environments and are based on a precomputed graph in the configuration space and mappings from workspace voxels to vertices and edges in the graph. However, DRMs are a kinematic path planner and require subsequent steps of smoothing and trajectory generation before execution. This makes it hard to replan while the robot is moving, it is so because the time parameterization should account for the current position and velocity of the robot. To cope with this issue, a predictive path-following controller is presented, which computes the optimal control actions for moving the robot along the planned paths while respecting the bounds on maximum velocities and accelerations. Furthermore, it enables continuous replanning, i.e., the computation of new paths at fixed intervals, which is particularly useful in combination with a prediction of moving obstacles. The real-time capable approach is evaluated in simulation scenarios with moving obstacles and is experimentally validated for a dual-arm robot with 12 degrees of freedom.

This paper presents a nonlinear model predictive control (MPC) strategy for heavy-duty multigroup transmissions. The underlying optimal control problem consists of three phases with unspecified end times to deal with the state-dependent switching of the hybrid dynamics and additionally accounts for several state and input constraints. The design objective is to maintain the output speed and output torque while minimizing the time needed to shift gears. A tailored nonlinear optimization algorithm on a shrinking horizon is presented in order to achieve real-time feasibility of the MPC scheme on an electronic control unit (ECU). Simulations against a high-fidelity model and runtime results demonstrate the performance of the MPC scheme for gear downshift and upshift as well as the algorithmic efficiency with computation times in the single-digit millisecond range on an ECU level. The real-world applicability is demonstrated by presenting experimental results for a 16 tons wheel loader.

Zusammenfassung Datenbasierte Modellbildungsverfahren haben auch für komplexe und hochdimensionale Systeme an Bedeutung gewonnen. Sie bieten den Vorteil einer deutlich verkürzten Entwicklungszeit im Vergleich zur physikalischen Modellierung. Der Nachteil vieler herkömmlicher Verfahren ist allerdings, dass selbst einfaches Wissen, wie etwa Extrapolationseigenschaften, nicht in der Modellgenerierung berücksichtigt werden können. Deshalb soll in diesem Beitrag eine Methodik vorgestellt werden, wie auf Basis der Gaußprozessregression solches Wissen auch für datenbasierte Verfahren genutzt werden kann. Desweiteren ist es in vielen physikalischen Systemen notwendig, dass die Modelle während der Laufzeit an individuell unterschiedliche Systeme angepasst werden können. Dazu wird ein Online-Adaptionsverfahren vorgestellt, welches die Unsicherheitsinformation des Gaußprozesses nutzt, um Änderungen im System zu detektieren und das Modell anzupassen.

Human robot collaboration requires specific properties of modern lightweight robots that differ from conventional robots. One of these is the property of reacting to external forces acting on the robot structure, which typically requires joint torque measurements. In contrast to that, this paper presents an approach for estimating the external joint torques based on two different information sources, the motor current and the torsional deformation. To obtain an accurate estimation based on the torsional deformation, disturbing effects and inaccuracies of the angular measurements have to be taken into account. An approach for modeling, identification and cancellation of these effects is presented. Furthermore, the fusion of both estimations is discussed and the validation of the approach on a lightweight robot is presented.

In this paper an optimal control approach based on a combination of the flatness theory and the internal model control (IMC) concept is designed to keep the controlled state within a predefined tube while respecting input constraints. This contribution uses ideas developed in the design of flatness-based feedforward IMC controllers for setpoint tracking and extends them to ‘tube tracking’. It shows the interesting result that for flat input-affine systems the control task of remaining within a tube while minimizing energy consumption and respecting input constraints can be expressed by a convex quadratic optimization problem. The computational feasibility of the developed control strategy is ensured by a purely analytical solution for the quadratic optimization problem derived based on the Karush-Kuhn-Tucker (KKT) optimality conditions. The control approach is illustrated by a simulation example.

Axial piston motors are core components in many hydro-mechanical systems as e.g. the powertrain of wheel loader vehicles. The optimal performance of the motor as well as the powertrain requires a fast and exact control of the motor’s swivel angle according to the a-priori unknown reference signal which is e.g. generated by the driver with a joystick or gas pedal operation. Therefore, it is essential that the swivel angle controller fully exploits the possible dynamics and the constrained resources of the nonlinear swivel angle adjustment system. In this work, a novel flatness-based feedforward control strategy for the swivel angle is presented, which is capable of considering the relevant state and input constraints in real-time, i.e. only by means of the currently available information and without relying on an online optimization. The proposed swivel angle controller is finally demonstrated and discussed with the results of both a simulation study and measurement data from a wheel loader vehicle.

This contribution presents a nonlinear model predictive control (MPC) scheme for the torque control of permanent magnet synchronous machines. The control scheme is based on the nonlinear dq-model including current-dependent inductivities and provides a desired torque in an energy-efficient way while accounting for constraints on the DC link current, phase currents, and hexagonal voltage constraints. The MPC algorithm uses an augmented Lagrangian method in combination with a real-time gradient method to allow for a computationally efficient solution. Experimental results for a standard industrial drive show the performance, robustness, and computational efficiency of the MPC with a sampling time of 500 μ s.

Zusammenfassung Die effiziente Lösung von Optimierungsproblemen in Echtzeit bildet die Grundlage vieler moderner Regelungs- und Schätzverfahren. So basieren die prädiktive Regelung sowie die Zustandsschätzung auf bewegtem Horizont auf der wiederholten Lösung beschränkter Optimierungsprobleme. Methodische sowie technologische Fortschritte ermöglichen den Einsatz optimierungsbasierter Verfahren in Echtzeit selbst für anspruchsvolle Regelungs- und Schätzprobleme mit Zeitkonstanten im Bereich von Mikro- oder sogar Nanosekunden. Nach einem Überblick über effiziente Lösungsansätze für die echtzeitfähige Umsetzung optimierungsbasierter Schätz- und Regelungsverfahren fokussiert sich diese Arbeit auf wesentliche technologische, regelungs- und systemtheoretische Aspekte für deren erfolgreichen Einsatz.

This paper extends the recently introduced ALADIN algorithm to non-convex continuous-time optimal control problems with nonlinear dynamics and linear coupling constraints. The algorithm alternates between solving a convexified local problem in a distributed manner and a linearized quadratic problem on a centralized entity while using the solution of both for an update step. This paper presents an analysis of the local convergence of the algorithm and shows a quadratic convergence rate. Furthermore, a globalization strategy is presented that ensures global convergence. The paper closes with a numerical evaluation of the algorithm.

This paper presents a safe optimization method for minimizing an unknown cost function subject to unknown inequality and equality constraints. The cost function as well as the constraints evaluation may be corrupted with Gaussian measurement noise with known uncertainty. The focus especially lies in the safe exploration of the cost function, which means that an evaluation of the cost function far away of previous evaluations is not favoured. Also evaluations in regions where the constraints are violated are undesired. This is the case, for example, in technical applications, where systems may become unstable or damaged, if constraints are violated. To this end, a combination of the expected improvement of the cost and its mean is minimized, while bounding the variance of the cost. The inequality and equality constraints are reformulated as constraints for the probability of the constraint violation. The optimization method is evaluated on numerical examples.

The hydraulic clutch actuation path used in heavy duty transmissions often shows a lot of variability due to manufacturing tolerances and ageing effects. Reason for this are in particular varying friction coefficients in the spools and external factors such as compliance with the specified service intervals or the choice of hydraulic fluid. As a direct consequence, the shift quality typically varies from one transmission to the next. To resolve this problem, this paper presents a machine learning algorithm for the feedforward control of the hydraulic clutch actuation path, a model-based and a data-based feedforward approach. The two approaches are evaluated and compared with each other in simulations with a high-fidelity model. As it turns out, the model-based version is to be preferred and therefore used in a real world evaluation on an embedded controller and a 16 tons wheel loader.

The winding process in electric motor manufacturing consists of individual subsystems such as the movement of the wire guide, the wire tension control system, and the movement of the coil. Although the overall process is already highly automated these days, for control the single subsystems are only considered isolated due to the complexity of the overall process. The individual subprocesses are controlled on the basis of target values which only have an indirect effect on the product quality and the relevant properties. As a result, there is no consideration of the entire, coupled winding process yet. However, a holistic view of the complete winding process offers the advantage that all influences can be incorporated to optimize relevant parameters such as the copper fill factor or other parameters. This paper presents a first step towards a generalized control concept for direct winding technologies and, in particular, presents a methodological description of the optimization of the relevant process variables. This holistic view is further extended to an optimization-based framework in order to consider relevant process parameters and control variables in the form of cost functions and to optimize the coil production regarding relevant characteristics.

The development of modern sensitive lightweight robots allows the use of robot arms in numerous new scenarios. Especially in applications where interaction between the robot and an object is desired, e.g. in assembly, conventional purely position-controlled robots fail. Former research has focused, among others, on control methods that center on robot-environment interaction. However, these methods often consider only separate scenarios, as for example a pure force control scenario. The present paper aims to address this drawback and proposes a control framework for robot-environment interaction that allows a wide range of possible interaction types. At the same time, the approach can be used for setpoint generation of position-controlled robot arms, where no interaction takes place. Thus, switching between different controller types for specific interaction kinds is not necessary. This versatility is achieved by a model predictive control-based framework which allows trajectory following control of joint or end-effector position as well as of forces for compliant or rigid robot-environment interactions. For this purpose, the robot motion is predicted by an approximated dynamic model and the force behavior by an interaction model. The characteristics of the approach are discussed on the basis of two scenarios on a lightweight robot.

The paper presents a distributed model predictive control (DMPC) scheme for continuous-time nonlinear systems based on the alternating direction method of multipliers (ADMM). A stopping criterion in the ADMM algorithm limits the iterations and therefore the required communication effort during the distributed MPC solution at the expense of a suboptimal solution. Stability results are presented for the suboptimal DMPC scheme under two different ADMM convergence assumptions. In particular, it is shown that the required iterations in each ADMM step are bounded, which is also confirmed in simulation studies.

A trajectory planning approach for electromagnetic heating systems is presented capable to optimize the electrical excitation and spatial configuration of the corresponding actuator (e. g. inductor or electrode). In order to accurately incorporate the electromagnetic and thermal phenomena, a PDE constrained optimization problem is formulated. The optimality conditions are derived in the function space of the original problem formulation following a first optimize then discretize approach to ensure that not only the system dynamics but rather the whole optimality system can be solved by FEM-based simulation software. The major advantage lies in coping with different types of electromagnetic heating systems. Numerical results illustrate the applicability and accuracy of the trajectory planning.

This paper proposes a tailored fixed-point iteration scheme for the model predictive torque control of permanent magnet synchronous machines. Both spherical voltage and current constraints are taken into account using a projection function and an augmented Lagrangian approach. The fixed-point scheme is a continuous control set approach and is based on the nonlinear dq-model. The inductivities and permanent magnet flux are modelled current-dependently and therefore account for saturation and parasitic effects. Experimental results on a standard dSpace hardware show the performance as well as the very small computational load of the proposed torque control scheme, which is therefore suitable for an embedded implementation.

This paper derives an accurate dynamical model of an indirectly controlled hydraulic actuation path for a wet friction clutch. The considered setup exhibits a relatively low pressure range, which necessitates to account for the variable compressibility of the hydraulic fluid due to entrained air. In addition, the model design accounts for the complex valve geometry as well as the draft angles of the valve housing due to injection moulding. The relevant hysteresis phenomena of the valves are modelled via Prandtl-Ishlinskii and LuGre operators, respectively. Simulation results show the accuracy of the model with an average error of 0.9% (180 mbar) compared to measurements. In addition, the necessity to respect the entrained air is verified by a counter-simulation with constant bulk modulus.

In order to balance emissions accurately during highly transient engine operation, novel approaches of diesel engine control must achieve an appropriate interplay of the cycle-by-cycle fuel injection, i.e. the start position and mass of each fuel injection pulse, and the air system control scheme. Accordingly, this paper proposes a control concept that adjusts the fuel injection parameters as manipulated variables in dependence of the transient air system dynamics. The approach is based on a cylinder model that predicts the emissions and torque by means of physical and Gaussian Process Regression models. Fuel injection adjustments are determined by numerical optimization to minimize emissions while providing the desired engine torque. The optimization also considers the uncertainty of the emission predictions. This controller is tested by a high fidelity reference engine model which is also briefly introduced. It combines the cylinder description with a 1-dimensional air system model built up in the simulation environment GT-suite. The entire engine model is parametrized and validated using test-bench measurements.

The real-time generation of kinematic trajectories w.r.t. state and input constraints is discussed for the stabilization of the lateral, longitudinal and vertical motion of objects such as (automated) vehicles in the Frenet frame. The goal is to exploit the property of differential flatness in order to achieve optimal trajectories as well as a flexible and selectable prioritization-based constraints satisfaction. This aim is subject to the absence of an online optimization and a low complexity of the planner’s architecture. With regard to practical application, a discrete-time implementation of the planner is presented and benchmarked with two modern MPC approaches in terms of optimality and CPU-time consumption by means of simulation studies.

This paper presents a method for modelling and controlling charge air pressure of a heavy-duty Diesel engine. The modelling method combines expert information about the system with a training dataset to provide a reasonable extrapolation behaviour as well as high accuracy. The dynamics of the gas path are modelled as a Wiener process with separate dynamics for each input. After identifying these dynamics, a controller based on input-output linearisation can be designed. The controller is shown to be able to track a set point of the gas path even after a sensor failure. To this end, the system behaviour is learned online to increase the accuracy. An evaluation against a reference model shows the performance of the method.

The hydraulics of heavy-duty transmissions typically lack pressure sensors, which implies that the hydraulic actuation system has to be controlled in a feedforward manner. In practical applications, this is often done by numerically inverting a static mapping, leading to undesired pressure errors and inaccurate clutch positioning especially in dynamic situations. This paper therefore investigates two feedforward control strategies for a hydraulic clutch actuation path. The first is a flatness-based feedforward control strategy that relies on a high accuracy model, and additionally accounts for input constraints. The second one is a data-driven neural network-based feedforward control strategy that relies on measurement data. The feedforward controls are first evaluated in simulations and subsequently evaluated experimentally for a real-world transmission that demonstrates the realizability on ECU level as well as the effectiveness of the flatness-based and neural network-based feedforward controls compared to the standard static mapping-based approach.

This paper presents a method for nonlinear system identification with Gaussian process regression. The unsupervised method is able to generate an approximation of the system with correct extrapolation behaviour, that is refined with input/output-data in the typical working area and sampled online data. Therefore, an offline model is generated, which consists of a nominal model set up by the extrapolation behaviour and a detailed model for the refinement. The method is able to keep track of time-varying systems by using the confidence information to incorporate new measurements into the online model. The performance of the proposed method is tested on different numerical examples.

Axial piston motors and pumps are core components in many hydromechanical systems as for instance the powertrain of wheel loader vehicles. The optimal performance of the individual components as well as the entire powertrain requires a fast and exact control of both the motor’s swivel angle as well as the pressure difference over the pump by means of the currently available information and despite their respective a-priori unknown reference signal generated by the driver with a joystick or gas pedal operation. Therefore, it is essential that the swivel angle and pressure controllers fully exploit the possible dynamics and the constrained resources of the nonlinear swivel angle displacement and the pressure adjustment system, respectively. In this work, a flatness-based feedforward control strategy for the motor’s swivel angle as well as a flatness-based tracking two-degree-of-freedom controller for the pump pressure are proposed. For the realization of the flat feedforward and the tracking controller, a constrained online trajectory generation by means of a nonlinear (switched) state variable filter is designed for each. Therefore, both controllers are capable of considering the relevant state and input constraints in real-time and without relying on an online optimization. The proposed control algorithms are both discussed and their performance is illustrated with measurement data from a wheel loader vehicle.

Zusammenfassung Der Beitrag stellt ein Verfahren zur stochastischen modellprädiktiven Regelung nichtlinearer Systeme vor, wobei das unsichere Systemverhalten durch eine stochastische Differentialgleichung beschrieben wird. Die Unscented-Transformation wird eingesetzt, um die Evolution der Wahrscheinlichkeitsverteilung durch eine Prädiktion von Mittelwert und Kovarianz zu ersetzen. Das resultierende deterministische Problem kann effizient numerisch mit einem Gradientenverfahren gelöst werden.

Since novel approaches of diesel engine control have to balance the emissions and the generated torque most accurately during highly transient engine operation, exact cycle-by-cycle estimates of these engine outputs are mandatory. Accordingly, this paper develops a control-oriented combustion cycle model to determine the indicated mean effective pressure as well as the nitrogen oxide and the smoke emissions. The proposed model has a hybrid structure, i.e. the gas exchange and compression are modeled physics-based with lumped mass and energy balances, whereas the combustion is approximated by a data-based approach due to the complex chemical reaction kinetics. Thus, the model outputs are described with respect to the time-varying signals of the transient air path conditions (intake pressure, oxygen concentration, and temperature) as well as the inputs adjusted by the fuel injection (start position and mass of each fuel injection pulse). Measurement data is used for the parametrization and validation of the model.

Thermal management of electric vehicles in low-temperature environments poses an interesting control problem. While thermal control of the cabin is vital for passenger comfort, energy consumption and battery aging always remain an essential concern. Since more reliable information about the short-term future electrical power flow is becoming available by more sophisticated cruise control systems and map information, on-line model predictive thermal management systems can utilize this knowledge to improve battery life maintaining passenger comfort. In this contribution, such a model predictive heating control is proposed based on an on-board capable fast gradient method to solve the nonlinear optimization problem. Direct control of simple electronic switches by the proposed method reduces the need for dedicated PWM controllers embedded within the heating actuators and allows for a cost-efficient and easy realization.

This contribution deals with planning optimal trajectories for radiofrequency and microwave ablation in the course of interstitial hyperthermia. Rigorous mathematical modeling of these processes leads to systems of coupled partial differential equations with Dirichlet boundary control. To tackle the optimal trajectory planning problem by means of dynamic optimization, the Dirichlet boundary controls are approximated by suitable Neumann boundary controls. Consequently, the formal Lagrangian technique can be applied to derive the optimality conditions. A gradient algorithm in combination with state-of-the-art FEM software (FEM -finite element method) is used to numerically solve the problems straightforward.

This paper proposes a model predictive torque control scheme for induction machines. The approach utilizes an augmented Lagrangian method in combination with a tailored gradient algorithm to efficiently solve the optimal control problem. The problem formulation accounts for hexagonal voltage constraints as well as constraints on the phase currents and the DC link current. A tailored calculation scheme for energy-efficient current setpoints improves the performance and the stability of the approach. Experimental results with computation times of less than 100 μ s on a d SPACE real-time platform prove the potential of the proposed torque control scheme.

Motion trajectory planning is one crucial aspect for automated vehicles, as it governs the own future behavior in a dynamically changing environment. A good utilization of a vehicle's characteristics requires the consideration of the nonlinear system dynamics within the optimization problem to be solved. In particular, real-time feasibility is essential for automated driving, in order to account for the fast changing surrounding, e.g. for moving objects. The key contributions of this paper are the presentation of a fast optimization algorithm for trajectory planning including the nonlinear system model. Further, a new concurrent operation scheme for two optimization algorithms is derived and investigated. The proposed algorithm operates in the submillisecond range on a standard PC. As an exemplary scenario, the task of driving along a challenging reference course is demonstrated.

This contribution presents a motion cueing algorithm (MCA) for driving simulators using nonlinear model predictive control (MPC). The goal of the MCA is to generate a realistic motion feeling while keeping the simulator within its workspace limits. The approach relies on a realtime gradient algorithm in combination with the augmented Lagrangian method in order to directly incorporate the system constraints into the optimization. Simulation results for a reference trajectory with typical driving situations demonstrate the performance as well as the computational efficiency of the approach.

This paper addresses the optimization-based planning of collision-free motions for a dual-arm robot with kinematic constraints. Such problems arise, for example, when the robot has to move an object with both arms, whereby the two arms and the gripped object form a closed kinematic chain. Such constrained problems are hard to solve with sampling-based planners, because the probability that a random sample satisfies the closure constraint is practically zero. In contrast, the solution of optimization problems with equality constraints is a well-understood field of research. This paper formulates the motion planning task as optimization problem and proposes a numerical solution using the augmented Lagrangian method for handling constraints. The planner is compared to RRTs, CHOMP and TrajOpt on a set of randomly generated problems for a dual-arm robot with twelve degrees of freedom highlighting the advantages of optimization-based planning.

The problem of constrained Online Trajectory Planning (OTP) for Flatness-based Feedforward Controllers (FFC) is discussed for online tracking problems with a-priori unknown reference signals for the system output. As plant, nonlinear minimum phase Single Input Single Output (SISO) systems with input constraints as well as polytopic constraints on the flat state are assumed. The goal is to achieve both, fast reference tracking and a prioritization-based constraint satisfaction despite avoiding an online optimization. Therefore, the OTP is set up by means of a switched State Variable Filter (SSVF). The switching results from the limitation of the filter’s highest derivative in accordance to the above requirements and is derived with a piecewise solution of an underlying optimization problem. The paper shows the derivation of the SSVF, discusses necessary stability conditions of the proposed concept, and finally demonstrates the SSVF’s performance by means of a simulation study. A comparison to a respective optimal control problem solution and model predictive controller (MPC) is furthermore provided.

The problem of stabilization by means of state feedback is discussed for linear single input single output systems while satisfying time-varying polytopic constraints on both the states and the control input. The core of the switched control concept derived in this work is a standard state feedback controller, stabilizing the system in the unconstrained case, whereas its control signal is optimally limited in order to achieve feasibility of the states and the input in the constrained case. For the derivation of the limiting function, feasible dynamic limits are designed which correspond to one additional control law per constraint. A switching logic for these limits is then constructed with the solution of an optimization problem. Thereby, an explicit order of constraints prioritization is taken into account in order to obtain a unique switching logic. Throughout the derivation, the property of differential flatness is exploited, which allows the reduction of the respective system to the control of a (constrained) integrator chain. The performance of the control approach as pure feedback as well as in a constrained two-degree-offreedom setup is finally discussed by means of simulation studies. Furthermore, a comparison of the achieved results with a model predictive control approach is carried out.

Many torque control schemes for permanent magnet synchronous machines require suitable reference values for the dq-currents. This contribution presents an algorithm to compute these references in an optimal and computationally efficient manner. The algorithm relies on the steady state dq-model with stator resistance and accounts for nonlinear constraints on the phase currents and voltages as well as on the DC link current, which is of relevance e.g. for battery management systems. The algorithm requires a minimum computation time to ensure realtime feasibility for PMSM torque controllers. Simulation results and computation times of less than 10 μs on CPU and dSpace level illustrate the performance of the algorithm and its suitability for an embedded real-time implementation.

Air path observation is important for the diagnosis and control of modern diesel engines. Recent air path observers assume the measurement of the mass air flow which is a justified assumption in the automotive domain. However, the mass air flow is usually not measured for series-produced off-highway engines as the pipework is customized. Due to the intense complexity of the air path, a tailored spherical simplex unscented Kalman filter is used to achieve real-time feasibility. In order to consider the dependency of the air path model uncertainty from the engine operating point, a nonlinear residual based adaptation scheme for the measurement noise covariance matrix is proposed. The high accuracy and the computational performance of the observer is demonstrated by GT-POWER simulation runs, testbench measurements, and a running time analysis.

Summary The paper presents a constraint transformation approach for nonlinear model predictive control (MPC) subject to a class of state and control constraints. The approach uses a two-stage transformation technique to incorporate the constraints into a new unconstrained MPC formulation with new variables. As part of the stability analysis, the relationship of the new unconstrained MPC scheme to an interior penalty formulation in the original variables is discussed. The approach is combined with an unconstrained gradient method that allows for computing the single MPC iterations in a real-time manner. The applicability of the approach, for example, to fast mechatronic systems, is demonstrated by numerical as well as experimental results. Copyright © 2015 John Wiley & Sons, Ltd.

Dynamic roadmaps (DRM) are a planning approach for robots in changing environments where fast replanning is required. DRMs are based on a precomputed graph in the configuration space and mappings from workspace voxels to vertices and edges in the graph, which allows for computation times below 100 ms. While dynamic roadmaps can in principle be applied to dual-arm motion planning, it may be beneficial to use independent roadmaps per arm. This paper proposes four different approaches for planning based on two separate DRMs that all take advantage of the availability of workspace mappings. A sequential approach first plans for a prioritized arm and then considers its motion as obstacle for the second arm. The other three planners coordinate the motion of the arms along fixed paths or graphs such that no collision occurs. Benchmarks are performed for two robot models with different ratios of overlapping workspace to investigate the pros and cons of the composition approaches and to compare them to a single roadmap for the dual-arm robot.

The paper presents an optimal control strategy for a heavy-duty multi-group transmission that allows for simultaneous shifting in all groups. The approach is presented for a two-group transmission without loss of generality. The optimal control problem (OCP) consists of three phases with state-dependent switching of the hybrid dynamics and free end-time characteristics as well as several input and state constraints. The objective is designed to minimize the gear shift time while maintaining the speed and torque at the output shaft. A tailored optimization algorithm is presented to numerically solve the nonlinear OCP in a highly efficient manner. A comparison with a standard SQP method as well as simulation and runtime results on CPU and ECU level demonstrate the performance of the algorithm for an embedded real time implementation.

This contribution demonstrates the practical realizability of a tailored real-time nonlinear model predictive control (MPC) scheme for off-highway diesel engines. Besides controlling the torque and emissions, the MPC accounts for inequality constraints such as the maximum cylinder pressure by means of an augmented Lagrangian formulation. In addition, the heat-up of the exhaust gas aftertreatment system, e.g. for the regeneration of a diesel particulate filter, is facilitated with a warm-start strategy that enables the smooth activation of the inequality constraints. Experimental results from a testbench of the off-highway diesel engine within a wide operation range demonstrate the efficiency of the control scheme.

This contribution introduces a nonlinear model predictive control (MPC) algorithm for diesel engines. Inequality constraints, e.g. emission limits, are taken into account by an augmented Lagrangian formulation in order to provide a time and memory efficient algorithm that is suitable for a future ECU implementation. In view of a practical application and for the sake of a modular framework, the MPC scheme assumes the existence of a subordinate air path controller and therefore accounts for the closed-loop air path dynamics within the MPC prediction. The performance and computational efficiency of the MPC scheme are demonstrated by means of GT-POWER simulations and a runtime analysis.

An approach is presented for the optimal actuator placement in the course of electromagnetic heating. As this problem strongly depends on the control inputs for the actuators, the approach is incorporated into a suitable optimization framework for the control design of multiphysics systems. A joint optimization problem is formulated for both the actuator placement and the controller design problem. The adjoint-based sensitivity analysis in conjunction with the formal Lagrangian technique is applied to derive the optimality conditions. Simulation results for a surface hardening process demonstrate the applicability and accuracy of the approach.

Thermal management for motors in electric drive trains is a pivotal issue in vehicular design. Generally, low operating temperatures of the motors are desirable in light of longevity as well as reduction in drive losses. However, this requires a significant cooling effort in form of powerful water pumps and large radiators which in turn increase air resistance and total vehicle weight, especially for the liquid-cooled motors. Taking into account knowledge regarding the power demand of the vehicle's trajectory in the near future, a present redundancy in the drive train can be exploited to reduce motor temperature without sacrificing drive performance nor efficiency. To this end, a recently published fixed-point algorithm for highly efficient nonlinear model predictive control is set up and its performance and computational efficiency are evaluated in simulations.

International audience; New methods are presented to address two issues in indirect optimal control: the calculation of a starting point for the numerical solution and the consideration of mixed state-input constraints. In the first method, an auxiliary optimal control problem is constructed from a given initial trajectory of the system. Its adjoint variables are simply zero. This auxiliary problem is then used within a homotopy approach to eventually reach the original optimal control problem and the desired optimal solution. The second method concerns the incorporation of mixed state- input constraints into the dynamics of the considered optimal control problem. It uses saturation functions which strictly satisfy the constraints. In this way, the original constrained optimal control problem is transformed into an unconstrained one with an additional regularization term. The two approaches are derived within a general framework. For sake of illustration, they are applied to the space shuttle reentry problem, which represents a challenging benchmark due to its high numerical sensitivity and the presence of input and heating constraints. The reentry problem is solved with a collocation method and demonstrates the applicability and accuracy of the proposed constructive methods.

International audience; This paper addresses the well-known Goddard problem in the formulation of Seywald and Cliff with the objective to maximize the altitude of a vertically ascending rocket sub ject to dynamic pressure and thrust constraints. The Goddard problem is used to propose a new method to systematically incorporate the constraints into the system dynamics by means of saturation functions. This procedure results in an unconstrained and penalized optimal control problem which strictly satisfies the constraints. The approach requires no knowledge of the switching structure of the optimal solution and avoids the explicit consideration of singular arcs. A collocation method is used to solve the BVPs derived from the optimality conditions and demonstrates the applicability of the method to constrained optimal control problems.