Christoph Rosmann

This paper deals with the integration of input move-blocking into the framework of suboptimal model predictive control. The blocked input parameterization is explicitly considered as a source of suboptimality. A straightforward integration approach is to hold back a manually generated stabilizing fallback solution in some buffer for the case that the optimizer does not find a better input move-blocked solution. An extended approach superimposes the manually generated stabilizing warm-start by the move-blocked control sequence and enables a stepwise improvement of the control performance. In addition, this contribution provides a detailed review of the literature on input move-blocked model predictive control and combines important results with the findings of suboptimal model predictive control. A numerical example supports the theoretical results and shows the effectiveness of the proposed approach.

This paper deals with the integration of input move-blocking into the framework of suboptimal model predictive control. The blocked input parameterization is explicitly considered as a source of suboptimality. A straightforward integration approach is to hold back a manually generated stabilizing fallback solution in some buffer for the case that the optimizer does not find a better input move-blocked solution. An extended approach superimposes the manually generated stabilizing warm-start by the move-blocked control sequence and enables a stepwise improvement of the control performance. In addition, this contribution provides a detailed review of the literature on input move-blocked model predictive control and combines important results with the findings of suboptimal model predictive control. A numerical example supports the theoretical results and shows the effectiveness of the proposed approach.

Zusammenfassung: In diesem Beitrag wird eine suboptimale modellprädiktive Regelung mit stabilisierenden Endbedingungen und einem ableitungsfreien Optimierungsalgorithmus für eine bestimmte Klasse nichtlinearer Systeme vorgestellt. Repräsentativ für diese Systemklasse stehen insbesondere elektromagnetische Aktuatoren. Durch die Kombination eines Freiheitsgrades auf dem ersten variablen Abschnitt des Prädiktionshorizonts mit endlichen Stellmengen können die rekursive Durchführbarkeit der Regelung und die asymptotische Stabilität der Gleichgewichtslage auf Basis der Erkenntnisse aus der klassischen suboptimalen modellprädiktiven Regelung nachgewiesen werden. Die vorgestellte Optimierungsstrategie ist mit überschaubarem Aufwand implementierbar, bedarf keiner externen Programmbibliotheken und adressiert somit industrielle Anwendungen. Die theoretischen Herleitungen werden durch numerische Auswertungen sowie dem Vergleich zur klassischen modellprädiktiven Regelung gestützt.

This paper deals with novel time-optimal point-to-point model predictive control concepts for nonlinear systems. Recent approaches in the literature apply a time transformation, however, which do not maintain recursive feasibility for a piecewise constant control parameterisation. The key idea in this paper is to introduce uniform grids with variable discretisation. A shrinking-horizon grid adaptation scheme ensures convergence to a specific region around the target state and recursive feasibility. The size of the region is configurable by design parameters. This facilitates the systematic dual-mode design for quasi-time-optimal control to restore asymptotic stability and establish a smooth stabilisation. Two nonlinear programme formulations with different sparsity patterns are introduced to realise and implement the underlying optimal control problem. For a class of numerical integration schemes, even nominal asymptotic stability and true time-optimality are achieved without dual-mode. A comparative analysis as well as experimental results demonstrate the effectiveness of the proposed techniques.

This paper deals with the development and analysis of novel time-optimal point-to-point model predictive control concepts for nonlinear systems. Recent approaches in the literature apply a time transformation, however, which do not maintain recursive feasibility for piecewise constant control parameterization. The key idea in this paper is to introduce uniform grids with variable discretization. A shrinking-horizon grid adaptation scheme ensures convergence to a specific region around the target state and recursive feasibility. The size of the region is configurable by design parameters. This facilitates the systematic dual-mode design for quasi-time-optimal control to restore asymptotic stability and establish a smooth stabilization. Two nonlinear program formulations with different sparsity patterns are introduced to realize and implement the underlying optimal control problem. For a class of numerical integration schemes, even nominal asymptotic stability and true time-optimality are achieved without dual-mode. A comparative analysis as well as experimental results demonstrate the effectiveness of the proposed techniques.

During a model-based system optimization of a proportional directional control valve, the system performance is simulated for a wide range of different design parameter sets. The behavior of the model, which is used to evaluate the system performance, changes whenever the optimization algorithm provides new parameter values. The closed-loop control response of a proportional valve is used as the metric of the system performance. Thus, to avoid evaluating the robustness of the valve controller, a new controller design is required whenever a variation of the plant parameters is carried out. The native controller of a proportional directional control valve is a nonlinear PID controller with numerous coupled parameters. This controller design requires a complex evolutionary multi-objective parameter optimization. This contribution introduces the model predictive control (MPC) in the context of a fully automated model-based system optimization of a proportional directional control valve. Since the plant is known exactly for every design variation, the plant model becomes a part of the control concept. By updating the prediction model, the controller exhibits a design adaptive characteristic. Due to the inherent system knowledge of the MPC setup within the model-based system optimization, the number of free controller parameters decreases significantly. These additional free parameters, like the weights of the user-defined objective function, can be included easily into the design optimization vector enabling a single holistic system optimization procedure.

This paper proposes a hypergraph formulation for solving MPC problems. The hypergraph approach exploits the sparse structure in the calculation of derivatives. It is therefore computationally more efficient in case of multiple-shooting, collocation and full-discretization methods compared to a dense formulation. Recent advances in realtime optimization rely on automatic differentiation (AD) to compute derivatives. An extensive analysis compares MPC variants with both hypergraph and AD on two benchmark control problems. Even though AD requires a computational overhead to set up the problem structure, solving the nonlinear program at each iteration is fast. The overhead in the hypergraph approach is negligible, and computational effort in the solving phase is inferior but comparable to AD. This observation favors the hypergraph representation for MPC problems with non-static problem structure.

During the development of mechatronic systems hard- and software components are integrated into a single system. Mostly, a digital control concept is designed to control the interactions of the different sub-systems from different domains and to reach the desired system performance requirements. In the case of a proportional directional control valve, the closed-loop control response is used as a metric of the system performance. The performance can be either improved by optimizing the controller as well as the valve's hardware design parameters. When performing a holistic model-based system optimization, the optimization vector contains the controller and the hardware design parameters. A variation of the design parameters requires a time-consuming Finite-Element- Method (FEM) simulation. In contrast, the impact of different controller parameters on the system performance can be simulated with a low computational effort. Actually, following the control theory, the controller parameters must only be adjusted when the plant changes its characteristic. This contribution presents a cascaded evolutionary multi-objective optimization process which enables the subordinated controller design in the context of a holistic multi-objective system optimization of a directional control valve. The required optimization time decreases significantly since the outer optimization loop mainly focuses on the hardware improvement without the impact of the controller robustness. A real industrial application motivates the developed approach, but the cascaded process is evaluated more generally investigating well-known benchmark functions from the literature for multi-objective optimization.