Julia Kersten

Sensitivity-based feedforward and feedback control for uncertain systems

In many control applications, we are interested in accurate trajectory tracking. This is especially true for cases in which exact analytic solutions are not available because initial states are not consistent with the desired state or output trajectories or because parameters are significantly uncertain. In these cases, control strategies can be derived on the basis of a verified sensitivity analysis. For that purpose, we have to define suitable performance indices which describe the deviation between the actual and desired trajectories. In this paper, an overview of different sensitivity-based control procedures is given. These procedures include tracking control for systems with bounded parameter uncertainties as well as measurement errors described by interval variables. Moreover, we present a first verified approach to automatic path following by means of an automatic modification of desired output trajectories. This procedure is necessary in cases in which exact trajectory tracking is not possible due to the violation of control constraints.

Verified Stability Analysis for Interval-Based Sliding Mode and Predictive Control Procedures with Applications to High-Temperature Fuel Cell Systems

Abstract In previous work, control-oriented models have been derived for solid oxide high-temperature fuel cell systems. In these models, interval variables have been used to describe uncertainty due to a limited knowledge about system parameters and to handle effects of electric load variations on the temperature distribution in the fuel cell stack module as well as bounded measurement uncertainty. To deal with these types of uncertainty both in the design of robust controllers and during their online usage, interval techniques can be employed successfully. These control procedures make use of the basic principles of either sliding mode control or predictive control. The corresponding algorithms and the prerequisites for their real-time capable implementation using software libraries for interval arithmetic and algorithmic differentiation are described in this paper. Experimental results show the efficiency of these control laws for a fuel cell test rig that is available at the Chair of Mechatronics at the University of Rostock.

Finite element modeling for heat transfer processes using the method of integro-differential relations with applications in control engineering.

Control design of spatially distributed thermal systems is a task that is necessary for a large variety of engineering applications. Early lumping techniques, that are applicable in this case, follow the methodology of first discretizing the infinite-dimensional system model and subsequently using the discretized model for a finite-dimensional control design. For that purpose, the governing partial differential equations are commonly reduced to a finite-dimensional set of ordinary differential equations. In this paper, the corresponding task is solved by an optimization-based version of the Method of Integro-Differential Relations (MIDR). On the one hand, the MIDR allows one to quantify and systematically influence the approximation quality and, on the other hand, to use the resulting models directly for control and state observer design. In the following, the MIDR is applied to a fundamental problem of linear heat transfer in tube-like structures for which cylindrical coordinates are a suitable choice for modeling the dynamic behavior in all three space directions. Illustrative simulation results of fundamental control and state estimation approaches conclude this paper. These simulation results serve as the basis for a future experimental validation of the presented modeling techniques on a laboratory test rig that is currently being built up at the Chair of Mechatronics at the University of Rostock.

Experimental validation of LMI approaches for robust control design of a spatially three-dimensional heat transfer process

In this paper, two alternative control procedures are compared for a spatially three-dimensional distributed heating system. In both cases, the system model is derived as a finite volume representation that assumes a piecewise homogeneous distribution of the temperature in each finite volume element. The parameterization of both control strategies is performed by using linear matrix inequalities in combination with a polytopic model for uncertain system parameters. The basic difference between both implementations is that either parameter-independent or parameter-dependent candidates for Lyapunov functions are assumed in the derivation of the control laws. It is shown experimentally that both approaches lead to an accurate tracking of smooth temperature trajectories. However, the parameter-dependent approach is less conservative and, in such a way, leads to a smaller amplification of measurement noise in an observer-based closed-loop control structure.

Observer-based decentralised control of a wind turbine with a hydrostatic transmission

In this paper, a decentralised control approach for a 5 MW wind turbine with a hydrostatic transmission is presented that covers the whole range from low to very high wind speeds. In addition to a linear control of the pitch angle, a multi-variable gain-scheduled PI state feedback control based on LQR techniques is proposed for the angular velocities of both the rotor and the generator. The sixth-order simulation model comprises the complete drive train dynamics, the generator torque dynamics as well as the rotor aerodynamics and is derived from first principles. To reduce the implementation effort, the multi-variable control structure is based on a simplified statespace model with three states and two inputs. Moreover, a reduced-order observer estimates the rotor torque as well as an unknown leakage volume flow for a disturbance compensation. The control performance is illustrated by simulation results, which show an excellent tracking behaviour for the controlled variables.

Active tower damping for an innovative wind turbine with a hydrostatic transmission

In this paper, a decentralised control approach for an innovative 5 MW wind turbine with a hydrostatic transmission is presented that covers the whole range from low to very high wind speeds. An active damping of tower oscillations is achieved by using the pitch angle as control input. An elastic multibody system is employed to derive a control-oriented model for the first tower bending mode, which serves for the design of a stabilising control law. The active oscillation damping is combined with a multi-variable gain-scheduled PI state feedback control that allows for tracking desired trajectories for the angular velocities of both rotor and generator. The overall control performance is illustrated by realistic simulation results, which show an improved damping of tower oscillations and excellent tracking behaviour for the controlled variables.

Control and robust tower oscillation damping for a wind turbine equipped with a hydrostatic drive train and a synchronous generator

In this paper, a model-based control is proposed for an innovative 5 MW wind turbine with a hydrostatic transmission and a synchronous generator. The proposed control is derived by solving Linear Matrix Inequalities (LMIs) so that given parameter uncertainties and state-dependent matrices can be considered adequately. It comprises both a SISO control for the rotor angular velocity by adjusting the hydrostatic transmission as well as an active oscillation damping of tower bending oscillations, where the pitch angle serves as control input. The control is capable to operate within the whole operating range from low to very high wind speeds. A disturbance observer is used to estimate the aerodynamic rotor torque as well as leakage effects in the hydrostatic transmission. Here, the wind speed can be reconstructed from the estimated rotor torque. The overall control performance is illustrated by realistic simulation results, which show an improved damping of tower oscillations and an excellent tracking behaviour for the controlled variables.

Intervallmethoden für Identifikation, Beobachter- und Reglersynthese von Finite-Volumen-Modellen thermischer Prozesse

Zusammenfassung Sowohl die Offline-Parameteridentifikation als auch die echtzeitfähige Online-Zustandsschätzung sind im Rahmen regelungstechnischer Anwendungen weit verbreitete Fragestellungen. Die Lösung dieser Fragestellungen ist insbesondere dann anspruchsvoll, wenn gemessene Größen und Parameter nicht mit absoluter Genauigkeit bekannt sind. In solchen Fällen lassen sich intervallbasierte Repräsentationen nutzen, um einerseits gesicherte Wertebereichsschranken unsicherer Parameter zu beschreiben und andererseits garantierte Einschlüsse aller möglichen Zustandstrajektorien zu berechnen. In diesem Artikel wird hierauf aufbauend ein intervallbasierter Ansatz zur verifizierten Parameteridentifikation und Beobachtersynthese vorgestellt. Dieser Ansatz wird darüber hinaus anhand eines Finite-Volumen-Modells eines örtlich verteilten Wärmeleitungsprozesses validiert. Für die effiziente Implementierung des Schätzverfahrens wird dabei die strukturelle Systemeigenschaft der Kooperativität ausgenutzt. Diese erlaubt es, zwei voneinander unabhängige Schrankensysteme zu definieren, aus welchen sich garantierte Unter- und Obergrenzen aller Zustände des unsicherheitsbehafteten Systemmodells berechnen lassen.

Interval methods for the implementation and verification of robust gain scheduling controllers

This paper presents a novel approach for an interval-based gain scheduling control design aiming at a guaranteed stabilization of the system dynamics over a predefined time horizon. Due to the goal of asymptotic stability, the design aims at the temporal reduction of the widths of intervals representing worst-case bounds of the system states at a specific point of time. The main idea of the control approach is the computation of feedback gains for an initial state interval with a subsequent verification step. In this step, it is examined whether the control is valid over a finitely long prediction window. If the verification fails, the gain is adjusted after computing a bounding box of states that are reachable over the complete prediction window. In such a way, controller gains can be calculated off-line so that predefined performance criteria on the closed-loop structure are satisfied. Besides using interval analysis for the underlying reachability analysis, linear matrix inequality (LMI) techniques are employed for an efficient solution of the robust and/ or optimal control design. The proposed design method is verified numerically for the control of an inverted pendulum as a prototypical benchmark application.

LMI approaches for a robust control of a wind turbine with a hydrostatic transmission

In this paper, two alternative Linear Matrix Inequality (LMI) approaches were used to derive a decentralised control for an innovative 5 MW wind turbine with a hydrostatic transmission. With LMIs, given parameter uncertainties can be considered adequately. The proposed control covers the whole range from low to very high wind speeds. An active damping of tower oscillations is achieved by using the pitch angle as control input. Moreover, a robust multi-variable drive train control is designed that allows for tracking of desired trajectories for the angular velocities of both the rotor and the generator. The overall control performance is illustrated by realistic simulation results, which show an improved damping of tower oscillations and an excellent tracking behaviour for the controlled variables despite parameter uncertainties.