Ulrich Konigorski

Partial-state synchronization of linear heterogeneous multi-agent systems

This article is devoted to the synchronization of heterogeneous, and hence non-identical, linear systems. The proposed solution results in a fully distributed control law solely relying on local measurements. In order to achieve this, it is shown that the problem can be decomposed into three sub-problems: First, the synchronization of identical exosystems provides a feasible trajectory which turns out to be the synchronization manifold. Second, a decentralized observer is proposed for estimating the absolute state based on the local measurements performed. Third, this estimate is used to derive a tracking control law, based on the full information output regulation problem, to follow the generated exosystem reference. The concept is illustrated by an example.

Pole placement by parametric output feedback

Abstract This note presents a new analytical solution to the problem of pole placement via constant output feedback under the condition m + p ≥ n , where n , m , and p are the number of states, inputs and outputs, respectively. The approach is based upon parametric eigenstructure assignment of linear time-invariant multivariable systems in combination with a special explicit formulation of the pole assignment equations. Thus, the resulting analytical solution explicitly offers all remaining m p − n degrees of freedom beyond eigenvalue assignment which can be used for additional design goals such as response shaping, minimizing the norm of the feedback matrix, and robust control, respectively.

Integrated electric vehicle control by differential parameterization

The design of a tracking controller for electric cars in x-by-wire structure is presented to assign trajectories for the coordinates of the vehicle structure, which are shown to be a flat output. The model of the car is a detailed nonlinear two-track vehicle with all degrees of freedom in the three-dimensional space provided with redundant actuation. Each tire is equipped with two salient pole permanent magnet (PM-)synchronous machines for steering and driving. For the controller design, an overall model with a special differential-algebraic structure is derived. The tire forces and the torques of the electrical machines are used as fictitious inputs. With this particular modeling it is possible to decouple the dynamic part of the model in the given coordinates at the highest relative degree. To get a consistent behavior it is necessary to account for some algebraic constraints, in this case given by the tire model and the torque equations of the PM-synchronous machines. It is possible to parameterize all constraints and coordinates of the drive units by the coordinates of the vehicle structure and its derivatives. All these parameterizations can be derived analytically. With an additional tracking controller the approach is robust against parameter variations and pulse-shaped disturbances. The control of the electrical machines is integrated in the overall control law. By introducing additional coupling conditions it is possible to generate the desired torque for steering and driving by minimum current.

On Linear Solutions of the Output Feedback Pole Assignment Problem

A new linear method for solving the output feedback pole assignment problem of linear systems is introduced, and new sufficient conditions are obtained.

Entwurf linearer Deskriptorsysteme durch Polvorgabe (Pole Assignment in Linear Descriptor Systems)

Abstract Der Beitrag beschreibt einen neuen Zugang zum Entwurf linearer Deskriptorsysteme durch Polvorgabe. Bei R-steuerbaren Deskriptorsystemen ermöglicht das vorgestellte Verfahren neben der Vorgabe sämtlicher endlicher Eigenwerte auch die gezielte Verschiebung der unendlichen Eigenwerte. Die resultierende Zustandsregelung liefert daher nicht nur eine vollständige Lösung des Polvorgabeproblems bei linearen Deskriptorsystemen, sondern ermöglicht gleichzeitig auch eine stabile Indexreduktion. Nach einer geeigneten Transformation werden dazu einige der Deskriptorvariablen als zusätzliche fiktive Eingangsgrößen interpretiert, die zusammen mit den realen Stellgrößen für den Entwurf einer konstanten Zustandsrückführung herangezogen werden können. Diese Rückführung wird in Anlehnung an den Entwurf einer Verkopplungsregelung anhand eines reduzierten expliziten Zustandsraummodells entworfen, wobei die Berücksichtigung der zusätzlichen algebraischen Nebenbedingungen problemlos möglich ist.

Ausgangsgrößenverkopplung bei linearen Mehrgrößensystemen

Prof. Dr.-Ing. Ulrich Konigorski ist Inhaber des Lehrstuhls für Regelungstechnik und Elektronik an der Technischen Universität Clausthal. Methodenorientierte Forschungsschwerpunkte sind der Entwurf linearer und nichtlinearer Mehrgrößensysteme, Ereignisdiskrete und hybride Systeme sowie die Anwendung von Walshfunktionen in der Systemtheorie. Anwendungsorientierte Schwerpunkte sind die digitale Regelung mechatronischer und elektromechanischer Systeme sowie der Entwurf von Fahrdynamikregelungssystemen.

A New Direct Approach to the Design of Structurally Constrained Controllers

Abstract The design of linear systems via state space methods is generally based on complete state feedback. However, in many practical control problems a controller with arbitrary structure constraints is required. Classical PI-control, decentral control and output feedback are examples for this kind of controllers. While such controller structures are of great practical relevance, their analytic design faces a lot of difficulties. In this paper, a numerical method for the design of structurally constrained controllers is presented. The method is based on the direct solution of a set of non-linear equations, which can easily be derived from the underlying pole assignment problem. The numerical efficiency of the proposed technique essentially stems from the fact, that one of the reliable and fast convergent gradient methods can be utilized. Furthermore only some determinants must be evaluated in each iteration step. After the description of the method, some details, concerning its implementation on a digital computer, are explained. Finally the efficiency of the proposed method is illustrated by two numerical examples.

Modellbildung und Vergleich von linearen und nichtlinearen Regelungskonzepten für Drei-Wege-Abgaskatalysatoren

Zusammenfassung In diesem Beitrag wird eine neue Methodik zum Erstellen von Zustandsraummodellen aus physikochemischen Katalysatormodellen vorgestellt und verallgemeinert. Basierend auf dem resultierenden Zustandsraummodell des Katalysators wird eine systemtheoretische Analyse durchgeführt. Lineare und nichtlineare Regelungskonzepte zur Minimierung der Schadstoffemissionen werden entworfen und ihre spezifischen Vor- und Nachteile diskutiert.

Control, simulation and stability analysis of nonlinear regular proper DAEs

In this paper we provide an algorithm for nonlinear regular proper DAEs to derive a controller for an associated state space system assuming the algebraic variables and the error of the algebraic equations as fictitious inputs and outputs, respectively. It is shown that the achieved controlled state space representation has the same solution as the original DAE in the case of consistent initial values. Therefore, it can be used for stability analysis, designing control laws, and the numerical integration with standard methods. In contrast to the realization in minimal coordinates this formulation can be derived straight-forward and the computation is easy to implement on a computer algebra system.

Observer Based Method for Joint Torque Estimation in Active Orthoses

Abstract This contribution presents a new approach of estimating the joint torques for an active orthosis. The new approach combines inverse dynamics and measured ground reaction forces. The joint torques can easily be computed from the ground reaction forces, but the measurement is usually flawed. An obsererver is employed to estimate the disturbance of the measurements and restore the original joint torques. A model of the human lower extremity is presented and additional seat forces are introduced to model the seat. Simulation results on the Sit-to-Stand movement illustrate the effectivity of the new approach.