Maximilian Manderla

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.

Modelling, simulation and control of a redundant parallel robotic manipulator based on invariant manifolds

In this article a systematic approach of modelling and control for a parallel robotic manipulator is presented. Regarding the framework of structured analysis of dynamical systems the derivation of a differential-algebraic model of the mechanical system is straightforward. Using some differential-geometric considerations based on invariant manifolds and the definition of fictitious additional input and output variables a suitable state feedback can be constructed which transforms the differential-algebraic representation into a state-space model for the robotic manipulator. On this basis a classical two-degree-of-freedom (2-DOF) control structure has been designed using the well-known input–output linearization and a linear time-variant Kalman filter-based output feedback. Finally, the control structure including a friction compensation is applied to the robotic system in the laboratory which shows the practical applicability of the proposed procedure.

Modelling and control of a redundant parallel robotic manipulator — Numerical simulation and experimental results

The aim of this contribution is a systematic approach of modelling, simulation and control of a parallel robotic manipulator. Regarding the framework of structured analysis of dynamical systems, the mathematical description yields a set of differential equations and some additional holonomic constraints which appear as algebraic relations between single state variables. By defining a number of ficticious additional input and output variables this descriptor representation can be interpreted as coupling or constraint control problem. A suitably constructed state feedback that keeps the closed loop system on an invariant manifold of consistent/allowed states yields a state-space model which functions as a basis for numerically stable simulation and exterior controller design. Using an extended Kalman filter as state observer the derived control law is applied to the robotic system in the lab and shows the general applicability of the proposed procedure.

Improved prediction of Pump Turbine Dynamic Behavior using a Thoma number dependent Hill Chart and Site Measurements

Water hammer phenomena are important issues for the design and the operation of hydro power plants. Especially, if several reversible pump-turbines are coupled hydraulically there may be strong unit interactions. The precise prediction of all relevant transients is challenging. Regarding a recent pump-storage project, dynamic measurements motivate an improved turbine modeling approach making use of a Thoma number dependency. The proposed method is validated for several transient scenarios and turns out to improve correlation between measurement and simulation results significantly. Starting from simple scenarios, this allows better prediction of more complex transients. By applying a fully automated simulation procedure broad operating ranges of the highly nonlinear system can be covered providing a consistent insight into the plant dynamics. This finally allows the optimization of the closing strategy and hence the overall power plant performance.

Parametrischer Entwurf dynamischer Ausgangsrückführungen für reguläre Deskriptorsysteme

Zusammenfassung Der Beitrag beschreibt ein neues Verfahren zur Synthese konstanter statischer und dynamischer Ausgangsrückführungen für reguläre lineare zeitinvariante Deskriptorsysteme. Neben der Vorgabe der Regelungseigenwerte und der Sicherstellung der Regularität des geschlossenen Regelkreises können sämtliche Entwurfsfreiheitsgrade und deren Auswirkung auf die Dynamik des geschlossenen Regelkreises in expliziter Form angegeben werden. Der Entwurf erfolgt durch die Aufspaltung des Problems in zwei duale Teilprobleme. Vollständige Steuer- und Beobachtbarkeit werden nicht gefordert. Abstract This paper presents a new parametric procedure for static and dynamic output feedback design of regular linear time-invariant descriptor systems. Besides eigenvalue assignment and closed-loop regularity a solution is obtained which explicitly shows the existing degrees of freedom and their effect on the closed-loop dynamics by dividing the problem into two dual subproblems. Complete controllability and observability are not required.

Vollständige Modale Synthese regulärer Deskriptorsysteme, Parametric Feedback Design of Regular Descriptor Systems

Zusammenfassung Der Beitrag beschreibt ein neues Verfahren zur Synthese konstanter Zustandsrückführungen für lineare, zeitinvariante Deskriptorsysteme. Ausgehend von bekannten parametrischen Entwurfsmethoden für gewöhnliche Zustandsraumbeschreibungen wird eine Synthesevorschrift angegeben, welche sämtliche Freiheitsgrade beim Entwurf regulärer Deskriptorsysteme und deren Auswirkungen auf die Dynamik des geschlossenen Regelkreises sichtbar macht. Insbesondere lassen sich alle steuerbaren endlichen sowie unendlichen Eigenwerte explizit vorgeben.

Active Vibration Control of Two Coupled Beams Using Descriptor System State Feedback

Based on two stiffly-coupled beams a non-standard approach of modelling and control is introduced, which is based on a descriptor representation of the system. A differential-algebraic model of the mechanical system can be derived intuitively, which directly serves for feedback design. The main contribution of this work is the presentation of a suitable parametric control law in terms of the full set of descriptor states. It is based on a classical coupling control and explicitly shows all degrees of freedom for feedback design. Exemplarily, damping assignment for the two-beam system is performed and some numerical and experimental results are provided for validation.Copyright

Pump Turbine Transients: A refined Simulation Model based on Prototype Measurements

Following theoretical investigations about draft tube pressure drops in complex pump turbine schemes, numerous measurements on a prototype are now available. A comparison with the simulation reveals the necessity of adapting the turbine hillchart depending on the actual condition during transient events. The re ned simulation model leads to improved correlation with the prototype results and enables a more accurate prediction of pressure values. The closing strategy was optimized and the most critical load case in terms of minimum draft tube pressure successfully tested.

Improved pump turbine transient behaviour prediction using a Thoma number-dependent hillchart model

Water hammer phenomena are important issues for high head hydro power plants. Especially, if several reversible pump-turbines are connected to the same waterways there may be strong interactions between the hydraulic machines. The prediction and coverage of all relevant load cases is challenging and difficult using classical simulation models. On the basis of a recent pump-storage project, dynamic measurements motivate an improved modeling approach making use of the Thoma number dependency of the actual turbine behaviour. The proposed approach is validated for several transient scenarios and turns out to increase correlation between measurement and simulation results significantly. By applying a fully automated simulation procedure broad operating ranges can be covered which provides a consistent insight into critical load case scenarios. This finally allows the optimization of the closing strategy and hence the overall power plant performance.

Design of causal state observers for regular descriptor systems

Abstract In this contribution a new framework for the design of causal state observers for regular descriptor systems is developed. The proposed procedure is derived on the basis of well-known and slightly modified parametric design concepts for state feedback controllers and generalized state observers. The resulting method can be applied under some necessary and sufficient, and thus minimal, existence conditions for causal state observers. The relation between the generalized observer and the observer in state space form is given by a suitable coordinate transformation. In general, neither controllability nor observability or any specific system representation is required. The separation principle holds. The proposed procedure is applied to two examples, namely a differentiating system which can be observed by a causal state observer and a double-beam vibration control problem.