Jörg Raisch

IMU-based joint angle measurement for gait analysis.

This contribution is concerned with joint angle calculation based on inertial measurement data in the context of human motion analysis. Unlike most robotic devices, the human body lacks even surfaces and right angles. Therefore, we focus on methods that avoid assuming certain orientations in which the sensors are mounted with respect to the body segments. After a review of available methods that may cope with this challenge, we present a set of new methods for: (1) joint axis and position identification; and (2) flexion/extension joint angle measurement. In particular, we propose methods that use only gyroscopes and accelerometers and, therefore, do not rely on a homogeneous magnetic field. We provide results from gait trials of a transfemoral amputee in which we compare the inertial measurement unit (IMU)-based methods to an optical 3D motion capture system. Unlike most authors, we place the optical markers on anatomical landmarks instead of attaching them to the IMUs. Root mean square errors of the knee flexion/extension angles are found to be less than 1° on the prosthesis and about 3° on the human leg. For the plantar/dorsiflexion of the ankle, both deviations are about 1°.

Conditions for stability of droop-controlled inverter-based microgrids

We consider the problem of stability analysis for droop-controlled inverter-based microgrids with meshed topologies. The inverter models include variable frequencies as well as voltage amplitudes. Conditions on the tuning gains and setpoints for frequency and voltage stability, together with desired active power sharing, are derived in the paper. First, we prove that for all practical choices of these parameters global boundedness of trajectories is ensured. Subsequently, assuming the microgrid is lossless, a port-Hamiltonian description is derived, from which sufficient conditions for stability are given. Finally, we propose for generic lossy microgrids a design criterion for the controller gains and setpoints such that a desired steady-state active power distribution is achieved. The analysis is validated via simulation on a microgrid based on the CIGRE (Conseil International des Grands Reseaux Electriques) benchmark medium voltage distribution network.

Subnetwork analysis reveals dynamic features of complex (bio)chemical networks

In analyzing and mathematical modeling of complex (bio)chemical reaction networks, formal methods that connect network structure and dynamic behavior are needed because often, quantitative knowledge of the networks is very limited. This applies to many important processes in cell biology. Chemical reaction network theory allows for the classification of the potential network behavior—for instance, with respect to the existence of multiple steady states—but is computationally limited to small systems. Here, we show that by analyzing subnetworks termed elementary flux modes, the applicability of the theory can be extended to more complex networks. For an example network inspired by cell cycle control in budding yeast, the approach allows for model discrimination, identification of key mechanisms for multistationarity, and robustness analysis. The presented methods will be helpful in modeling and analyzing other complex reaction networks.

Supervisory control of hybrid systems within a behavioural framework

Abstract This contribution addresses the synthesis of supervisory control for hybrid systems Σ with discrete external signals. Such systems are in general neither l -complete nor can they be represented by finite state machines. We find an l -complete approximation (abstraction) Σ l for Σ , represent it by a finite state machine, and investigate the control problem for the approximation. If a solution exists, we synthesize the maximally permissive supervisor for Σ l . We show that it also solves the control problem for the hybrid system Σ . If no solution exists, approximation accuracy can be increased by computing a k -complete abstraction Σ k , k>l . This paper is entirely set within the framework on Willems’ behavioural systems theory.

Voltage Stability and Reactive Power Sharing in Inverter-Based Microgrids With Consensus-Based Distributed Voltage Control

We propose a consensus-based distributed voltage control (DVC) that solves the problem of reactive power sharing in autonomous inverter-based microgrids with dominantly inductive power lines and arbitrary electrical topology. Opposed to other control strategies available thus far, the control presented here does guarantee a desired reactive power distribution in steady state while only requiring distributed communication among inverters, i.e., no central computing nor communication unit is needed. For inductive impedance loads and under the assumption of small phase angle differences between the output voltages of the inverters, we prove that the choice of the control parameters uniquely determines the corresponding equilibrium point of the closed-loop voltage and reactive power dynamics. In addition, for the case of uniform time constants of the power measurement filters, a necessary and sufficient condition for local exponential stability of that equilibrium point is given. The compatibility of the DVC with the usual frequency droop control for inverters is shown and the performance of the proposed DVC is compared with the usual voltage droop control via simulation of a microgrid based on the Conseil International des Grands Réseaux Electriques (CIGRE) benchmark medium voltage distribution network.

Synchronization of droop-controlled microgrids with distributed rotational and electronic generation

We consider the problem of frequency synchronization and power sharing in a lossy droop-controlled autonomous microgrid with distributed rotational and electronic generation (MDREG). At first, we establish equivalence of the dynamics of a regulated synchronous generator and a droop-controlled inverter with low pass filter. We then give a necessary and sufficient condition for local synchronization of the microgrid by using ideas from graph theory and second order consensus algorithms. In addition, we show that sources in an MDREG can achieve a desired active power distribution via frequency droop control and provide synchronization conditions for a lossless microgrid as a special case. Our analysis is further validated via a simulation example of a lossy microgrid based on the CIGRE benchmark medium voltage distribution network.

A survey on modeling of microgrids-From fundamental physics to phasors and voltage sources

Microgrids are an increasingly popular class of electrical systems that facilitate the integration of renewable distributed generation units. Their analysis and controller design requires the development of advanced (typically model-based) techniques naturally posing an interesting challenge to the control community. Although there are widely accepted reduced order models to describe the dynamic behavior of microgrids, they are typically presented without details about the reduction procedure|hampering the understanding of the physical phenomena behind them. The present paper aims to provide a complete modular model derivation of a three-phase inverter-based microgrid. Starting from fundamental physics, we present detailed dynamical models of the main microgrid components and clearly state the underlying assumptions which lead to the standard reduced model representation with inverters represented as controllable voltage sources, as well as static network interconnections and loads.

A Totally Ordered Set of Discrete Abstractions for a given Hybrid Continuous System

This contribution proposes a hierarchy of discrete abstractions for a given hybrid or continuous system with quantized measurements and symbolic control inputs. The continuous (or hybrid) base system and its discrete abstractions form a totally ordered set of models; ordering is in the sense of set inclusion of model behaviours or, equivalently, in terms of approximation accuracy. The ordering is shown to be invariant under feedback; this provides theoretical justification for designing feedback control for the underlying hybrid system on the basis of a discrete abstraction. Also, within this ordered set, the notion of a “least accurate” (and therefore least complex) model which allows a given set of specifications to be met makes sense. The discrete abstractions are realized as nondeterministic automata; they are in observer-canonical form and hence, by construction, observable. Non-reachable states are also “weeded out” by construction, leaving a minimal state set for each approximating automaton.

Max-consensus in a max-plus algebraic setting: The case of fixed communication topologies

Consensus algorithms have been studied in the field of distributed computing for decades. Recently consensus algorithms have attracted renewed attention because they can be exploited for distributed cooperative control. The purpose of this paper is the analysis of a specific class of consensus algorithms called max-consensus. This class of algorithms is needed for applications such as minimum time rendezvous and leader election. A new approach using max-plus algebra is proposed to analyze convergence of max-consensus algorithm. In this paper we focus on the problem of achieving max-consensus in time-invariant communication topologies. Conditions to achieve max-consensus are discussed and the convergence rate of the algorithm for different communication topologies is studied.

On the Maximum Principle for Impulsive Hybrid Systems

In this contribution, we consider a class of hybrid systems with continuous dynamics and jumps in the continuous state (impulsive hybrid systems). By using a newly elaborated version of the Pontryagin-type Maximum Principle (MP) for optimal control processes governed by hybrid dynamics with autonomous location transitions, we extend the necessary optimality conditions to a class of Impulsive Hybrid Optimal Control Problems (IHOCPs). For these problems, we obtain a concise characterization of the Impulsive Hybrid MP (IHMP), namely, the corresponding boundary-value problem and some additional relations. As in the classical case, the proposed IHMP provides a basis for diverse computational algorithms for the treatment of IHOCPs.