Christian Stöcker

Event-based control of nonlinear systems: An input-output linearization approach

This paper proposes a new event-based control method for nonlinear SISO systems that are input-output linearizable and have internal dynamics. The main control objective is disturbance rejection while simultaneously reducing the feedback communication effort compared to a continuous control loop. The event-triggered control loop is shown to be ultimately bounded and, moreover, a bound for the deviation between this control loop and the continuous reference system is derived, which depends on the threshold of the event generator. Hence, by appropriately choosing the event threshold the event-based controller can be made to mimic the continuous control with desired accuracy. The novel control approach is evaluated by its application to a continuous stirred tank reactor.

Event-based control

Event-based control is a control methodology that is currently being developed as a means to reduce the communication between the sensors, the controller and the actuators in a control loop. The sampling instants are not determined periodically by a clock, but by an event generator, which adapts the information flow in the feedback loop to the current behavior of the closed-loop system. A communication among the components is invoked only after an event has indicated that the control error exceeds a tolerable bound.

Stability analysis of interconnected event-based control loops*

Abstract In event-based control the feedback link within a control loop is only closed when an event indicates the need for information exchange among the sensors, controller and actuators to maintain a required loop performance. The event-based control loop is a hybrid dynamical system, which is characterized by a sequence of continuous state flows and discontinuous state jumps at the event times. This paper analyzes the stability of interconnected decentralized event-based control loops where events are triggered asynchronously. A stability criterion is derived using the comparison principle. It is shown that conditions that are sufficient to prove the stability of the continuous control system imply ultimate boundedness of the event-based state-feedback loop. The conservatism of the proposed stability test is evaluated for a thermofluid process.

Distributed event-based control of physically interconnected systems

This paper investigates event-based control of systems that are composed of physically interconnected subsystems. The event-based controller consists of a control input generator and an event generator. The main aim for the design of these components is (i) to approximate the behavior of a continuous state-feedback control by the event-based control with adjustable accuracy and (ii) to reduce the feedback communication compared to a decentralized event-based control approach proposed in literature. In the event-based control loop i, the triggering of events is caused by the coupling input to subsystem i. The proposed event-based control approach diminishes the influence of these interconnections by using an approximate model, which estimates the behavior of the neighbors of subsystem i, for the control input generation. Events are triggered based on two different conditions: The first one causes a transmission of the current subsystem state locally from event generator i to control input generator i. The second type of event is triggered whenever the state of the approximate model needs to be reset. This brings up a new kind of event-based control where the event generator i requests current state information from the neighbors of subsystem i. The event-based controller works in a distributed manner, because it uses both local state information as well as information from neighbor systems. It is shown that the deviation between the behavior of the continuous and the event-based control system depends upon the parameter of the first triggering condition only, whereas the minimum inter-event times can be adjusted by means of the parameter of the second triggering condition.

Distributed control of interconnected systems with event-based information requests

Abstract This paper proposes a new approach to distributed control of physically interconnected subsystems which combines continuous and event-based state feedback. The main aim of the controller is to suppress the propagation of a disturbance within an interconnection of subsystems. The novelty of this approach is that the controllers request current state information from the neighboring systems at the event times. Events are generated based on a condition for which only local information are applied. The disturbance rejection behavior of the control approach with event-based information requests is demonstrated in an illustrative example which shows that the disturbance propagation is considerably reduced compared to a continuous decentralized state-feedback controller.

Event-based control of input-output linearizable systems

Abstract This paper proposes a new event-based control method for nonlinear systems that are input-output linearizable. The control input generator uses a copy of a continuous reference system to generate an exponential control input that keeps the state of the disturbed plant in a bounded surrounding of the setpoint. An upper bound for the deviation of the event-based control loop to the reference system is derived, which depends on the event threshold of the event generator. Hence, by appropriately choosing the event threshold, the event-based control can be made to mimic the continuous control with arbitrary accuracy. The proposed event-based control method is applied to a cooling process.

Event-based control with incomplete state measurement and guaranteed performance*

Abstract The present paper proposes a novel method for the design of event-based controllers for the disturbance rejection in systems for which only a part of the state is measurable. The design approach is based on the decomposition of the system into subsystems where the state is either measurable or not accessible for measurement. The triggering conditions of the event-based controllers solely depend upon the measurable states. The idea of the design approach is to adjust the triggering conditions such that the deviation between the disturbance rejection behavior of the event-based control system and a continuous-time state-feedback system is less than a desired bound, which is defined as level of performance. This design method is formulated as a linear programming problem. The design of the triggering conditions and the behavior of the event-based control system is illustrated for an interconnected two-tank system.

Zwei Methoden zur ereignisbasierten Regelung gekoppelter Systeme und ihre experimentelle Erprobung

Zusammenfassung Das Ziel der ereignisbasierten Regelung ist die Verringerung des Kommunikationsaufwands innerhalb eines Regelkreises, indem die Rückführung nur dann geschlossen wird, wenn ein Ereignis eine hinreichend große Regelabweichung anzeigt. In diesem Beitrag werden Bedingungen für die Struktur einer ereignisbasierten Regelung gekoppelter Systeme angegeben, unter denen das Verhalten des ereignisbasierten Regelkreises nur beschränkt von dem eines kontinuierlichen Regelkreises abweicht. Davon ausgehend werden zwei neue Methoden zur verteilten und dezentralen ereignisbasierten Regelung gekoppelter Systeme vorgestellt. Beide Ansätze werden in Simulationen und Experimenten an einem thermofluiden Prozess erprobt. Abstract Event-based control aims at reducing the communication effort within a control loop by closing the feedback only if an event indicates a significant control error. This paper derives a condition to the structure of the event-based control of interconnected systems on that the difference between the behavior of event-based control loop and a continuous reference system is bounded. Based on this condition, two novel methods for distributed and decentralized event-based control are developed. Both approaches are evaluated by means of their simulative and experimental application to a thermofluid process.

DFG Priority Programme 1305: Control Theory of Digitally Networked Dynamical Systems

Abstract The application of modern means of communication, like wireless LAN or Ethernet, enables novel concepts and structures for control engineering. Data can be transmitted between sensors, actuators, and controllers over long distances. Information can even be exchanged between moving objects which was impossible in conventional point to point wired realizations of control loops. However, besides these advantages the use of networks within a control loop also brings up new challenges due to nondeterministic effects like delays and dropouts of data packets. But for yet, there does not exist a theory for the modeling, analysis and design of such complex systems. The connection of several components of a control loop over a communication network represents a digitally networked dynamical system, which is subject of the Priority Programme 1305 “Control Theory of Digitally Networked Dynamical Systems”. The goal of this priority programme, which is founded by the German Research Foundation (DFG) over a period of six years, is to develop a comprehensive theory for this new class of systems. Here, three defined cross-sectional issues are worked out by 13 research groups and their solutions are experimentally proved in demonstration and benchmark processes. Within this priority programme several research groups from the disciplines of control engineering, mathematics and information technology cooperate. Zusammenfassung Der Einsatz moderner Kommunikationsmittel, wie z. B. WLAN oder Ethernet, ermöglicht bei der Regelung von Prozessen neuartige Konzepte und Strukturen. So lassen sich Daten zwischen Sensoren, Aktoren und Regler über große Entfernungen übertragen oder sogar Informationen zwischen sich bewegenden Objekten austauschen, was bei der herkömmlichen drahtgebundenen Realisierung von Regelkreisen unmöglich ist. Abgesehen von diesen Vorteilen, ergeben sich aus der Realisierung von Regelkreisen über ein Netzwerk auch neue Herausforderungen, da diese Netze durch ein nichtdeterministischen Verhalten im Sinne von Verzögerungen und Paketausfällen charakterisiert sind. Für die Modellierung, Analyse und den Steuerungsentwurf solcher Systeme existiert bislang jedoch keine ausgearbeitete Theorie. Die Zusammenschaltung der Regelkreiskomponenten über ein Netzwerk stellt ein digital vernetztes dynamisches System dar, welches Gegenstand der Untersuchungen im Schwerpunktprogramm 1305 “Regelungstheorie digital vernetzter dynamischer Systeme” ist. Ziel dieses, von der Deutschen Forschungsgemeinschaft über einen Zeitraum von sechs Jahren geförderten Schwerpunktprogramms ist die Entwicklung einer umfassenden Theorie für diese neue Klasse von Systemen. Dabei werden drei definierte Querschnittsprobleme von 13 Forschergruppen bearbeitet und deren Lösungen an Demonstrations- und Benchmarkprozessen experimentell erprobt. In dem Schwerpunktprogramm arbeiten Forschergruppen der Disziplinen Regelungstechnik, Mathematik und Informationstechnik eng zusammen.