6 research outputs found
Admissible target paths in economic models
Social Psychology;econometrics
Output feedback control and robustness in the gap metric
Zusammenfassung
Mueller, Markus:
Output feedback control and robustness in the gap metric
Ilmenau : Univ.-Verl. Ilmenau, 2009. - 254 S.
ISBN 978-3-939473-60-2
Die vorgelegte Arbeit behandelt den Entwurf und die Robustheit von drei
verschiedenen Regelstrategien für lineare Differentialgleichungssysteme mit
mehrdimensionalen Ein- und Ausgangssignalen (MIMO): Stabilisierung durch
Ausgangs-Ableitungs-Rückführung, Lambda-tracking und Funnel-Regelung.
Damit diese Regler bei der Anwendung auf ein lineares System die gewünschten
Stabilisierung/Regelung erbringen, ist eine explizite Kenntnis der
Systemmatrizen nicht notwendig. Es müssen nur strukturelle Eigenschaften des
Systems bekannt sein: der Relativgrad, dass das System minimalphasig ist, und
dass die sogenannte "high-frequency gain" Matrix positiv definit ist. Diese
stukturellen Eigenschaften werden für MIMO-Systeme in den ersten Kapiteln der
Arbeit ausführlich behandelt. Für MIMO-Systeme mit nicht striktem Relativgrad
wird eine Normalform hergeleitet, die die gleichen Eigenschaften wie die
bekannte Normalform für SISO-Systeme oder MIMO-Systeme mit striktem Relativgrad
aufweist.
Die Normalform sowie Minimalphasigkeit und Positivität der "high-frequency
gain" Matrix bilden die Grundlage dafür, dass die oben genannten
Regelstrategien Systeme mit diesen Eigenschaften im jeweiligen Sinn
stabilisieren.
Robustheit bzw. robuste Stabilisierung beschreibt folgendes Prinzip: falls
ein geschlossener Kreis aus einem linearen System und einem Regler in gewissem
Sinne stabil ist und die Gap-Metrik (der Abstand) zwischen dem im geschlossenen
Kreis betrachteten System und einem anderen "neuen" System hinreichend klein
ist, so ist der geschlossene Kreis aus dem "neuen" System und dem gleichen
Regler wieder stabil. Die gleiche Aussage stimmt auch für den Fall, dass man
den Regler und nicht das System austauscht.
Für Ausgangs-Ableitungs-Rückführung wird gezeigt, dass, falls diese ein System
stabilisiert, die auftretenden Ableitungen des Ausgangs durch
Euler-Approximationen der Ableitungen ersetzt werden können, falls diese
hinreichend genau sind.
Für Lambda-tracking und Funnel-Regelung wird gezeigt, dass beide Regler auch
für die Stabilisierung linearer Systeme verwendet werden können, die einen
geringen Abstand zu einem System haben, dass die o.g. Voraussetzungen erfüllt,
selbst diese Voraussetzungen aber nicht erfüllen.Abstract:
This dissertation considers the design and robustness analysis of three different control strategies for linear systems of differential equations with multidimensional input and output signals (MIMO): high-gain output derivative feedback control, lambda-tracking and funnel control. To apply these control strategies to linear systems and achieve the desired control objectives (stabilization or tracking), the explicit system's data needs not to be known, but certain structural properties of the systems are required. The system's relative degree must be known, the system must be minimum phase and the so-called "high-frequency gain" matrix must be positive definite.
These properties are considered in detail for linear MIMO-systems with non-strict relative degree. A normal form is developed which has the same properties as the well-known normal form for SISO-systems or MIMO-systems with strict relative degree.
Normal form, minimum phase property and positivity of the high-frequency gain matrix are the crucial assumptions for the application of the control strategies mentioned above. It is shown that each controller achieves certain control objectives when applied to any system which satisfies these assumptions.
The result on robustness and robust stability are as follows: if a closed-loop system represented by the application of a controller to a linear plant is stable (in some sense), and the gap metric (i.e. the distance) between the stabilised system and a different "new" system is sufficiently small, then the closed-loop system represented by the application of the controller to the "new" system is again stable. This conclusion holds also true when changing the roles of system and controller.
For high-gain output derivative feedback control it is shown that the controller still stabilizes a system when the derivatives of the output are replaced by Euler approximations of the derivatives, provided the approximation is sufficiently precise.
For lambda-tracking and funnel control it is shown that both controllers may be applied to systems which are "close" (in terms of a small gap) to any system from the class of minimum phase systems, with relative degree one and positive definite high-frequency gain matrix, but not necessarily satisfy any of these assumptions
A Predictive Fuzzy-Neural Autopilot for the Guidance of Small Motorised Marine Craft
This thesis investigates the design and evaluation of a control system, that is able to adapt
quickly to changes in environment and steering characteristics. This type of controller is
particularly suited for applications with wide-ranging working conditions such as those experienced
by small motorised craft.
A small motorised craft is assumed to be highly agile and prone to disturbances, being
thrown off-course very easily when travelling at high speed 'but rather heavy and sluggish
at low speeds. Unlike large vessels, the steering characteristics of the craft will change
tremendously with a change in forward speed. Any new design of autopilot needs to be to
compensate for these changes in dynamic characteristics to maintain near optimal levels of
performance.
This study identities the problems that need to be overcome and the variables involved.
A self-organising fuzzy logic controller is developed and tested in simulation. This type of
controller learns on-line but has certain performance limitations.
The major original contribution of this research investigation is the development of an
improved self-adaptive and predictive control concept, the Predictive Self-organising Fuzzy
Logic Controller (PSoFLC). The novel feature of the control algorithm is that is uses a
neural network as a predictive simulator of the boat's future response and this network is
then incorporated into the control loop to improve the course changing, as well as course
keeping capabilities of the autopilot investigated.
The autopilot is tested in simulation to validate the working principle of the concept and
to demonstrate the self-tuning of the control parameters. Further work is required to establish
the suitability of the proposed novel concept to other control
Underwater Vehicles
For the latest twenty to thirty years, a significant number of AUVs has been created for the solving of wide spectrum of scientific and applied tasks of ocean development and research. For the short time period the AUVs have shown the efficiency at performance of complex search and inspection works and opened a number of new important applications. Initially the information about AUVs had mainly review-advertising character but now more attention is paid to practical achievements, problems and systems technologies. AUVs are losing their prototype status and have become a fully operational, reliable and effective tool and modern multi-purpose AUVs represent the new class of underwater robotic objects with inherent tasks and practical applications, particular features of technology, systems structure and functional properties