In this paper, the supervisory control of hybrid systems is introduced and discussed at length. Such control systems typically arise in the computer control of continuous processes, for example, in manufacturing and chemical processes, in transportation systems, and in communication networks. A functional architecture of hybrid control systems consisting of a continuous plant, a discrete-event controller, and an interface is used to introduce and describe analysis and synthesis concepts and approaches. Our approach highlights the interaction between the continuous and discrete dynamics, which is the cornerstone of any hybrid system study. Discrete abstractions are used to approximate the continuous plant. Properties of the discrete abstractions to be appropriate representations of the continuous plant are presented, and important concepts such as determinism and controllability are discussed. Supervisory control design methodologies are presented to satisfy control specifications described by formal languages. Several examples are used throughout the paper to illustrate our approach.

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Supervisory control of hybrid systems

Petri nets (PNs) are widely used to model discrete event dynamic systems (computer systems, manufacturing systems, communication systems, etc). Continuous Petri nets (in which the markings are real numbers and the transition firings are continuous) were defined more recently; such a PN may model a continuous system or approximate a discrete system. A hybrid Petri net can be obtained if one part is discrete and another part is continuous. This paper is basically a survey of the work of the authors' team on hybrid PNs (definition, properties, modeling). In addition, it contains new material such as the definition of extended hybrid PNs and several applications, explanations and comments about the timings in Petri nets, more on the conflict resolution in hybrid PNs, and connection between hybrid PNs and hybrid automata. The paper is illustrated by many examples.

On Hybrid Petri Nets

We consider in this paper first-order hybrid Petri nets, a model that consists of continuous places holding fluid, discrete places containing a nonnegative integer number of tokens, and transitions, either discrete or continuous. We set up a linear algebraic formalism to study the first-order continuous behavior of this model and show how its control can be framed as a conflict resolution policy that aims at optimizing a given objective function. The use of linear algebra leads to sensitivity analysis that allows one to study of how changes in the structure of the model influence the optimal behavior. As an example of application, we show how the proposed formalism can be applied to flexible manufacturing systems with arbitrary layout and different classes of products.

First-order hybrid Petri nets: a model for optimization and control

https://pure.tue.nl/ws/files/2223736/200412146.pdf

Hybrid process algebra

On fluidification of Petri Nets: from discrete to hybrid and continuous models

Differential Petri nets are a new extension of Petri nets. Through the introduction of the differential place, the differential transition, and suitable evolution rules, it is possible to model concurrently discrete-event processes and continuous-time dynamic processes, represented by systems of linear ordinary differential equations. This model can contribute to the performance analysis and design of industrial supervisory control systems and of hybrid control systems in general.

Differential Petri nets: representing continuous systems in a discrete-event world

The aim of the presented work is the control of Timed Event Graph to meet tight temporal constraints. The problem of temporal constraints is formulated in terms of control of linear Max-Plus models. First, the synthesis of a control law that ensures the satisfaction of a single constraint for a single input system is presented. Then, the single input multi-constraints problem is tackled and finally, the method is extended to the multi-inputs, multi-constraints problem. The proposed method is illustrated on the example of a simple production process.

/pdf/max-plus-control-design-for-temporal-constraints-meeting-in-2ji5coip99.pdf

Max-Plus Control Design for Temporal Constraints Meeting in Timed Event Graphs

This paper presents a new type of Petri nets, batches Petri nets. This model, an extension of the hybrid Petri nets, allows one to integrate a formalisation of parts circulation on accumulation conveyors. The batches Petri net is defined with the introduction of a new kind of place and transition: the batch place and batch transition. Evolution rules are determined in order to do the simulation of systems composed by accumulation phenomena. >

Batches Petri nets

Supervisory control systems play a central role in modern industrial automation. However, control theory has recently made significant advances in modeling mixed continuous/discrete event systems ("hybrid control systems"), whose typical instantiations include the industrial supervisory controller. This article shows how differential Petri nets, a model for hybrid control systems, can be used to represent industrial supervisory systems in a unified way. Typical industrial automation tests can be modeled, whereas the effect of communication protocols and software can be straightforwardly included using conventional Petri nets. Therefore, a global model for the operation of an industrial control system can be formed and its behavior analyzed

Differential Petri net models for industrial automation and supervisory control

In road transportation networks, such as freeways, motorways or highways, variable speed limit (VSL) control is one of the most efficient strategies to substantially improve traffic flow and solve or reduce the congestion problem. One way to design control strategies applicable in real time is to represent the vehicle flows with a hybrid dynamic model. In this context, Batches Petri Nets (BPN) and their extensions, are well adapted for the modeling of such systems as they intend to model variable delays on continuous flows by adding special nodes, called batch nodes, to the continuous and hybrid Petri nets. Using BPN with controllable batch speed, this paper studies a portion of the A12 highway in The Netherlands. This hybrid representation leads to the evaluation of several real time VSL control laws in accordance with the accumulation front of vehicles.

Isabel Demongodin

Papers

Differential Petri nets: representing continuous systems in a discrete-event world

Max-Plus Control Design for Temporal Constraints Meeting in Timed Event Graphs

Batches Petri nets

Differential Petri net models for industrial automation and supervisory control

Modeling and Analysis of Transportation Networks Using Batches Petri Nets with Controllable Batch Speed