Michael Tittus

Hybrid systems in process control

Modeling and control of hybrid systems, with particular emphasis on process control applications, are considered in this article. Based on a number of observations on typical mixed discrete and continuous features for such applications, a fairly general model structure for hybrid systems is proposed. This model structure, which clearly separates the open-loop plant from the closed-loop system, is suitable for analysis and synthesis of hybrid control systems. To illustrate this, three different approaches for control-law synthesis based on continuous and discrete specifications are discussed. In the first one, the hybrid plant model is replaced by a purely discrete event model, related to the continuous specification, and a supervisor is synthesized applying supervisory control theory suggested by Ramadge and Wonham (1987). The other two methods directly utilize the continuous specification for determination of a control event generator, where time-optimal aspects are introduced as an option in the last approach.

Control design for integrator hybrid systems

The authors define controllability for hybrid systems as the existence of correct control laws that transfer the hybrid plant between predefined subsets of the hybrid state space. A methodology for analyzing controllability and synthesizing control laws for a class of hybrid systems, applicable especially in batch control, is proposed. They use a framework consisting of a hybrid plant and a hybrid controller that interact in a feedback fashion.

Control-law synthesis for linear hybrid systems

Based on the framework of hybrid automata the notion of controllability for a hybrid system with respect to given specifications is discussed. A hybrid system is defined as being controllable if there exists at least one acceptable run between each ordered pair of marked states, that is, the system can be controlled to satisfy all specifications while transferring between two marked states. Given certain restrictions, controllability can be decided for the class of linear hybrid systems and, if controllable, a set of control laws can be synthesized that guarantee a correct execution of the acceptable run. An algorithm for the generation of such control laws is presented. In general, the problem is only semidecidable since the algorithm does not necessarily terminate.<<ETX>>

Controlling and coordinating recipes in batch applications

Starting with a model of the plant and a number of product specifications (recipes), a formalism is presented to design a discrete supervisor that controls and coordinates the simultaneous execution of these recipes. The paper introduces general, reusable Petri net blocks used to model recipes and uses an extension of the Wonham-Ramadge framework to synthesize a supervisor.

Deadlock avoidance in batch processes

Abstract A Petri net based approach for the modeling of batch plants as well as products is presented. Allocating non-sharable resources for product recipes can lead to deadlocks. In this paper we focus on the detection of potential deadlock situations using a graph structure derived from synchronization issues that arise when moving a batch between resources. It is shown that different graph patterns define potential deadlocks. These patterns even suggest how to implement a Petri net supervisor to avoid these deadlocks.

Specification of a batch plant using process algebra and Petri nets

A modelling framework for general routing and resource allocation systems is presented. The task is to specify desired routes for individual objects (products, data packets, vehicles), which are to be served by a number of shared resources (machines, computers, communication links). Based on simple booking models for the resources and routing specifications for the objects, a controller that synchronizes the objects utilization of the available resources is automatically generated. A high level language is presented in order to simplify the specification of desired routes. This modelling language combines Petri nets and process algebra. Process operators are introduced for specification of alternative, synchronization, start and stop process, and restriction, which are applied in order to model join and split operations. This language results in a compact and efficient representation of complex routing specifications.

Modeling and specification of discrete event systems using combined process algebra and Petri nets

A modeling framework for general routing and resource booking problems is presented. The task is to specify desired routes for individual objects (products, data packets, vehicles), which are to be served by a number of shared resources (machines, computers, communication links). Based on simple booking models for the resources and routing specifications for the objects, a controller that synchronizes the objects utilization of the available resources is automatically generated. A high level language is presented in order to simplify the specification of desired routes. This modeling language combines Petri nets and process algebra. Process operators are introduced for specification of alternative and synchronization, which are applied in order to model join and split operations. Multiple as well as alternative resources are easily specified utilizing sets of resources. These sets and operators imply a very compact and efficient representation of complex routing specifications. In fact, the representation is suitable for verification and synthesis based on symbolic tools such as binary decision diagrams.

On the Use of Multiple Models and Formal Control Synthesis in Batch Control

Abstract This paper takes a closer look on control design in batch processes and points out possibilities to use formal mathematical methods for control synthesis. The control synthesis process is divided into two parts: static and dynamic resource allocation. Both design activities require information about different aspects of the system and hence, different models. Suitable models for these resource allocations are proposed and it is shown how formal methods can be used to solve the allocation problems.

Modeling, specification and controller synthesis for discrete event systems

Based on some modeling primitives from automata, Petri nets and process algebra, an architecture for a general routing and resource booking problem is presented. The architecture is based on general models for a set of resources, desired routing specifications for a set of objects (products, data packets, vehicles) and a controller that synchronizes the objects utilization of the available resources. High level graphical routing specifications for the objects are also introduced, together with corresponding Petri nets, in order to simplify the specification of desired routes. Two specific operators, event synchronization and arbitrary order including an algebra of events, are then used in the formal Petri net specifications.

Modeling primitives and specification structures for supervisory control

Three different modeling languages for discrete event systems are compared, automata, Petri nets and process algebra, and it is shown how a couple of basic primitives can be modeled in these languages. Based on these modeling primitives an architecture for a general routing and resource booking problem is presented. The architecture is based on general models for a set of resources, desired routing specifications for a set of objects (products, data packets, vehicles) and a controller that synchronizes the objects utilization of the available resources. High level graphical routing specifications for the objects are also introduced, together with corresponding Petri nets, in order to simplify the specification of desired routes. As applications of the suggested architecture we consider cell controllers for flexible manufacturing systems and multi-purpose batch plants in chemical processing industry.