Hybrid System Control

Introduction

The period preceding 1868 was characterised by the development of automatic control systems through intuition and invention. Efforts to increase the accuracy of the control sytem led to slower attenuation of transient oscillations and even unstable system.

It then become imperative to develop a theory of automatic control. A number of mathematical and analytical methods have been developed to tackle the increasing complexity of control systems.In the last twenty years, digital computers have been employed especially for process control systems in which many variables are measured and controlled simultanouly by a computer.

A system which is modelled by differential and/or difference equations is called a continuous sytem since the functions solved are continuous. A system which is modelled by computer program is called a discrete or logic system since the if-then-else statement separates the input data into discrete cases. Hybrid systems are those contaning mixtures of logic and continuous dynamics.

The reason for using hybrid system control

The demand for increased levels of automation and system integration have forced control engineers to deal with increasingly larger and more complicated systems. Recent technological advances, such as faster computers, cheaper and more reliable sensors and the integration of control considerations in the product design, have made it possible to extend the practical applications of automatic control to systems that were impossible to deal with in the past. This has left control engineers with a substantial challenge, as the standard design and analysis tools are sometimes inadequate to deal with the complexity of large scale systems. Designers are sometimes forced to use a combination of techniques from the areas of continuous and discrete control. This typically leads to a hierarchical control structure, with continuous controllers carrying out tasks of regulation and tracking at a lower level and discrete controllers supervising their operation and taking more abstract, strategic decisions.

The overview of hybrid system control

A large class of hybrid systems can be described by the architecture of the following figure.

A typical hybrid system is arranged in two (or more) layers. Different levels of abstractions of the plant model are used at each layer of the hierarchy. In the bottom layer the plant model is usually described by means of differential and/or difference equations. This layer contains the actual plant and any conventional controllers working at the same level of abstraction. In the top layer the plant description is more abstract. Typical choices of description language at this level are finite state machines, fuzzy logic, Petri nets, etc. Typically the controllers designed at this level are discrete event supervisory controllers. The two levels communicate by means of an interface that plays the role of a translator between signals and symbols.

The control architecture described above appears in a wide variety of applications and forms the heart of most hybrid system formalisms. This results from the requirement that control systems are expected to be autonomous (e.g., in case of highway automation, the vehicles are supposed to be driven automatically without human intervention), requiring the controller not only to calculate feedback control laws for specific tasks but also to plan the sequence of actions in order to achieve the specified goal. Planning is inherently a discrete process which is represented by the higher layers of the hierarchy whereas the continuous time control laws that execute each action constitute the lower layers. Switching controllers, Intelligent Control, Expert Control, and Motion Control, among others, make use of the structure of the above figure.

The problem faced by hybrid system control

Although, the theory for design and verification of discrete event and continuous dynamical systems is well developed, a comprehensive theory for hybrid systems is still in a rudimentary phase. For most of these systems designed so far, the design approach has been ``divide and conquer''; that is, the continuous and discrete controllers are designed independently and then combined by an interface which is designed for the specific problem. A discrete event abstraction of the continuous dynamics is used in designing the controller at the discrete layer and vice versa. Performance of such a design or the composite hybrid system depends on the correctness of abstractions at each layer. Design of the interface is thus utmost important as it defines the information structure between different layers of the hierarchy. Design of interfaces for a general hybrid dynamical system is still an open question.

The applications of hybrid system control

Hybrid control systems are typically found when continuous processes interact with, or are supervised by, sequential machines. Such systems frequently arise from computer aided control of continuous processes and such hybrid systems arise in varied contexts such as manufacturing, communication networks, autopilot design, computer synchronization, traffic control, and industrial process control, for example. Another important way in which hybrid systems arise is from the hierarchical organization of complex control systems. In these systems, a hierarchical organization helps manage complexity and higher levels in the hierarchy require less detailed models (discrete abstractions) of the functioning of the lower levels, necessitating the interaction of discrete and continuous components. Examples of such systems include flexible manufacturing and chemical process control systems, interconnected power systems, intelligent vehicle highway systems, air traffic management systems, and computer communication networks. More generally, hybrid systems arise from the interaction of discrete planning algorithms and continuous control algorithms. As such, hybrid systems provide the basic framework and methodology for the synthesis and analysis of autonomous and intelligent systems. Examples of this type not already mentioned above include biological motor control models, robotic systems, data base retrieval systems and medical informatics systems.

Conclusions

Although hybrid system control is used to model complex systems and there is a large potential for its applications, the design and analysis of hybrid controllers can be very complicated, as the interaction between the continuous and discerete domains can give rise to patterns of behaviour that are hard to predict. Therefore different approaches to model hybrid system have been motivated to deal with modelling and verification.

References

There is an interesting case study of hybrid systems on manufacturing, which is written byAhmad Kamil