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Introduction - Models and Dynamic Systems

This chapter is a presentation of the issues surrounding the design and implementation of automatic control solutions for industrial applications. Currently, there is an increasing demand for setups that are productive and offer a good yield for the provider by means of modern concepts such as "embedded optimization" and "low-cost automation". In this context, Automation and Applied Informatics, through their theoretical tools, as well as hardware and software resources, contribute toward the development of applications using the existing technologies as well as the emergent ones. Automation makes it possible to describe the evolution of a real process using an abstract mathematical model, and to introduce the necessary methods and mechanisms to design the advanced control systems that ensure an optimal operation of the process. On the other hand, Informatics, due to the hardware material and software tools available and the efficiency of its powerful computing and communication which contribute toward operations involving data processing, model development, design and identification of control methods, is vital for the optimization, surveillance and protection of industrial processes. The different classes of dynamic models (systems) associated with the processes, as well as the most important algorithms, methods and techniques used in the design of the control systems for industrial facilities, are briefly presented here.

1.1. Overview

The design and implementation of digital control systems for industrial applications has, as a primary objective, the valorization of Automatic Control and Informatics tools in order to improve the quality of products, to ensure the safety of personnel, protect industrial facilities and the environment, and decrease as much as possible the production costs.

This objective is a response to the increasing demands in efficiency and autonomous operating requirements of companies, the need to reduce the role of the operator during process use (facilities, machines and equipment start to communicate with each other using the mechanisms involved in the concept of the internet of things) and the augmenting integration of automation into high-performance production technologies.

Two main categories of Industrial Automatic Control that are required are as follows: first, the mathematical formulism that allows the process to be represented by a mathematical model that expresses its dynamics, and second, the concepts and methods used in the control and optimization of the process [OGA 90, KUO 91, AST 97, GEN 97, POP 06].

A mathematical model is set using the laws that govern the functioning of the process or by using a collection of data acquired from the process.

The control algorithms are calculated based on the model, using numerical methods so as to ensure the level of performance desired in terms of the real processes. In the following step, which has become mandatory, an optimal operating point is found in the real operating conditions using an adequate decision criterion for the process.

The digital methods for computing and programming also ensure acquisition and processing of the data in real time and assist the design of control systems, as well as aiding the control and surveillance of industrial applications.

The classic control solution ensures a good response around a nominal operating point. To achieve a more widespread performance around the nominal point, this type of control must be improved using adaptive, robust, predictive, multimodel or intelligent techniques.

Normally, the exploitation of the process takes place within an "admissibility domain"; this operating domain of the process is imposed by technological limitations.

A standard control process configuration is organized in several steps over two important automation levels: the control (execution) level and the supervisory (decision) level. The supervisory level calculates, based on logical user demands, the optimal decision that can be implemented effectively by the action of the control systems at the execution level. In terms of regulation, the process evolves around the nominal operating point (NP) under the effect of the advanced control strategy, while conserving performance, in a prespecified vicinity of the NP.

The supervisory system finds the optimal operating point (OP) in the admissibility domain for the suitable optimization techniques, and the decision of the supervisor is transferred automatically from NP to OP. Sometimes, the case arises in which the process leaves the admissible operating domain, at the fault point, in which case the abnormal situation is detected and diagnosed so as to eliminate the cause of the fault as soon as possible. After the reconfiguration of the control systems, so that they become more tolerant to faults, the process operates in a normal state [POP 06, GEV 95, BOR 93].

In this context, our work, located in the control level area, proposes the necessary ingredients for the design and implementation of modern control systems as part of industrial applications and is notably directed toward systems engineering specialists.

We must note the complementarity that exists between this work and two books on optimization in engineering sciences [BOR 13, STE 14], which explain the methodology and techniques required for the implementation of the supervisory level in high-performing solutions of control in industrial processes.

1.2. Industrial process modeling

A mathematical model is the abstract representation of the behavior of a process (in this case, industrial). In other words, it is a dynamic system associated with the process that describes its behavior in a simple manner and allows a better understanding of the examined phenomena in order to carry out simulations, thus avoiding the need to conduct experiments that could be costly or get in the way of the process.

The model obtained will always be at best an idealization of the physical reality, considering that a hypothesis had to be made to obtain it. Furthermore, the search for a model can take on various forms, depending on the objective in question, the tools available and the nature and complexity of the phenomenon or process involved. In the engineering sciences domain, at the origin of the estimation of a dynamic model there is a set of equations that uses the conservation principle relative to certain physical generalized quantities: matter, mass, energy, amount of movement and electric charge. This mechanism of model estimation is reflected by the creation of balance equations for each of these quantities when they are implicated [DAU 04, POP 06, POP 11].

Most often, we start by writing the balance equation that expresses the preservation of a quantity W (mass or energy) over a time dt. The general form of this type of equation is the following:

(Variation dW of W in the system) = (entering quantity of W in the system) - (exiting quantity of W in the system) + (accumulated quantity of W) - (consumed quantity of W). For example, in the case of a representative chemical process, this can be written as

or again,

where rf and rc represent, respectively, the direct and reverse reaction rates for the transformation of the value W in the system.

The conservation principle of the global mass of the system can be written as

where ? is the density of the matter in the system, ?e is the density of the matter in the entering flow, ?s is the density of the matter in the exiting flow, Qe is the entering flow rate, Qs is the exiting flow rate, V is the volume of the system and M is the total mass of the system.

For the conservation of each component, it is known that

where ca is the molar concentration of component A in the system, is the is the molar concentration of component A in the entering flow, ca,out is the molar concentration of component A in the exiting flow, Qe is the entering flow rate, Qs is the exiting flow rate, V is the volume of the system, na is the number of moles in the system and raf, rac are the reaction rates of component A in the direct and reverse direction of the reaction.

For the conservation of energy:

where E is the total energy of the system, U is the internal energy, K is the kinetic energy, P is the potential energy, he is the specific enthalpy of the matter in the entering flow, hs is the specific enthalpy of the matter in the exiting flow, Qc is the quantity of heat exchanged between the system and the environment and Fs is the action of the external forces acting on the system.

For the more complex processes, there is also the possibility of a synthetic representation of the main characteristics of the process from equations constructed in a systemic way to a certain degree of precision.

There are two important classes of models used in Automatic Control: state space models (SSMs) based on the structural state concept, and the input-output models (IOMs) based on the concept of...