Behaviour of Controlled Processes

The purpose of a controller is to keep the controlled variable at its setpoint or bring it to setpoint. The determination of the behaviour of the controlled system is essentially not different from the determination of the behaviour of the uncontrolled system. The controlled behaviour depends strongly on the controller parameters and the type of controller that is used. Tuning of the controller parameters should lead to a matching of the behaviour of the controlled process to desired and/or specified behaviour for changes in setpoint or disturbances that act on the process. 

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The behaviour of processes under non-steady-state conditions is a complex and specialised subject and beyond the scope of this book. It can be important in process design when assessing the behaviour of a process from the point of view of safety and control. 

The approaches described previously assume that reactions will be suppressed, without giving any specific mechanism, and then rationalise the behaviour of the process using calculated metastable equilibria. A more innovative approach was taken by Saunders (1984) and Saunders and Miodownik (1985, 1987) for the prediction of phases formed by vapour co-deposition of alloys. It was postulated that the formation of phases on the substrate is controlled by the diffiisional breakdown of iiiUy intermixed depositing atoms so that three kinetic regimes are observed ... 

When a continuous change in the control parametr b results in exceeding the value b0 = 1/4, we have a loss of stability by the fixed point x (1). The new stable fixed point, x (2) = 1 — (1/4b), close to x,(1) for b close to b0, appears. Such a catastrophe is called bifurcation. Catastrophic behaviour of the process (3.83) for b > b0 is revealed in the fact that the solution (3.87) for b = b0 + e diverges to infinity for an arbitrarily small positive e. 

The description of the dynamic behaviour of the process is fundamental for the design of the control system. The required setpoints of the relevant process parameters must be known for devising the safety function (cf. Case Study 4.2). 

The dynamic behaviour of batch process units changes with time and this makes their precision control difficult. The aim of this paper is to highlight that the slave process of batch process units can have a more complex dynamics than the master loop has, and very often this could be the reason for the non-satisfying control performance. Since the slave process is determined by the mechanical construction of the unit, the above mentioned problem can be effectively handled by a model-based controller designed using an appropriate nonlinear tendency model. The paper presents the structure of the tendency model of typical slave processes and presents a case study where real-time control results show that the proposed methodology gives superior control performance over the widely applied cascade PID control scheme. 

While the use of filtering to reduce the effect of measurement noise affects the dynamic behaviour of any process, in the case of level control its impact is usually substantial and ideally should be avoided. 

It can cope with process variability and redefine the optimal operating conditions online. Nevertheless, the control of the PSD in emulsion polymerization by means of closed-loop strategies is a challenging problem [1]. Difficulties associated with the online measurement of the PSD can limit operational options and make the control problem a formidable task. In addition, the nonhnear behaviour of the process causes conventional control strategies to fail in ensuring a consistent product quality. 

Especially in an operating environment where quality has become more important than quantity, there is a strong desire to develop input-output models that can be used in advanced control applications, in order to develop control strategies for quality improvement. These models are usually discrete hnear transfer function (difference equation) type models, which provide a representation of the dynamic behaviour of the process at discrete sampling... 

In this book a combination of the principles of separation processes, process modelling, process control and numerical methods is used to describe the dynamic behaviour of separation processes. The text is largely mathematical and analytical in nature. Adsorption processes are commonly operated in a cyclic manner involving complex sequences of individual steps which are dynamic in nature and three chapters in this book specifically address this separation process. Chapter 11 covers the fundamentals of adsorption processes and includes physical adsorption of pure gases and mixtures, mass transfer by convective transport and the roles of pore and surface diffusion in the adsorption process. Chapter 12 addresses the separation of multicomponent mixtures by the use of adsorption columns and includes the Gleuckauf, film resistance and diffusion models and adiabatic operation of a fixed bed adsorption column together with periodic operation. Chapter 14 addresses the thermodynamics of the physical adsorption of pure gases and multicomponent gas mixtures. 

Most chemically reacting systems tliat we encounter are not tliennodynamically controlled since reactions are often carried out under non-equilibrium conditions where flows of matter or energy prevent tire system from relaxing to equilibrium. Almost all biochemical reactions in living systems are of tliis type as are industrial processes carried out in open chemical reactors. In addition, tire transient dynamics of closed systems may occur on long time scales and resemble tire sustained behaviour of systems in non-equilibrium conditions. A reacting system may behave in unusual ways tliere may be more tlian one stable steady state, tire system may oscillate, sometimes witli a complicated pattern of oscillations, or even show chaotic variations of chemical concentrations. 

Fig.l. Prediction of the deformation behaviour of the material where three different processes may be rate and stress- controlled dashed line) ... 

The study of corrosion is essentially the study of the nature of the metal reaction products (corrosion products) and of their influence on the reaction rate. It is evident that the behaviour of metals and alloys in most practical environments is highly dependent on the solubility, structure, thickness, adhesion, etc. of the solid metal compounds that form during a corrosion reaction. These may be formed naturally by reaction with their environment (during processing of the metal and/or during subsequent exposure) or as a result of some deliberate pretreatment process that is used to produce thicker films or to modify the nature of existing films. The importance of these solid reaction products is due to the fact that they frequently form a kinetic barrier that isolates the metal from its environment and thus controls the rate of the reaction the protection afforded to the metal will, of course, depend on the physical and chemical properties outlined above. 

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