barcode reader project in c#.net The Unsteady State in Software

Printer USS Code 128 in Software The Unsteady State

The Unsteady State
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If a machine is to be used to control the process, it is necessary to decide in advance precisely what changes are to be made in the heat input q for every possible situation that might occur. We cannot rely on the judgment of the machine as we could on that of the operator. Machines do not think; they simply perform a predetermined task in a predetermined manner. To be able to make these control decisions in advance, we must know how the tank temperature T changes in response to changes in Ti and q: This necessitates
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INTRODUCTORY
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writing the unsteady-state, or transient, energy balance for the process. The input and output terms in this balance are the same as those used in the steady-state balance, Eq. (1.1). In addition, there is a transient accumulation of energy in the tank, which may be written Accumulation = pVC $ where p = fluid density V = volume of fluid in the tank t = independent variable, time By the assumption of constant and equal inlet and outlet flow rates, the term pV, which is the mass of fluid in the tank, is constant. Since Accumulation = input - output we have
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PVC% = wC(Ti-T)+q (1.3)
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units/time*
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Equation (1.1) is the steady-state solution of IQ. (1.3), obtained by setting the derivative to zero. We shall make use of E$. (1.3) presently.
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Control
As discussed above, the controller is to do the same job that the human operator was to do, except that the controller is told in advance exactly how to do it. This means that the controller will use the existing values of T and TR to adjust the heat input according to a predetermined formula. Let the difference between these temperatures, TR - T, be called error. Clearly, the larger this error, the less we are satisfied with the present state of affairs and vice versa. In fact, we are completely satisfied only when the error is exactly zero. Based on these considerations, it is natural to suggest that the controller should change the heat input by an amount proportional to the error. Thus, a plausible formula for the controller to follow is
q(t) = wC(TR -
Ti,) + K,(TR - T)
(1.4)
where K, is a (positive) constant of proportionality. This is called proportional control. In effect, the controller is instructed to maintain the heat input at the
*A rigorous application of the first law of thermodynamics would yield a term representing the transient change of internal energy with temperatme at constant pressure. Use of the specific heat, at either constant pressue or constant volume, is an adequate engineering approximation for most liquids and will be applied extensively in this text.
PROCESS SYSTEMS ANALYSIS AND CONTROL
steady-state design value qs as long as T is equal to TR [compare Eq. (1.2)], i.e., as long as the error is zero. If T deviates from TR, causing an error, the controller is to use the magnitude of the error to change the heat input proportionally. (Readers should satisfy themselves that this change is in the right direction.) We shall reserve the right to vary the parameter K, to suit our needs. This degree of freedom forms a part of our instructions to the controller. The concept of using information about the deviation of the system from its desired state to control the system is calledfeedback control. Information about the state of the system is fed back to a controller, which utilizes this information to change the system in some way. In the present case, the information is the temperature T and the change is made in q. When the term wC(TR - Ti,) is abbreviated to qs, Ftq. (1.4) becomes
4 = 4s + Kc(TR - T) (1.h)
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