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Notice that the manipulated variable is affected equally by the load and set point, which are multiplied. In level and pressure processes, the set point is added and contributes little to the forward loop. Because temperature and composition measurements are both subject to dead-time and multiple lags, they are relatively difficult to control. As a result, it is perfectly reasonable to expect that feedforward can be more readily justified in these applications. But along with the need, there likewise exists the problem of defining these processes well enough to use computing control. In addition, nonlinear operations and dynamic characterization are required. Yet multipliers and dividers did not come into common usage in control systems until about 1960. It is easy to understand, therefore, why level control was perhaps the first but hardly the most significant application of the feedforward principle.
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Application to a Heat Exchanger
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The most easily understood demonstration of feedforward is in the control of a heat exchanger. The computation is a heat balance, where the correct supply of heat is calculated to match the measured load. The process is pictured in Fig. 8.3. Steam flow W, is to be manipulated to heat a variable flow of process fluid W, from inlet temperature T, to the desired outlet temperature Tz. The steady-state heat balance is readily derived: Q = W,H, = W,C,(Tz - T,) where Q = H, = C, = Solving for heat transfer rate latent heat of the steam heat capacity of the liquid the manipulated variable,
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W, = W,K(Tz - T1) The coefficient K combines C,/H, with the scaling factors of the two flowmeters, and is included as an adjustable constant in the computer;
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FIG 8.3. The feedforward control system calculates the correct steam flow to match the heat load.
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Tz is the set point; W, and T1 are load variables. Witness the multiplication of flow by temperature. In the control computer that is shown in Fig. 8.4, the coefficient K is introduced as the gain of the summing amplifier. The measurement of liquid flow is linearized before multiplying; then steam flow must also be linearized, to be compatible with its set point. Steam flow is begun automatically by increasing both the liquid flow and the set point, since it is proportional to their product. If the exit temperature fails to reach the set point, it indicates that the ratio of steam flow to liquid flow is incorrect. In practice, this ratio is easily corrected by adjusting K until the offset is eliminated. This is the principal calibrating adjustment for the system; it sets the gain of the forward loop. If the system is perfectly accurate, exit temperature will respond to a change in liquid flow as shown in Fig. 8.5. Two failings of the steady-state control calculation should be noted: 1. Each load change is followed by a period of dynamic imbalance, which makes its appearance as a transient temperature error. 2. The possibility of offset exists at load conditions other than that at which the system was originally calibrated. On the other hand, the performance of the system exhibits a high level of intelligence. It is inherently stable and possesses strong tendencies toward self-regulation. Should liquid flow be lost for any reason, steam flow will be automatically discontinued. Feedback control systems ordinarily react the other way upon loss of flow, because the measurement of exit temperature is no longer affected by heat input. The importance of basing control calculations on mass and energy balancing cannot be stressed too highly. First, they are the easiest equations to write for a process, and they ordinarily contain a minimum of unknown variables. Second, they are not subject to change with time. It was not necessary, for example, to know the heat transfer area or coefficient or the temperature gradient across the heat-exchanger tubes in order to write their control equation. And should the heat transfer coefficient change, as it surely will with velocity, or fouling, etc., control is unaffected. It may be necessary for the steam valve to open wider to raise the shell pressure in the event of a reduction in heat transfer coefficient, but steam flow consistent with the heat balance equation will be maintained nonetheless.
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