Dynamic compensation

Feedforward control can also be applied by multiplying the liquid flow measurement—after dynamic compensation—by the output of the temperature controller, the result used to set steam flow in cascade. Feedforward is capable of a reduction in integrated error as much as a hundredfold but requires the use of a steam-flow loop and dynamic compensator to approach this. 

A cocurrent evaporator train with its controls is illustrated in Fig. 8-54. The control system applies equally well to countercurrent or mixed-feed evaporators, the princip difference being the tuning of the dynamic compensator/(t), which must be done in the field to minimize the short-term effects of changes in feed flow on product quality. Solid concentration in the product is usually measured as density feedback trim is applied by the AC adjusting slope m of the density function, which is the only term related to x. This recahbrates the system whenever x must move to a new set point. 

This is the steady state compensator. The lead-lag element with lead time constant xFLD and lag time constant XpLG is the dynamic compensator. Any dead time in the transfer functions in (10-7) is omitted in this implementation. 

The amplifier network provides signal conversion and suitable static and dynamic compensation for good positioner performance. Control from this block usually reduces to a form of proportional or proportional plus derivative control. The output from this block in the case of a pneumatic positioner is a single connection to the spring and diaphragm actuator or two connections for push/pull operation of a... 

Feedforward control system that provides constant separation by manipulating the distillate flow (top). At the bottom, a variety of dynamic compensators are shown, which can be used to match the "dynamic personality" of the process. 

For noninteracting control loops with zero dead time, the integral setting (minutes per repeat) is about 50% and the derivative, about 18% of the period of oscillation (P). As dead time rises, these percentages drop. If the dead time reaches 50% of the time constant, I = 40%, D = 16%, and if dead time equals the time constant, I = 33% and D = 13%. When tuning the feedforward control loops, one has to separately consider the steady-state portion of the heat transfer process (flow times temperature difference) and its dynamic compensation. The dynamic compensation of the steady-state model by a lead/lag element is necessary, because the response is not instantaneous but affected by both the dead time and the time constant of the process. 

Pole and zero placement using a dynamic compensator for an SISO system can be accomplished by specifying analytically the closed loop servo response (e.g., first or second order with deadtime). Suppose that the specified response is defined by P(s) solving the closed loop equation (5) yields an analytical... 

Brasch, F. M. and Pearson, J. B., "Pole Placement Using Dynamic Compensators," IEEE Trans. Auto. Cont., 1970, AC-15, 34. 

Block Diagram Analysis One shortcoming of this feedforward design procedure is that it is based on the steady-state characteristics of the process and, as such, neglects process (Ramies (i.e., how fast the controlled variable responds to changes in the load and manipulated variables). Thus, it is often necessary to include dynamic compensation in the feedforward controller. The most direct method of designing the FF dynamic compensator is to use a block dir rram of a general process, as shown in Fig. 8-34, where G, represents the disturbance transmitter, (iis the feedforward controller, Cj relates the disturbance to the controlled variable, G is the valve, Gp is the process, G is the output transmitter, and G is the feedback controller. All blocks correspond to transfer fimetions (via Laplace transforms). 

Thus, it may be concluded that potentiostatic transients can be, malyzed correctly only if the value of iR is negligible throughout the liansient or if it is dynamically compensated for in real time, during K the course of the transient. 

Supercritical fluid chromatographic pumps must have both a wide range of compensation and use dynamic compressibility compensation to produce accurate and reproducible flow and composition. Whereas water has a compressibility factor of 75 x 10 /bar, methanol is more compressible at 120 X 10 /bar. Carbon dioxide has widely varying compressibility from 95 to 395 X 10 /bar at 5°C, depending on the pump delivery pressure (column head pressure). The viscosity of pure carbon dioxide is 1 /20 the viscosity of pure methanol. During composition programming, the viscosity of the mixed fluid and the column head pressure increases as the modifier concentration increases. Without dynamic compensation, the actual delivery of the carbon dioxide would roll off. The total flow would be less than the set points and the modifier concentration would be more than the set points. 

A schematic of the stripping section of a distillation column with a ratio controller for the bottom products composition is shown in Figure 15.53. This application is similar to ratio control except that dynamic compensation is added to the measured column feed rate. If the steam flow to the reboiler were increased immediately for an increase in column feed rate, the corrective action would initially be an overcorrection. This results because, when a feed rate change occurs, it takes some time for the bottom product composition to respond. The purpose of the dynamic compensation (DC) element is to allow for the correct timing for the compensation for feed rate changes. 

The dynamic element for this case can be simply a lag element, e.g., a digital filter described by Equation (15.10). The wastewater neutralization case (Figure 15.52) does not require dynamic compensation, since the process pH responses to feed rate changes and NaOH flow rate changes have similar dynamic behavior. 

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