Compensator gain constant

Because of the tremendous sensitivity of the curve in the region of neutrality, it is always necessary to trim the ratio wtih a feedback loop. In addition, the nonlinearity of the measurement should be compensated by using the continuous nonlinear controller described at the end of Chap. 5. A diagram of the recommended system appears in Fig. 10.14. The flow signals are linearized to maintain loop gain constant over the full range of flow. 

Here the objective is to find required feedforward compensator gain to hold terminal composition constant as various external factors uy. 

The schematic and Bode plot for the single-pole method of compensation are given in Figure B-16. At dc it exhibits the full open-loop gain of the op amp, and its gain drops at -20dB/decade from dc. It also has a constant -270 degree phase shift. Any phase shift contributed by the control-to-output characteristic... 

If the process gain varies with load, such as the case of a heat transfer process, the gain product of the loop can be held constant by using a valve whose gain variation with load compensates for the process gain variation. 

When the thickness of the ApBq layer has reached its highest value xmax, a stationary state is established in which the mass loss of the solid phase due to evaporation is just compensated by the mass gain due to partial chemical reactions proceeding at the layer interfaces with initial substances A and B. Subsequently, the mass of the ApBq layer adherent to phase A remains constant, whereas the mass of its evaporated portion increases linearly. As a result, the mass of a solid specimen (substance A plus layer ApBq) first increases, goes through a maximum, then begins to decrease and at t0 proves equal to its initial value (Fig. 5.21). Thereafter, mass loss takes place instead of mass gain. 

The optimum gradient steepness is different for the less and the more retained component. It varies with the separation factor. For the less retained component, the production rate usually reaches a plateau without a maximum and, in most cases, there is no production rate gain above G = 0.4-0.6. Although the cycle time should decrease when the gradient steepness is increased, the optimum column efficiency increases with increasing gradient steepness and these two effects compensate each other, resulting in a nearly constant cycle time. 

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