Steadystate Performance

Integral action degrades the dynamic response of a control loop. We will demonstrate this quantitatively in Chap. 10. It makes the control loop more oscillatory and moves it toward instability. But integral action is usually needed if it is desirable to have zero offset. This is another example of an engineering trade-off that must be made between dynamic performance and steadystate performance. 

The steadystate error is another time-domain specification. It is not a dynamic specification, but it is an important performance criterion. In many loops (but not all) a steadystate error of zero is desired, i.e, the value of the controlled variable should eventually level out at the setpoint. 

In order to design feedback controllers, we must have some way to evaluate their effect on the performance of the closedloop system, both dynamically and at steadystate. 

The usual steadystate performance specification is zero steadystate error. We will show below that this steadystate performance depends on both the system (process and controller) and the type of disturbance. This is different from the question of stability of the system which, as we have previously shown, is only a function of the system (roots of the characteristic equation) and does not depend on the input. 

A new value of frequency is specified and the calculations repeated. Table 12.3 gives a FORTRAN program that performs alt these calculations, The initial part of the program solves for all the steadystate compositions and flow rates, given feed composition and feed flow rate and the desired bottoms and distillate compositions, by converging on the correct value of vapor boilup Vg. Next the coeflicients for the linearized equations arc calculated. Then the stepping technique is used to calculate the intermediate g s and the final P(j transfer functions in the frequency domain. 

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