Plant deadtime

However, there are two practical problems with this ideal choice of the feedback controller C, y. First, it assumes that the model is perfect More importantly it assumes that the inverse of the plant model Cmo) physically realizable. This is almost never true since most plants have deadtime and/or numerator polynomials that are of lower order than denominator polynomials. 

The basic idea in multivariable IMC is the same as in single-loop IMC. The ideal controller would be the inverse of the plant transfer function matrix. This would give perfect control. However, the inverse of the plant transfer function matrix is not physically realizable because of deadtimes, higher-order denominators than numerators, and RHP zeros (which would give an openloop unstable controller). 

The discrete transfer function has three parameters that need to be identified nk, b, and a I. Of course, if we are identifying an unknown plant, we do not know what the real order of the systems is. A crucial part of the identification problem is the determination of what model structure yields the best fit to the real plant. In addition to finding the deadtime (nk), we must find the number of terms (na) and the number of bk terms (nb) to use in the model. 

Deadtime and Lags. Most temperature and composition controllers need to be tuned because the dynamics lags in these loops carmot be neglected. Deadtimes and lags degrade dynamic performance, so not including realistic dynamic lags in the simulation of these loops can lead to a prediction of dynamic performance that is unrealistically better than what will actually be seen in the plant. 

The filter adds lag and, because it increases the order of the system, also increases the apparent deadtime. Adding a filter after a controller has been tuned is therefore inadvisable. Either the plant test should be repeated to identify the new dynamics or, if the model identification package permits it, the original test data may be used with the filter simulated in the package. 

There are level controllers that have substantial deadtimes. Consider the process in Figure 4.19. Level in the base of the distillation column is controlled by manipulating the reboiler duty. Unlike most level controllers it would be difficult (and probably umeliable) to predict the relationship between F Vand MV. Further the reboiler introduces a large lag. The only practical way of identifying the process dynamics would be a plant test, as described in Chapter 2. The controller would then be tuned by applying one of the methods described in Chapter 3. This, unlike most level controllers, is likely to benefit from the use of derivative action. 

Perhaps the earliest, and most well-known technique, is that developed by Smith (Reference 1). It still employs a PID controller but in addition includes a. fast model that predicts how the process will behave in the future. The controller uses the output of this model, rather than the actual PV, and can therefore be tuned as if there is no deadtime. A plant model is also included. Its purpose is to check whether the actual PV eventually matches the prediction and, if not, generate a correction term. Figure 7.1 shows the configuration. 

The trend for the control PV shows a typical transient disturbance immediately the process deadtime has elapsed. This comes from the corrector and is caused by a mismatch between the actual and the predicted PV. It might arise because of a difference between the process deadtime and the deadtime in the plant model. It might also be caused by the plant model being hrst order plus deadtime whereas the process probably has a higher order. It is this transient that can limit how large a gain may be used in the PID controller. The controller will respond to it as if it is a load disturbance and the action it takes will later, when the deadtime has elapsed, cause a disturbance in the actual PV. This will then repeat at... 

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