Single loop with feedforward compensation, derivative, PI controller, overrides, and predictor set from external signals. The configuration shown is for "increase-decrease" controller action; for "increase-increase" action, the -1 box shown in the measured variable channel would be moved to the set-point channel.
A single feedforward function is shown but, as will be indicated later, additional functions may be required for more complex control systems. This feedforward function is also shown ahead of overrides and limiters, which might not always be the case.
It may be noted that Laplace transform symbolism has been used in this and the next two illustrations to represent reset, derivative, and feedforward functions. Although not totally valid for digital computers or microprocessors, it is nearly so when high sampling rates are used. It is not valid for nonlinear functions, and either difference equations or z-transforms are better suited for some digital applications. The basic structure of Figure 12.1, however, is being increasingly accepted by control engineers.
The theory and mathematics involved in combining feedforward compensation, overrides, controllers (PI and PID), and anti reset-windup have been covered in detail elsewhere7 and are reviewed briefly below. At this point we wish to point out that (1) the feedforward function, Kgr^s/(tffs + 1), commonly termed "impulse feedforward," is a convenient way of feeding forward without interfering with reset when external reset feedback is used, and (2) making the feedforward time constant, equal to the reset time constant, tr, is usually desirable. This approach to feedforward also provides a convenient way to connect interaction compensators (decouplers) into control loops.
Note that tr is the reset time constant, rd is the derivative time constant, and a is a constant, usually in the range 6—20. Derivative is shown here as a separate unit, but is sometimes combined with PI in analog devices. Care should be taken to avoid putting derivative inside the reset loop.
Following is a brief review of the mathematics of a PI controller with external reset feedback and impulse feedforward compensation. The basic PI controller equations are:
If there are no overrides and no feedforward signal, 6v(s) = 6c(s) and we can combine equations (12.1) and (12.2) to get the conventional PI controller equation:
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