Interactive PID controller

There is, however, a quite different version of the PID algorithm. For reasons which will become apparent, the controller with which we have been working is known as the noninteractive form. 

While the interactive and noninteractive algorithms can be mned to give identical performance, this is subject to the restriction that 7) 0.257). This constraint will only be violated if the process has a very large 6 x ratio. Indeed if no derivative action is required, then the algorithms will perform identically without the need to change tuning. 

If TyTi is at the limit of 0.25 then, by combining Equations (3.41) and (3.42) we can see that the value of will be the same as that for 

In general, the interactive controller requires a much larger derivative tuning constant than the noninteractive equivalent. 

To switch from the interactive to the noninteractive version requires tuning to be changed as follows. 

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In Example 8.12, we used the interacting form of a PID controller. Derive the magnitude and phase angle equations for the ideal non-interacting PID controller. (It is called non-interacting because the three controller modes are simply added together.) See that this function will have the same frequency asymptotes. 

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