MV overshoot

Figure 16.2 Illustration of the squid giant axon action potential and its dependence on external Na+. The resting membrane potential (Em) is about -60 mV. Following stimulation (S), the initial Na+-dependent depolarization phase of the action potential that rises above 0 mV (overshoot) is gradually reduced in amplitude and delayed in time with reduction in extracellular Na+. Similar experiments were originally conducted by Hodgkin, Huxley, and Katz in the 1930s/1950s using the voltage clamp technique (Section 16.5.1.1).

It is important we distinguish between the MV overshoot and the PV overshoot. A number of published tuning methods permit definition of the allowable PV overshoot. However this does not satisfy the need to place a defined limit on the movement of the MV. An easy check to determine whether a tuning method takes account of this is to determine what tuning constants would be derived if 6 is set to zero. Each of the methods above would give the result... 

While direct synthesis enables the engineer to decide how aggressive the control should be, he or she has to manipulate X by trial-and-error. While there are several published techniques for selecting X, there is no predictable relationship between its value and MV overshoot. Under a different set of process dynamics the relationship between X and MV overshoot will change. This is illustrated in Figure 3.29. The curves were plotted by testing the mning... 

Of course it is possible from this chart to construct another allowing the engineer to choose a value for X to give the required MV overshoot. Indeed this has been done and the... 

And, from this chart, simple formulae could be developed. For example for a 15 % MV overshoot. 

Figure 3.30 Value of X necessary to give required MV overshoot...

Figures 3.31 to 3.33 give the recommended tuning for the preferred algorithm (noninter-active, proportional-on-PV, integral-on-Zin, derivative-on-PV and no derivative filtering). It is assumed that the scan interval is small compared to the process dynamics. The mning is designed to minimise ITAE subject to a maximum MV overshoot of 15 % on a self-...

Figures 3.37 to 3.39 give the tuning for the same controller but this time showing the effect of removing the constraint on MV overshoot. The result is that as the 6lx ratio approaches zero the tuning is the same as that given by many of the published methods, as shown in Equation (3.84).

Figure 3.37 Effect of MV overshoot constraint on controller gain...

No matter how fast the response to the DV, T2 should not be set to zero. This would cause a full-scale kick to the MV when the DV changes We should check the TUT2 ratio in any case. For example, if this is greater than 1.15 then the MV overshoot will be greater than 15%. We may need to reduce Tl and make the same compromise that we do for PID control, i.e. accept a slower return to SP in order to avoid harming the process with excessive changes to the MV. Or, if 0 is nonzero, it is possible to partially compensate for the reduction in Tl by reducing 0. 

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