The dynamics of control valve travel

The dynamics of the valve-positioning system may be described in terms of its small-signal and large-signal characteristics. The small-signal characteristics may be represented to reasonable accuracy by a first-order exponential lag, which will obey the canonical equation  

The large-signal characteristics of the valve-positioning system are dominated by the maximum speed/minimum stroke time of the valve. We may calculate the maximum speed by dividing the range of valve travel from fully closed to fully open by the minimum stroke time. Giving the minimum stroke time the symbol and using the convention of normalized valve travel, the maximum velocity of the valve actuator will thus be 

The transition from small-signal to large-signal behaviour occurs when the velocity predicted by equation (22.53) exceeds the limiting value given by equation (22.54). We may thus simulate the behaviour of valve travel easily using the Mim function introduced in Section 22.2, equation (22.2)  

Valve manufacturers may usually be prevailed upon to provide the stroke time, which is easily 

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