time delay term in the syathesis equation. A. Tavkir series approoimation of the time defay term was used. Af alternative approansitson h the Pade aporoximatone. e3t=1+(7)1(1)t To derive a PI control algorithm structure (and hence the controller settings) via the direct synthesis methodology given a first order plus dead time (FOPDT) model of a process an approximation was made to the time delay term in the synthesis equation. A Taylor series approximation of the time delay term was used. An alternative approximation is the Pade approximation, es1+(2e)s1(2e)s Following the direct synthesis approach use this approximation to derive a PID control law structure and specify the corresponding control algorithm settings