and k p equal to or greater than 1 tuner 10 will give a solution for t p and related coefficients for chosen tuning processes if k p is less than 1 one the tuner 10 cannot give a solution and by reason of microprocessor 12 and its programming the operator will receive instructions on display 18 and printer 16 advising of the failure and recommending re trying with k s at double the previous value the discussion thus far has dealt with processes or systems which are closed loop or self balancing systems open loop or non self balancing systems give a different response see fig6 and require a different analysis the transfer function g p s for such an open loop system is equ2 where l p is the dead time and t p is the time constant of the process and s is the laplace transform operator the tuner 10 in determining the step response characteristics of an open loop process or system relies upon the relationships set forth in equation 1 and 2 supra to synthesize the step signal response from the pulse signal response then it can be shown the area s s in fig7 can be expressed by the equation where the transfer function g p s of the process can be expressed as follows equ3 where s indicates the laplace transform operator t p1 and t p2.