16 the control variable is the position at which the final control element needs to operate in order for the process variable to reach and maintain the setpoint the final control element may be any variable output device while a valve is shown in fig1 any variable output device may be used an embodiment of the controller of this invention is illustrated in fig2 asymptotic approach algorithm flowchart the controller has a means 20 to calculate an error signal the controller compares the error signal 15 to zero if the error signal 15 is negative the controller 39 s output 16 is set to zero if the error signal 15 is positive the output 16 is calculated using an inverted polynomial equation having the form y a x p b x u2212 c or the form y a x p u2212 b such as a time domain polynomial equation 28 of the type as follows returning to fig2 the control variable 16 is checked to ensure that it is less than 100 30 if it is not the control variable 16 is set to 100 34 the control variable is checked to ensure that it is positive 32 if it is less than 100 if negative the control variable 16 is set to zero 24 the controller checks to determine if integral correction 36 is to be executed if integral correction 36 is selected the controller checks to determine if the process variable 13 is within a user selected error band e i for.