Remember that we are working in deviation variables. Assume that we are not making a setpoint change, so r(s) = 0. Since we do not want the output variable to change, that is equivalent to saying that we desire y(s) = 0. From Equation (10.6) we can see that the only way to assure y(s) = 0 is for the following relationship to hold
In this expression all the transfer functions are determined for a particular system, except for the feed-forward controller, gcf(s). Solving Equation (10.7) for gcf(s), we find
If we make the simplifying assumption that the disturbance measurement has ...