Lead-lag transfer functions have the same order numerator polynomial as denominator polynomial. This occurs when the input has a direct effect on the output variable. In terms of the state space model (3.2), this means that D ≠ 0.
Consider a lead-lag transfer function where the numerator and denominator polynomials are first order:
For a step input of magnitude Δu, the output response is
A dimensionless output can be defined by dividing Equation (3.48) by kpΔu, and t/τp is a natural dimensionless ...