Process Control: Modeling, Design, and Simulation

3.8. Lead-Lag Behavior

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:

Equation 3.47

For a step input of magnitude Δu, the output response is

Equation 3.48

A dimensionless output can be defined by dividing Equation (3.48) by k_pΔu, and t/τ_p is a natural dimensionless ...