Using the step responses of (1) an integrating element and (2) a first-order process to an input change of magnitude M. 

(a) Show that the step response for an input change M of a first-order process G₁(s) = K₁ / τs + 1

can be approximately modeled by the step response of an integrator.

G₀(s) = K₀ / s for low values of t — i.e.,t ≪ τ.
(b) What is the relation between K₀ and K₁ if the two responses match for t ≪ τ ?
(c) This relationship motivates the use of an integrator model to approximate a first-order process by means of a single-parameter model. Explain how you would analyze a single step test to find K₀ and a time delay (if one exists).