Project ForgeMatch step-response curves P (smooth rise to a plateau), Q (continuously rising, never leveling), R (initial dip below zero before rising to a positive plateau), S (initial overshoot spike then decay to a lower plateau) with transfer functions I (K(ξs+1)/(s(τs+1))), II (K(ξs+1)/(τs+1), ξ>τ>0), III (K/(τs+1)), IV (K(ξs+1)/((τ1s+1)(τ2s+1)), ξ<0). The correct match is
- AP-III, Q-IV; R-II, S-I
- P-III, Q-I; R-IV, S-II
- CP-IV, Q-III; R-II, S-I
- DP-III, Q-II; R-IV, S-I
Explanation
P (settles to a plateau, no overshoot) matches a simple first-order system III. Q (never settles, ramps) matches the integrator I (pole at s=0). R (inverse response — initial dip before rising) matches IV with a right-half-plane zero (ξ<0). S (fast initial jump then decay) matches a lead-dominant element II (ξ>τ>0). So P-III, Q-I, R-IV, S-II.
Source: GATE CH 2019 (2019)
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