PID Control Loop Bench

Interactive PID / compensator design against any Laplace plant
Negative feedback · Y(s)/X(s) = G(s)/(1+G(s)H(s)), G(s)=C(s)·P(s)
Controller/Process/Test input stacked on the right third, the chosen diagram(s) on the left two-thirds, everything else below.
⋮⋮ 01Controller C(s)
C(s) = …
Ideal PID form: C(s) = Kp + Ki/s + Kd·s. Switch to Laplace to type any compensator directly.
⋮⋮ 02Process P(s)
P(s) = …
Write polynomials in s: + - * ^ ( ) and one division, e.g. (s+1)/(s^2+2s+1).
⋮⋮ 03Test input x(t)
Sine frequency slider sweeps 0.05–50 Hz (log scale) and marks ω on the Bode, phase and Nyquist diagrams even in Step/Ramp mode. Duration auto-fits the dominant time constant unless edited.
⋮⋮ 04Feedback H(s)
H(s) = …
The feedback path fed back into the summing junction: Z(s) = X(s) − H(s)Y(s). Loop gain L(s) = G(s)H(s) with G(s) = C(s)·P(s); H(s) = 1 is the unity-feedback case.
⋮⋮ Time response step, r→y
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⋮⋮ Pole–zero map closed loop T(s)
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⋮⋮ Bode — magnitude open loop L(jω)
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⋮⋮ Bode — phase open loop L(jω)
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⋮⋮ Nyquist diagram open loop L(jω)
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⋮⋮ Root locus gain K sweep of L(s)
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