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PID control.

A PID controller closed around the plant G(s) = ωₙ² / (s² + 2ζωₙs + ωₙ²). The loop is simulated from its true state equations; the closed-loop poles come from the characteristic cubic s³ + (2ζωₙ+K_d)s² + (ωₙ²+K_p)s + K_i = 0. Push the poles into the left half-plane and watch overshoot and settling time respond.