PID controller transfer function G(s) = K_p + K_i/s + K_d s; Pade rational form

PID (Proportional-Integral-Derivative) controller framework (Minorsky 1922; Ziegler-Nichols 1942 Trans ASME 64, 759). Setup: closed-loop linear control system with reference r(t), process output y(t), error e = r - y, control u = K_p e +…