In the PID equation K[((s+a)^2)/s] what values correspond to the PID coefficients Kp, Ki, Kd?

I'm trying to understand how to obtain the Kp, Ki, Kd values after finding a combination of K and a that works for me. Do I just expand the equation and take the coefficients?

Answers 2

  • It is in frequency domain instead of time domain.

    $$ G(s)=\frac{K(s+a)^2}{s} = \frac{Ks^2+2Kas+Ka^2}{s} $$

    according to the Laplace form of the PID controller $$ G(s)=\frac{K_ds^2+K_ps+K_i}{s} $$

    so $$ K_d = K, K_p = 2Ka, K_i = Ka^2 $$

  • The general PID form in Laplace domain is: $$ G(s)=\frac{K_ds^2+K_ps+K_i}{s} $$ The equation you've mentioned has a $Ks^3$ in the numerator. Hence, it cannot be transformed into PID form unless $K=0$, but that does not do you any good I guess.

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