# 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?

• 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.