I just have a quick question. In my lecture notes, he defined the PID controller as
And then he said that this is equal to the following
How did he do that? What is k, z1 and z2 equal?
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Sign up to join this communityI just have a quick question. In my lecture notes, he defined the PID controller as
And then he said that this is equal to the following
How did he do that? What is k, z1 and z2 equal?
Okay:
$$\begin{align*} k_p + \frac{k_i}{s}+k_d\:s&=\frac{k\left(s+z_1\right)\left(s+z_2\right)}{s}\\\\ k_d\:s^2+k_p\:s + k_i&=k\:s^2 + k\left(z_1+z_2\right)s + k\:z_1\:z_2\\\\\therefore\\\\k&=k_d\\\\ k\left(z_1+z_2\right)&=k_p\\\\ k\:z_1\:z_2&=k_i \end{align*}$$
If you accept that \$k=k_d\$ solves for \$k\$, then that's two remaining equations and two remaining unknowns:
$$\begin{align*} z_1+z_2&=\frac{k_p}{k_d}\\\\ z_1\cdot z_2&=\frac{k_i}{k_d} \end{align*}$$
Can you move forward from here using the quadratic equation?