I am trying to solve an assignment where the zeros of a PID-controller is given and the polynomial controller-constants need to be found.
The polynomial form of a standard PID-controller should be defined as: $\dfrac{Kd\cdot s^2+Kp\cdot s + Ki}{s}$
And the zeros of the transfer-function are defined as:
- $z_1 = 1$
- $z_2 = 3$
I thought, that the correct way would be to solve for the constants using the quadratic equation, but then I end up with 3 unknown parameters in 2 equations. \begin{equation} \begin{split} & \dfrac{-b \pm \sqrt{b^2-4\cdot a\cdot c}}{2\cdot a} = [-1,-3]\\ & \dfrac{-Kp \pm \sqrt{Kp^2-4\cdot Kd\cdot Ki}}{2\cdot Kd} = [-1,-3] \end{split} \end{equation}
I know how to solve it in Matlab with poly([-1;-3]) but I cannot seem to figure it out by hand