# How do I get a closed-loop PID controller from a transfer function?

I have the transfer function below:

$$T_c(s) = \frac{s+k_i}{m_0s^3+s+k_i}$$

It is assumed that $k_p=1$ and $k_d=0$. I am given that $x_l(t)=[x_l(t),y_l(t)]^T$ is the trajectory and the tracking error is $e(t)=x(t)-(x_l(t)-10)$. I found the roots in terms of $k_i$, but I can't figure out what to do next or what other information I need.

A PID contoller looks like this, I assume that $T_c(s)$ is your plant\process model. So plug in $T_c(s)$ for the process model, the control model is shown below.