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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.

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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.

enter image description here

Then follow the instructions here

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