Return to Question

Using Tustin method* (*approximation like suggested by TimWescott) and a sampling time of $10^{-3}s$ I got these:

Using Tustin method and a sampling time of $10^{-3}s$ I got these:

Using Tustin method and a sampling time of $10^{-3}s$ I got these:

Using Tustin method* (*approximation like suggested by TimWescott) and a sampling time of $10^{-3}s$ I got these:

So $K_{\small{p}} = 3, K_{\small{i}} = 1, K_{\small{d}} = 2$ (note that I needed to put an high frequency pole into derivative term to keep it real)

Using Tustin method and a sampling time of 1e-3 I got these:

So $K_{\small{p}} = 3, K_{\small{i}} = 1, K_{\small{d}} = 2$. Please note that I needed to put an high frequency pole into derivative term to keep it real. That pole has been put reasonably away from the bandwidth limit of the plant (cut-off frequency about $2 rad/s$).

Using Tustin method and a sampling time of $10^{-3}s$ I got these: