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PIV Controller

How could I tune the above PIV controller? I am trying to get the system to have a settling time of < 1 second, P.O < 15% and zero steady state error.

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It may prove useful to generate the closed loop transfer function with the $K$, $C_{1}$, $C_{2}$ and $Gm$ terms.

$$\frac{C(s)}{R(s)} = \frac{G(s)}{1+G(s)H(s)}$$

It may look something like;

$$\frac{Gm(C_{1}+K)}{1+Gm(C_{1}+C_{2})}$$ initially

You may also want to convert the Gm transfer function into two 2nd order equations of the form;

$$\frac{(As - B)}{(s^2 + 2\zeta_1\omega_{n1} s + \omega_{n1} ^2) (s^2 + 2\zeta_2 \omega_{n2} s + \omega_{n2} ^2)}$$

by finding the roots of the $Gm$ denominator. You could think about creating the partial fractions of this. You will then know the natural frequencies $(\omega_{n1} , \omega_{n2} )$ and damping factors $(\zeta_1, \zeta_2)$ of the plant $Gm$. This will give you an idea if the plant is stable and the iteration rate needed for your PI(V) control.

The closed loop transfer function above will give you an idea that with $(C_{1}+K)$ and $(C_{1}+C_{2})$ you may like to think about setting $K_p$ negative and greater than the feed forward term $K$, until you get an under damped response. Then adjust the $K_i$ and $K_v$ terms until the required rise time and overshoot are achieved.

$K_p=-190$, $K_i=-19$, and $K_v=-3.5$ will give a fast response but play around for the one you want.

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  • $\begingroup$ Actually, $G_m$ can be simplified in $\frac{-6267}{\left(s+274\right) \left(s^2-3269.55\right)}$ $\endgroup$ Mar 29, 2015 at 22:22

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