For the system shown in Fig. 1, design a PID controller...

For the system shown in Fig. 1, design a PID controller using Ziegler-Nichols method to determine the coefficients $K_p$, $\tau_i$ and $\tau_d$. R(s) + $K_p(1 + \frac{1}{\tau_i s} + \tau_d s)$ $\frac{5}{(s+1)^3}$ Fig. 1 The parameters settings are given in the following table, where $K_{cr}$ is the critical gain and $T_{cr}$ is the critical time. \begin{tabular}{|l|l|l|l|} \hline Controller & $K_p$ & $\tau_i$ & $\tau_d$ \\ \hline PID & $0.6 K_{cr}$ & $0.5 T_{cr}$ & $0.125 T_{cr}$ \\ \hline \end{tabular}

Transcript

00:01 Hello students, in this question we are given a pid controller with transfer function g c of s is equal to kp times 1 plus 1 by t is plus tds.

00:20 So the values the sekhner -nicolas turning rule for determination we have to use for the values of parameters of kp, ti and td and we need to calculate the sustained oscillation pcr and critical gain.

00:39 So to apply sekhner -nicolas training rule to determine the values of parameters.

00:45 So first we need to do is determine the sustained oscillation period and critical gain.

00:51 So to find per which is the oscillation period sustained oscillation period.

00:59 So we need to create a closed loop system by connecting pid control pid control to the transfer function.

01:14 This is a transfer function.

01:15 Okay, this is transfer function.

01:16 So we need to create a closed loop closed loop system connecting these two.

01:25 Okay, and then we can analyze a closed loop system and we can observe the output response to identify the sustained oscillation period which is per we can just observe it.

01:38 This is the first part now to find kcr.

01:41 We need to we need we increase the value of kp gradually until the output response starts to oscillate.

01:51 So output oscillates.

01:58 Okay with sustained oscillations and the critical gain kcr is the value of kp at which sustained oscillation occurs.

02:08 So kcr is equal to kp at that point...

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