Question

The feed-forward transfer function for a unit-feedback control system is $1 /(s+1)$, as shown in Figure P12.1. A unit step signal is input to the system. Determine the minimum error of the system response by using a fuzzy optimization method for the time period, $0<t<10 \mathrm{~s}$, and a fuzzy constraint given as Figure Can't Copy $$ \mu_c(t)=\left\{\begin{array}{cc} 1, & 0 \leq t \leq 1 \\ \mathrm{e}^{1-t}, & t>1 \end{array}\right. $$

   The feed-forward transfer function for a unit-feedback control system is $1 /(s+1)$, as shown in Figure P12.1. A unit step signal is input to the system. Determine the minimum error of the system response by using a fuzzy optimization method for the time period, $0<t<10 \mathrm{~s}$, and a fuzzy constraint given as
Figure Can't Copy

$$
\mu_c(t)=\left\{\begin{array}{cc}
1, & 0 \leq t \leq 1 \\
\mathrm{e}^{1-t}, & t>1
\end{array}\right.
$$

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Fuzzy Logic with Engineering Applications

Fuzzy Logic with Engineering Applications

Timothy J. Ross 4th Edition

Chapter 12, Problem 1

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Step 1

The given feed-forward transfer function for the unit-feedback control system is \( G(s) = \frac{1}{s+1} \). The input to the system is a unit step signal, which can be represented as \( R(s) = \frac{1}{s} \). Show more…

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The feed-forward transfer function for a unit-feedback control system is $1 /(s+1)$, as shown in Figure P12.1. A unit step signal is input to the system. Determine the minimum error of the system response by using a fuzzy optimization method for the time period, $0<t<10 \mathrm{~s}$, and a fuzzy constraint given as Figure Can't Copy $$ \mu_c(t)=\left\{\begin{array}{cc} 1, & 0 \leq t \leq 1 \\ \mathrm{e}^{1-t}, & t>1 \end{array}\right. $$

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