курсовая работа / analiz_sistemy_sintez_korrektiruyushih_ustroystv_opredelenie / swp / Ф(S)

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%TCIDATA{Created=Tue Feb 22 21:45:33 2005}
%TCIDATA{LastRevised=Saturday, March 19, 2005 22:18:22}
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\newtheorem{theorem}{Theorem}
\newtheorem{acknowledgement}[theorem]{Acknowledgement}
\newtheorem{algorithm}[theorem]{Algorithm}
\newtheorem{axiom}[theorem]{Axiom}
\newtheorem{case}[theorem]{Case}
\newtheorem{claim}[theorem]{Claim}
\newtheorem{conclusion}[theorem]{Conclusion}
\newtheorem{condition}[theorem]{Condition}
\newtheorem{conjecture}[theorem]{Conjecture}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{criterion}[theorem]{Criterion}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{example}[theorem]{Example}
\newtheorem{exercise}[theorem]{Exercise}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{notation}[theorem]{Notation}
\newtheorem{problem}[theorem]{Problem}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{remark}[theorem]{Remark}
\newtheorem{solution}[theorem]{Solution}
\newtheorem{summary}[theorem]{Summary}
\newenvironment{proof}[1][Proof]{\textbf{#1.} }{\ \rule{0.5em}{0.5em}}
\input{tcilatex}

\begin{document}


\bigskip

$W_{\U{420} \U{410} \U{417} }(s)=W_{1}(s)W_{2}(s)\frac{1}{s}W_{0}(s)\frac{1}{%
s}=k_{1}\frac{55}{0.015s+1}\frac{1}{s^{2}}\frac{1.5}{0.04s^{2}+0.16s+1}=%
\frac{82.5k_{1}}{0.0006s^{5}+0.0424s^{4}+0.175s^{3}+s^{2}}$

\bigskip $==================================================================$

\bigskip

\bigskip

\bigskip

\bigskip

\bigskip

$W_{zamkn}(s)=\frac{W_{1}(s)W_{2}(s)\frac{1}{s}W_{0}(s)\frac{1}{s}}{%
1+W_{1}(s)W_{2}(s)\frac{1}{s}W_{0}(s)\frac{1}{s}}=\frac{\frac{82.5k_{1}}{%
0.0006s^{5}+0.0424s^{4}+0.175s^{3}+s^{2}}}{1+\frac{82.5k_{1}}{%
0.0006s^{5}+0.0424s^{4}+0.175s^{3}+s^{2}}}=\frac{\allowbreak 4.\,\allowbreak
125\times 10^{5}k_{1}}{3s^{5}+212s^{4}+875s^{3}+5000s^{2}+4.\,\allowbreak
125\times 10^{5}k_{1}}$

\bigskip

$\Phi _{g}(s)=\frac{W_{1}(s)W_{2}(s)\frac{1}{s}W_{0}(s)\frac{1}{s}}{%
1+W_{1}(s)W_{2}(s)\frac{1}{s}W_{0}(s)\frac{1}{s}}=\frac{\allowbreak
4.\,\allowbreak 125\times 10^{5}k_{1}}{3s^{5}+212s^{4}+875s^{3}+5000s^{2}+4.%
\,\allowbreak 125\times 10^{5}k_{1}}$

$\Phi _{f}(s)=\frac{W_{0}(s)\frac{1}{s}}{1+W_{1}(s)W_{2}(s)\frac{1}{s}%
W_{0}(s)\frac{1}{s}}=\frac{\frac{1.5}{0.04s^{3}+0.16s^{2}+s}}{1+\frac{%
82.5k_{1}}{0.0006s^{5}+0.0424s^{4}+0.175s^{3}+s^{2}}}=\allowbreak \frac{%
112.5s^{2}+7500s}{3s^{5}+212s^{4}+875s^{3}+5000s^{2}+4.\,\allowbreak
125\times 10^{5}k_{1}}$

\bigskip

$\Phi _{\varepsilon }(s)=\frac{1}{1+W_{1}(s)W_{2}(s)\frac{1}{s}W_{0}(s)\frac{%
1}{s}}=\frac{1}{1+\frac{82.5k_{1}}{0.0006s^{5}+0.0424s^{4}+0.175s^{3}+s^{2}}}%
=\allowbreak \frac{3s^{5}+212s^{4}+875s^{3}+5000s^{2}}{%
3s^{5}+212s^{4}+875s^{3}+5000s^{2}+4.\,\allowbreak 125\times 10^{5}k_{1}}$

$===========================================================$

\bigskip

$\allowbreak \frac{d\Phi _{\varepsilon }(s)}{ds}=\frac{d(\frac{%
3.0s^{5}+212.0s^{4}+875.0s^{3}+5000.0s^{2}}{%
3.0s^{5}+212.0s^{4}+875.0s^{3}+5000.0s^{2}+4.\,\allowbreak 125\times
10^{5}k_{1}})}{ds}=$

$\frac{15s^{4}+848s^{3}+2625s^{2}+10000s}{%
3s^{5}+212s^{4}+875s^{3}+5000s^{2}+4.\,\allowbreak 125\times 10^{5}k_{1}}%
-\allowbreak \frac{(3s^{5}+212s^{4}+875s^{3}+5000s^{2})\left(
15s^{4}+848s^{3}+2625s^{2}+10000s\right) }{\left(
3s^{5}+212s^{4}+875s^{3}+5000s^{2}+4.\,\allowbreak 125\times
10^{5}k_{1}\right) ^{2}}\allowbreak \allowbreak =$

\bigskip

$=\frac{4.\,\allowbreak 125\times 10^{5}s\left(
15s^{3}+848s^{2}+2625s+10000\right) k_{1}}{\left(
3s^{5}+212s^{4}+875s^{3}+5000s^{2}+4.\,\allowbreak 125\times
10^{5}k_{1}\right) ^{2}}\allowbreak $

\bigskip

\bigskip $C_{1}=\frac{d\Phi _{\varepsilon }(s)}{ds}|_{s=0}=0$

\smallskip \bigskip $\frac{d^{2}\Phi _{\varepsilon }(s)}{ds^{2}}=\frac{%
\allowbreak d(\frac{4.\,\allowbreak 125\times 10^{5}s\left(
15s^{3}+848s^{2}+2625s+10000\right) k_{1}}{\left(
3s^{5}+212s^{4}+875s^{3}+5000s^{2}+4.\,\allowbreak 125\times
10^{5}k_{1}\right) ^{2}}\allowbreak )}{ds}=$

$\allowbreak =\frac{4.\,\allowbreak 125\times 10^{5}\left(
15s^{3}+848s^{2}+2625s+10000\right) k_{1}}{\left(
3s^{5}+212s^{4}+875s^{3}+5000s^{2}+4.\,\allowbreak 125\times
10^{5}k_{1}\right) ^{2}}+\frac{\allowbreak 4.\,\allowbreak 125\times
10^{5}s\left( 45s^{2}+1696s+2625\right) \allowbreak k_{1}}{\left(
3s^{5}+212s^{4}+875s^{3}+5000s^{2}+4.\,\allowbreak 125\times
10^{5}k_{1}\right) ^{2}}\allowbreak -\allowbreak $

$\bigskip $

$\frac{\allowbreak 8.\,\allowbreak 25\times 10^{5}s\left(
15s^{3}+848s^{2}+2625s+10000\right) k_{1}\allowbreak \left(
15s^{4}+848s^{3}+2625s^{2}+10000s\right) }{\left(
3s^{5}+212s^{4}+875s^{3}+5000s^{2}+4.\,\allowbreak 125\times
10^{5}k_{1}\right) ^{3}}$

\bigskip

$\frac{C_{2}}{2!}=\frac{d^{2}\Phi _{\varepsilon }(s)}{ds^{2}}%
|_{s=0}=4.\,\allowbreak 125\times 10^{5}\left( 10000\right) \allowbreak 
\frac{k_{1}}{2\left( 4.\,\allowbreak 125\times 10^{5}k_{1}\right) ^{2}}%
=\allowbreak \frac{2.\,\allowbreak 424\,2\times 10^{-2}}{2k_{1}}=\allowbreak 
\frac{0.0\,\allowbreak 121\,21}{k_{1}}$

\bigskip

$\varepsilon _{ust.}=\lim \varepsilon (t)=C_{0}g(t)+C_{1}\left[ g^{\prime
}(t)\right] _{\max }+\frac{C_{2}}{2!}\left[ g^{\prime \prime }(t)\right]
_{\max }+...$

\bigskip $\varepsilon _{ust.}=\varepsilon _{stat.}+\varepsilon
_{v}+\varepsilon _{w}$

$g^{\prime }(t)=60$

$g^{\prime \prime }(t)=20$

$\varepsilon _{dop.}=1$

\bigskip

$\varepsilon _{dop.}=\varepsilon _{stat.}+\varepsilon _{v}+\varepsilon
_{w}=0+0+\frac{2.\,\allowbreak 424\,2\times 10^{-2}}{2k_{1}}\ast 20=1$

\bigskip $=>k_{1}=0.24242$

$\varepsilon _{ust.}=\frac{0.0\,\allowbreak 121\,21}{k_{1}}\ast
20=\allowbreak \frac{0.\,\allowbreak 24242}{0.\,\allowbreak 24242}=1$

\bigskip

$K=k_{1}k_{2}k_{0}=0.\,\allowbreak 24242\ast 55\ast 1.5=20$

=================================================================

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