5.4.2.1. Feedback Control System
Consider a system where we heat the water in a tank. We set a
temperature, say 70 degrees. We compare the set temperature (set
value) with the actual temperature (the process value). The error is
used to control the heater. In case the set value minus the process
value is positive we need to heat the water, in case the difference
(error) is negative we should cool the water.
In a process diagram this leads to a block diagram like:
We assume that all blocks in such a scheme represent linear time
invariant systems. In that case each system can be represented with
its transfer function \(H_i(s)\). Representing all blocks in the \(s\)
domain we get:
System Message: WARNING/2 (\bXInput{A}
\bXComp[4]{B}{A}
\bXLink[$Q_\text{set}(s)$]{A}{B}
\bXBloc[4]{C}{$H_{\text{C}$}(s)}{B}
\bXLink[$\Delta q$]{B}{C}
\bXBloc{D}{$H_{\text{T}(s)$}{C}
\bXLink[]{C}{D}
\bXBloc{E}{$H_{\text{S}}(s)${D}
\bXLink[]{D}{E}
\bXOutput[4]{F}{E}
\bXLink[$Q$]{E}{F}
\bXReturn{E-F}{B}{})
! Missing } inserted.\n<inserted text> \n }\nl.22 \\bXBloc[4]{C}{$H_{\\text{C}$}(s)}{B}\n \n\n! Package pgf Error: No shape named s is known.\n\nSee the pgf package documentation for explanation.\nType H <return> for immediate help.\n ... \n \nl.22 \\bXBloc[4]{C}{$H_{\\text{C}$}(s)}{B}\n \n! Undefined control sequence.\n\\tikz@invoke@collected@onpath ...mmand \\tikz@temp \n \\pgf@stop \\tikz@node@is@a@...\nl.22 \\bXBloc[4]{C}{$H_{\\text{C}$}(s)}{B}\n \n! Undefined control sequence.\n\\@next ...bal \\pgflinewidth =\\tikzscope@linewidth \n \\tikz@path@do@at@end \nl.22 \\bXBloc[4]{C}{$H_{\\text{C}$}(s)}{B}\n \n! Missing number, treated as zero.\n<to be read again> \n \\let \nl.22 \\bXBloc[4]{C}{$H_{\\text{C}$}(s)}{B}\n \n! Illegal unit of measure (pt inserted).\n<to be read again> \n \\let \nl.22 \\bXBloc[4]{C}{$H_{\\text{C}$}(s)}{B}\n \n)\nRunaway argument?\n{$H_{\\text {T}(s)$}{C} \\bXLink []{C}{D} \\bXBloc {E}{$H_{\\text {S}}(s)\\ETC.\n! File ended while scanning use of \\\\bXBloc.\n<inserted text> \n \\par \n<*> tikz.tex\n \n! Emergency stop.\n<*> tikz.tex\n \n! ==> Fatal error occurred, no output PDF file produced!\nTranscript written on tikz.log.\n
![\bXInput{A}
\bXComp[4]{B}{A}
\bXLink[$q_\text{set}$]{A}{B}
\bXBloc[4]{C}{Controller}{B}
\bXLink[$\Delta q$]{B}{C}
\bXBloc{D}{Tank}{C}
\bXLink[]{C}{D}
\bXBloc{E}{Temp. Sensor}{D}
\bXLink[]{D}{E}
\bXOutput[4]{F}{E}
\bXLink[$q$]{E}{F}
\bXReturn{E-F}{B}{}](../../_images/tikz-c0dfff174663fd9ecebbee92a657af8bfcd393f4.png)