1 \RequirePackage{lmodern
}
2 \RequirePackage{SIunits
}
5 \newcommand{\Gtrue}{G^
{0}}
6 \newcommand{\Gpart}{G_
{1}}
7 \newcommand{\Gopen}{G_
{\mathrm{o
}}}
8 \newcommand{\Gclosed}{G_
{\mathrm{c
}}}
9 \newcommand{\Gdelta}{G_
{\mathrm{\Delta}}}
10 \newcommand{\deltasub}[2][]{{#2}_
{#1\mathrm{\Delta}}}
11 \newcommand{\Fy}{F_
{\mathrm{y
}}}
12 \newcommand{\Fr}{F_
{\mathrm{r
}}}
13 \newcommand{\Ff}{F_
{\mathrm{f
}}}
14 \newcommand{\Flead}{F_
{\mathrm{lead
}}}
15 \newcommand{\FPD}{F_
{\mathrm{PD
}}}
16 \newcommand{\tauD}{\tau_{\mathrm{D
}}}
17 \newcommand{\Flag}{F_
{\mathrm{lag
}}}
18 \newcommand{\tauI}{\tau_{\mathrm{I
}}}
19 \newcommand{\refsubsymb}{\mathrm{ref
}}
20 \newcommand{\refsub}[1]{#1_
{\refsubsymb}}
21 \newcommand{\bandwidth}{\omega_{\mathrm{B
}}}
22 \newcommand{\omegasamp}{\omega_{\mathrm{s
}}}
23 \newcommand{\gaincross}{\omega_{\mathrm{c
}}}
24 \newcommand{\gaincrossdes}{\omega_{\mathrm{c,d
}}}
25 \newcommand{\phasecross}{\omega_{\mathrm{p
}}}
26 \newcommand{\resonancefreq}{\omega_{\mathrm{r
}}}
27 \newcommand{\resonancegain}{M_
{\mathrm{p
}}}
28 \newcommand{\gainmargin}{A_
{\mathrm{m
}}}
29 \newcommand{\gainmargindes}{A_
{\mathrm{m,d
}}}
30 \newcommand{\phasemargin}{\varphi_{\mathrm{m
}}}
31 \newcommand{\phasemargindes}{\varphi_{\mathrm{m,d
}}}
32 \newcommand{\risetime}{T_
{\mathrm{r
}}}
33 \newcommand{\settlingtime}{T_
{\mathrm{s
}}}
34 \newcommand{\overshoot}{M
}
35 \newcommand{\obsmat}{\mathcal{O
}}
36 \newcommand{\ctrlmat}{\mathcal{S
}}
37 \newcommand{\sensitivityFunction}{S
}
38 \newcommand{\complementarySensitivityFunction}{T
}
40 % A few commands for block diagram drawing without heavy packages
41 %\providecommand{\dfrac}[2]{{\displaystyle\frac{#1}{#2}}}
44 % Notation for problem 3.31
46 \newcommand{\utankflow}{F_
{\mathrm{t,in
}}} % used to be $F_{i}$
47 \newcommand{\utanktemp}{T_
{\mathrm{t,in
}}} % used to be $T_{i}$
48 \newcommand{\utankdens}{\rho_{\mathrm{t,in
}}} % used to be $\rho_{i}$
49 \newcommand{\utankcapa}{c^
{\mathrm{p
}}_
{\mathrm{t,in
}}} % used to be $c_{p}$
50 \newcommand{\ucoolflow}{F_
{\mathrm{c,in
}}} % used to be $F_{k_{i}}$
51 \newcommand{\ucooltemp}{T_
{\mathrm{c,in
}}} % used to be $T_{k_{i}}$
52 \newcommand{\ucooldens}{\rho_{\mathrm{c,in
}}} % used to be $\rho_{k_{i}}$
53 \newcommand{\ucoolcapa}{c^
{\mathrm{p
}}_
{\mathrm{t,in
}}} % used to be $c_{p...???
54 \newcommand{\ytankflow}{F_
{\mathrm{t
}}} % used to be $F$
55 \newcommand{\ytanktemp}{T_
{\mathrm{t
}}} % used to be $T$
56 \newcommand{\ytankdens}{\rho_{\mathrm{t
}}} % used to be $\rho$
57 \newcommand{\ytankcapa}{c^
{\mathrm{p
}}_
{\mathrm{t
}}} % used to be $c_{p}$
58 \newcommand{\rtanktemp}{\refsub{T
}} % used to be $ref$ or $T_{ref}$
59 \newcommand{\ycoolflow}{F_
{\mathrm{c
}}} % used to be $F_{k}$
60 \newcommand{\ycooltemp}{T_
{\mathrm{c
}}} % used to be $T_{k}$
61 \newcommand{\ycooldens}{\rho_{\mathrm{c
}}} % used to be $\rho{k}$
62 \newcommand{\ycoolcapa}{c^
{\mathrm{p
}}_
{\mathrm{c
}}} % used to be $c_{p_{k}}$
63 \newcommand{\tankvol}{V_
{\mathrm{t
}}} % used to be $V$
64 \newcommand{\coolvol}{V_
{\mathrm{c
}}} % used to be $V_{k}$
67 % Notation for problem 4.2
69 \newcommand{\Grudder}{G_
{\mathrm{r
}}}
70 \newcommand{\Gship}{G_
{\mathrm{s
}}}