trunk/doc/howto-ivp.lyx

#LyX 1.4.3 created this file. For more info see http://www.lyx.org/
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\begin_body

\begin_layout Chapter
The modeling of a simple dynamic tank
\begin_inset LatexCommand \index{dynamic tank}

\end_inset


\begin_inset LatexCommand \label{cha:ivp}

\end_inset


\end_layout

\begin_layout Standard
This chapter assumes you have read Chapter
\color black
\InsetSpace ~

\begin_inset LatexCommand \vref{cha:model1}

\end_inset

 and Chapter\InsetSpace ~

\begin_inset LatexCommand \vref{cha:model2}

\end_inset

, which introduce you to ASCEND modeling concepts.
\end_layout

\begin_layout Standard
The purpose of this chapter is to be a good first step along the path to
 learning how to use ASCEND for dynamic simulations
\begin_inset LatexCommand \index{dynamic simulation}

\end_inset


\begin_inset Foot
status open

\begin_layout Standard
Some further information on this topic is available in the report by Perry
 and Allan 
\begin_inset LatexCommand \cite{Perry1996}

\end_inset


\end_layout

\end_inset

.
 We shall lead you through the steps for creating a simple model.
 You will also learn the standard methods that we employ for our dynamic
 libraries
\begin_inset LatexCommand \index{dynamic libraries}

\end_inset

.
 We will present our reasons for the steps we take.
 
\end_layout

\begin_layout Subsubsection*
The problem
\end_layout

\begin_layout List
\labelwidthstring 00.00.0000
Step\InsetSpace ~
1: We would like to create a dynamic model of a simple tank.
\end_layout

\begin_layout Subsubsection*
Topics covered in this chapter are:
\end_layout

\begin_layout Itemize
Converting the word description to an ASCEND model.
\end_layout

\begin_layout Itemize
Solving the model.
\end_layout

\begin_layout Itemize
Creating a script to load and execute an instance of the model.
\end_layout

\begin_layout Itemize
Integrating
\begin_inset LatexCommand \index{integrating}

\end_inset

 the model.
\end_layout

\begin_layout Itemize
View Integration Results.
\end_layout

\begin_layout Section
Converting the word description
\newline
into an ASCEND model
\end_layout

\begin_layout Standard
As stated in Section\InsetSpace ~

\begin_inset LatexCommand \vref{sec:model1.converting-the-word}

\end_inset


\color none
, we need to make an instance of a type and solve the instance.
 So we shall start by creating a tank type definition.
 We will have to create our type definition as a text file using a text
 editor.
 (Possible text editors
\begin_inset LatexCommand \index{text editor}

\end_inset

 are Word
\begin_inset LatexCommand \index{Word}

\end_inset

, Emacs
\begin_inset LatexCommand \index{Emacs}

\end_inset

, Notepad
\begin_inset LatexCommand \index{Notepad}

\end_inset

, pico
\begin_inset LatexCommand \index{pico}

\end_inset

, vi
\begin_inset LatexCommand \index{vi}

\end_inset

, etc.
 We shall discuss editors shortly.)
\end_layout

\begin_layout Standard
We need first to decide the parts to our model.
 In this case we know that we need the variables listed in Table\InsetSpace ~

\begin_inset LatexCommand \eqref{cap:Variables-required-for}

\end_inset

We readily fill in the first three columns in this table, and we can also
 fill out the fourth column if we know the units that are associated with
 each of the parts.
 To find the ASCEND variable type needed for the fourth column use the find
 menu on the library window and select ATOM by units
\begin_inset LatexCommand \index{atom, select by units}

\end_inset

.
 The result of this search will be all the ASCEND variable type that have
 the units you entered.
\end_layout

\begin_layout Standard
\begin_inset Float table
wide false
sideways false
status open

\begin_layout Caption
\begin_inset LatexCommand \label{cap:Variables-required-for}

\end_inset

Variables required for model
\end_layout

\begin_layout Standard
\begin_inset Tabular
<lyxtabular version="3" rows="8" columns="4">
<features>
<column alignment="center" valignment="top" leftline="true" width="0">
<column alignment="center" valignment="top" leftline="true" width="1.5in">
<column alignment="center" valignment="top" leftline="true" width="1.5in">
<column alignment="center" valignment="top" leftline="true" rightline="true" width="1in">
<row topline="true" bottomline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
Symbol
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
Meaning
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
Typical Units
\begin_inset Foot
status collapsed

\begin_layout Standard
as entered into ASCEND
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
ASCEND variable type
\end_layout

\end_inset
</cell>
</row>
<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\family typewriter
M
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
Moles in Tank
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
mol, kmol
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
mole
\end_layout

\end_inset
</cell>
</row>
<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\family typewriter
dM_dt
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
Rate of change of Moles in tank (derivative)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
mol/sec, kmol/sec
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
molar_rate
\end_layout

\end_inset
</cell>
</row>
<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\family typewriter
input
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
Feed flow rate
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
mol/sec, kmol/sec
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
molar_rate
\end_layout

\end_inset
</cell>
</row>
<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\family typewriter
output
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
Output flow rate
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
mol/sec, kmol/sec
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
molar_rate
\end_layout

\end_inset
</cell>
</row>
<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\family typewriter
Volume
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
Volume of liquid in the tank
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
m^3,ft^3
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
volume
\end_layout

\end_inset
</cell>
</row>
<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\family typewriter
density
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
Molar density of tank fluid
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
mol/m^3,mol/ft^3
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
molar_density
\end_layout

\end_inset
</cell>
</row>
<row topline="true" bottomline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\family typewriter
dynamic
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
Boolean for switching between dynamic and steady state simulations
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
N/A
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
boolean
\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
We would like to be able to compute the number of moles in the tank for
 a given volume assuming steady state
\begin_inset LatexCommand \index{steady state}

\end_inset

 (dM_dt = 0).
 We would also like to be able to calculate how the volume changes if we
 are not at steady state.
 The following equations describe the simple tank system.
\end_layout

\begin_layout Standard
The first equation is the differential equation that relates the input and
 output flows to the accumulation in the tank.
 The second equation is the relation of the moles in the tank to the volume
 of liquid and should be rearranged to avoid division
\begin_inset LatexCommand \index{division, avoid}

\end_inset

.
 These equations are all that is need for a simple tank.
\end_layout

\begin_layout Standard
\begin_inset Formula \begin{equation}
dM\_dt=input-output\label{eq:ivp.dMdt}\end{equation}

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula \begin{equation}
Volume=\frac{M}{density}\label{eq:ivp.Volume}\end{equation}

\end_inset


\end_layout

\begin_layout Subsubsection*
The first version of the code for tank
\end_layout

\begin_layout LyX-Code
REQUIRE "ivpsystem.a4l";
\end_layout

\begin_layout LyX-Code
REQUIRE "atoms.a4l";
\end_layout

\begin_layout LyX-Code
MODEL tank
\begin_inset LatexCommand \index{tank, dynamic MODEL}

\end_inset

;
\end_layout

\begin_layout LyX-Code
(* List of Variables *)
\end_layout

\begin_layout LyX-Code
dM_dt IS_A molar_rate;
\end_layout

\begin_layout LyX-Code
M IS_A mole;
\end_layout

\begin_layout LyX-Code
input IS_A molar_rate;
\end_layout

\begin_layout LyX-Code
output IS_A molar_rate;
\end_layout

\begin_layout LyX-Code
Volume IS_A volume;
\end_layout

\begin_layout LyX-Code
density IS_A real_constant;
\end_layout

\begin_layout LyX-Code
dynamic IS_A boolean;
\end_layout

\begin_layout LyX-Code
t IS_A time;
\end_layout

\begin_layout LyX-Code
(* Equations *)
\end_layout

\begin_layout LyX-Code
dM_dt = input - output;
\end_layout

\begin_layout LyX-Code
M = Volume * density;
\end_layout

\begin_layout LyX-Code
(* Assignment of values to Constants *)
\end_layout

\begin_layout LyX-Code
density :==10 {mol/m^3};
\end_layout

\begin_layout LyX-Code

\end_layout

\begin_layout LyX-Code
METHODS
\end_layout

\begin_layout LyX-Code

\end_layout

\begin_layout LyX-Code
METHOD check_self;
\end_layout

\begin_layout LyX-Code
IF (input < 1e-4 {mole/s}) THEN
\end_layout

\begin_layout LyX-Code
STOP {Input dried up in tank};
\end_layout

\begin_layout LyX-Code
END IF;
\end_layout

\begin_layout LyX-Code
IF (output < 1e-4 {mole/s}) THEN
\end_layout

\begin_layout LyX-Code
STOP {Output dried up in tank}; 
\end_layout

\begin_layout LyX-Code
END IF; 
\end_layout

\begin_layout LyX-Code
END check_self;
\end_layout

\begin_layout LyX-Code
METHOD check_all;
\end_layout

\begin_layout LyX-Code
RUN check_self;
\end_layout

\begin_layout LyX-Code
END check_all;
\end_layout

\begin_layout LyX-Code

\end_layout

\begin_layout LyX-Code
METHOD default_self;
\end_layout

\begin_layout LyX-Code
dynamic := FALSE;
\end_layout

\begin_layout LyX-Code
t :=0 {sec};
\end_layout

\begin_layout LyX-Code
dM_dt :=0 {mol/sec};
\end_layout

\begin_layout LyX-Code
dM_dt.lower_bound := -1e49 {mol/sec};
\end_layout

\begin_layout LyX-Code
END default_self;
\end_layout

\begin_layout LyX-Code

\end_layout

\begin_layout LyX-Code
METHOD default_all;
\end_layout

\begin_layout LyX-Code
RUN default_self;
\end_layout

\begin_layout LyX-Code
END default_all;
\end_layout

\begin_layout LyX-Code

\end_layout

\begin_layout LyX-Code
METHOD bound_self;
\end_layout

\begin_layout LyX-Code
END bound_self;
\end_layout

\begin_layout LyX-Code

\end_layout

\begin_layout LyX-Code
METHOD bound_all;
\end_layout

\begin_layout LyX-Code
RUN bound_self;
\end_layout

\begin_layout LyX-Code
END bound_all;
\end_layout

\begin_layout LyX-Code

\end_layout

\begin_layout LyX-Code
METHOD scale_self; 
\end_layout

\begin_layout LyX-Code
END scale_self;
\end_layout

\begin_layout LyX-Code

\end_layout

\begin_layout LyX-Code
METHOD scale_all;
\end_layout

\begin_layout LyX-Code
RUN scale_self;
\end_layout

\begin_layout LyX-Code
END scale_all;
\end_layout

\begin_layout LyX-Code

\end_layout

\begin_layout LyX-Code
METHOD seqmod;
\end_layout

\begin_layout LyX-Code
dM_dt.fixed :=TRUE;
\end_layout

\begin_layout LyX-Code
M.fixed :=FALSE;
\end_layout

\begin_layout LyX-Code
Volume.fixed :=TRUE;
\end_layout

\begin_layout LyX-Code
input.fixed :=TRUE;
\end_layout

\begin_layout LyX-Code
output.fixed :=FALSE;
\end_layout

\begin_layout LyX-Code
IF dynamic THEN
\end_layout

\begin_layout LyX-Code
dM_dt.fixed :=FALSE;
\end_layout

\begin_layout LyX-Code
M.fixed :=TRUE;
\end_layout

\begin_layout LyX-Code
Volume.fixed :=FALSE;
\end_layout

\begin_layout LyX-Code
output.fixed :=TRUE;
\end_layout

\begin_layout LyX-Code
END IF;
\end_layout

\begin_layout LyX-Code
END seqmod;
\end_layout

\begin_layout LyX-Code

\end_layout

\begin_layout LyX-Code
METHOD specify;
\end_layout

\begin_layout LyX-Code
input.fixed :=TRUE;
\end_layout

\begin_layout LyX-Code
RUN seqmod;
\end_layout

\begin_layout LyX-Code
END specify;
\end_layout

\begin_layout LyX-Code

\end_layout

\begin_layout LyX-Code
METHOD set_ode;
\end_layout

\begin_layout LyX-Code
(* set ODE_TYPE -1=independent variable,
\end_layout

\begin_layout LyX-Code
0=algebraic variable, 1=state variable,
\end_layout

\begin_layout LyX-Code
2=derivative *)
\end_layout

\begin_layout LyX-Code
t.ode_type :=-1;
\end_layout

\begin_layout LyX-Code
dM_dt.ode_type :=2;
\end_layout

\begin_layout LyX-Code
M.ode_type :=1;
\end_layout

\begin_layout LyX-Code
(* Set ODE_ID *)
\end_layout

\begin_layout LyX-Code
dM_dt.ode_id :=1;
\end_layout

\begin_layout LyX-Code
M.ode_id :=1;
\end_layout

\begin_layout LyX-Code
END set_ode;
\end_layout

\begin_layout LyX-Code

\end_layout

\begin_layout LyX-Code
METHOD set_obs;
\end_layout

\begin_layout LyX-Code
(* Set OBS_ID to any integer value greater 
\end_layout

\begin_layout LyX-Code
than 0, the variable will be recorded 
\end_layout

\begin_layout LyX-Code
(i.e., observed) *)
\end_layout

\begin_layout LyX-Code
M.obs_id :=1;
\end_layout

\begin_layout LyX-Code
Volume.obs_id :=2;
\end_layout

\begin_layout LyX-Code
input.obs_id :=3;
\end_layout

\begin_layout LyX-Code
output.obs_id :=4;
\end_layout

\begin_layout LyX-Code
END set_obs;
\end_layout

\begin_layout LyX-Code

\end_layout

\begin_layout LyX-Code
METHOD values;
\end_layout

\begin_layout LyX-Code
Volume :=5 {m^3};
\end_layout

\begin_layout LyX-Code
input :=100 {mole/s}; 
\end_layout

\begin_layout LyX-Code
END values;
\end_layout

\begin_layout LyX-Code
END tank; 
\end_layout

\begin_layout Standard
Our model definition has the following structure for it so far:
\end_layout

\begin_layout Itemize
MODEL statement
\end_layout

\begin_layout Itemize
list of variables we intend to use in the type definition
\end_layout

\begin_layout Itemize
equations
\end_layout

\begin_layout Itemize
METHODS
\end_layout

\begin_layout Itemize
END statement
\end_layout

\begin_layout Standard
While we have put the statements in this order, we could mix them up and
 intermix the middle two types of statements, even going to the extreme
 of defining the variables after we first use them.
 Once the 
\family typewriter
METHODS
\family default
 section is started no new equations or variables can be declared.
 The 
\family typewriter
MODEL
\family default
 and 
\family typewriter
END
\family default
 statements begin and end the type definition.
\end_layout

\begin_layout Standard
There are two new methods added to a dynamic model that you would not see
 in a steady state model, and they are the 
\family typewriter
set_ode
\family default
 and 
\family typewriter
set_obs
\family default
 methods.
 The 
\family typewriter
set_ode
\family default
 method is used to setup the model for integration.
 The 
\family typewriter
set_obs
\family default
 method is used to tell ASCEND which variables you would like to observe
 in the output of the integration.
\end_layout

\begin_layout Standard
Now we need to discuss the how and why of the two new methods.
 The 
\family typewriter
set_ode
\family default
 method is used to set up the equations and variables described in the model
 for integration by LSODE
\begin_inset LatexCommand \index{LSODE}

\end_inset

.
 In order for LSODE to be able to integrate the model, it needs to know
 which variable is the independent variable - in this case 
\family typewriter
t
\family default
 (time), which variables are the derivatives, and which are the states.
 The way we do this is we have to add a few extra attributes to each variable.
 In Section\InsetSpace ~

\begin_inset LatexCommand \ref{sec:model1.converting-the-word}

\end_inset


\color none
, the idea of an atom was discussed with its units, default value, bounds
 etc.
 We need to add 5 more of this type of parameter.
 These attributes
\begin_inset LatexCommand \index{attributes, ODE variables}

\end_inset

 are 
\family typewriter
\color black
ode_type
\family default
\color none
, 
\family typewriter
ode_id
\family default
,
\family typewriter
 obs_id
\family default
, 
\family typewriter
ode_rtol
\family default
 and 
\family typewriter
ode_atol
\family default
.
 
\end_layout

\begin_layout Standard
This now brings us to the reason there is a 
\family typewriter
system.a4l
\family default
 and an 
\family typewriter
ivpsystem.a4l
\family default

\begin_inset LatexCommand \index{ivpsystem.a4l}

\end_inset

.
 For a steady state model the new attributes discussed above are not needed,
 and would take up memory and introduce confusion; therefore, they are excluded
 for the system library.
 If a dynamic simulations is to be loaded and solved, the ivpsystem library
 needs to be loaded instead of the system library so the extra attributes
 will be present with each part.
\end_layout

\begin_layout Standard
We will now go through the purpose of each of these attributes.
 First 
\family typewriter
ode_type
\family default
 is to tell the system what type of variable it is.
 A value of -1 for 
\family typewriter
ode_type
\family default
 means the variable is the independent variable, 0 means it is an algebraic
 variable (default), 1 means it is a state variable, and finally 2 means
 it is a derivative.
 
\end_layout

\begin_layout Standard
The attribute 
\family typewriter
ode_id
\family default
 is used to match the state variables with their derivatives and only needs
 to be used if the variable is a state or derivative.
 In the example 
\family typewriter
M
\family default
 is a state and 
\family typewriter
dM_dt
\family default
 is the derivative.
 Therefore they both need to have the same 
\family typewriter
ode_id
\family default
 so ASCEND will know that they belong together.
 Each state and derivative pair needs to have a different 
\family typewriter
ode_id
\family default
; however, it does not matter what the number is as long as it is a positive
 integer and no other state and derivative pair has the same number.
 
\end_layout

\begin_layout Standard
Next 
\family typewriter
obs_id
\family default
 is used by the user to flag a variable for observation while integrating.
 For any integer value of 
\family typewriter
obs_id
\family default
 greater then 0 the variable will be observed.
 The result of flagging a variable for observation is that its values will
 be in a data column in one of two output files.
 One of the files of data produced with each integration contains the values
 of the states and the second the values of the variables flagged for observatio
n.
 The default file names are 
\family typewriter
y.dat
\family default
 and 
\family typewriter
obs.dat
\family default
 respectfully; however, they can be changed in the solver options
\begin_inset LatexCommand \index{options, solver}

\end_inset

 general menu.
 
\end_layout

\begin_layout Standard
Last, but not least, are the error control attributes for LSODE: 
\family typewriter
ode_rtol
\family default
 and 
\family typewriter
ode_atol
\family default
.
 Both of these come directly from the LSODE attributes rtol and atol which
 are the local relative and absolute error tolerances for the variable respectiv
ely.
\end_layout

\begin_layout Standard
There is one other thing about methods that we need to discuss before moving
 on and that is the 
\family typewriter
seqmod
\family default
 method.
 If you have not already noticed, it is a little different from the other
 examples as it has an IF statement in it.
 This is an important part of the dynamic simulation.
 It switches the degrees of freedom depending on if we are computing an
 initial condition or performing an integration step.
 We use the boolean 
\family typewriter
dynamic
\family default

\begin_inset LatexCommand \index{dynamic, boolean variable}

\end_inset

 to control whether we are going to solve the model as a steady state model
 (
\family typewriter
dynamic := FALSE;
\family default
) or as a dynamic model (
\family typewriter
dynamic := TRUE;
\family default
).
 For the current example, we have a simple tank and, for steady state, we
 would like to calculate the number of moles and output flow rate for a
 fixed tank volume and input flow rate.
 Also, for the model to be at steady state, we have to fix the derivative
 and set it equal to zero, 
\family typewriter
(dM_dt.fixed :=TRUE; dM_dt :=0 {mole/s};.

\family default
 The derivative is normally set to zero in the 
\family typewriter
default_self
\family default
 method to prepare the model to solve for initial steady-state conditions.)
 If we then want to integrate this model for a fixed output flow (as when
 pumping the liquid out under flow control), we would free up the volume
 and fix the output flow rate.
 The model will then compute how the liquid volume will change with time.
 
\end_layout

\begin_layout Standard
In dynamic simulation, an initial value integration package, such as LSODE,
 repeatedly asks the model to compute the time derivatives for the state
 variables, given fixed values for the states.
 Using values for 
\family typewriter
dM_dt
\family default
 computed by the model, the integration package will then update the state
 variable, 
\family typewriter
M
\family default
, to its new value.
 To accommodate this calculation, we therefore fix the state variable, 
\family typewriter
M
\family default
, and free up the derivative, 
\family typewriter
dM_dt
\family default
.
\end_layout

\begin_layout Section
Solving an ASCEND instance
\end_layout

\begin_layout Standard
We are now ready to read in and compile an instance of our tank model.
 We are assuming that you understand how to use the scripting window, and
 we will show how to go about reading, compiling, solving and integrating
 a dynamic model using the following script.
\end_layout

\begin_layout Subsubsection*
Script code
\begin_inset LatexCommand \index{script, solve dynamic model}

\end_inset


\end_layout

\begin_layout LyX-Code
DELETE TYPES;
\end_layout

\begin_layout LyX-Code
READ FILE "example.a4c";
\end_layout

\begin_layout LyX-Code
COMPILE ex OF tank;
\end_layout

\begin_layout LyX-Code
BROWSE ex;
\end_layout

\begin_layout LyX-Code
RUN {ex.default_self};
\end_layout

\begin_layout LyX-Code
RUN {ex.reset};
\end_layout

\begin_layout LyX-Code
RUN {ex.values};
\end_layout

\begin_layout LyX-Code
SOLVE ex WITH QRSlv;
\end_layout

\begin_layout LyX-Code
RUN {ex.check_all};
\end_layout

\begin_layout LyX-Code
ASSIGN {ex.dynamic} TRUE;
\end_layout

\begin_layout LyX-Code
RUN {ex.reset};
\end_layout

\begin_layout LyX-Code
RUN {ex.set_ode};
\end_layout

\begin_layout LyX-Code
RUN {ex.set_obs};
\end_layout

\begin_layout LyX-Code
# User will need to edit the next line to correct path 
\end_layout

\begin_layout LyX-Code
# to the models directory
\end_layout

\begin_layout LyX-Code
source "$env(ASCENDDIST)/models/set_intervals.tcl";
\end_layout

\begin_layout LyX-Code
set_int 500 10 {s};
\end_layout

\begin_layout LyX-Code
INTEGRATE ex FROM 0 TO 50 WITH BLSODE;
\end_layout

\begin_layout LyX-Code
ASSIGN {ex.input} 120 {mole/s};
\end_layout

\begin_layout LyX-Code
INTEGRATE ex FROM 50 TO 499 WITH BLSODE;
\end_layout

\begin_layout LyX-Code
# In order to view integration results for both the
\end_layout

\begin_layout LyX-Code
# integrations the user will have to go to the solver 
\end_layout

\begin_layout LyX-Code
# window, select options, general and turn off the 
\end_layout

\begin_layout LyX-Code
# overwrite integrator logs toggle.
\end_layout

\begin_layout LyX-Code
# (NOTE: If you were then to run a different model or this 
\end_layout

\begin_layout LyX-Code
# same simulation again it would still write to the same 
\end_layout

\begin_layout LyX-Code
# files)
\end_layout

\begin_layout LyX-Code
# In order to see both sets of data at the same time on
\end_layout

\begin_layout LyX-Code
# one plot you will have to merge the two sets of data in
\end_layout

\begin_layout LyX-Code
# the file.
 This is done with following command.
\end_layout

\begin_layout LyX-Code
asc_merge_data_file ascend new_obs.dat obs.dat;
\end_layout

\begin_layout LyX-Code
# This command can also be used to convert data into a
\end_layout

\begin_layout LyX-Code
# format that can be loaded into matlab for further work.
\end_layout

\begin_layout LyX-Code
asc_merge_data_file matlab matlab_obs.m obs.dat;
\end_layout

\begin_layout LyX-Code
# This command can also be used to convert data into a
\end_layout

\begin_layout LyX-Code
# format that can be loaded into excel as a tab delimited
\end_layout

\begin_layout LyX-Code
# text file.
\end_layout

\begin_layout LyX-Code
asc_merge_data_file excel excel_obs.txt obs.dat;
\end_layout

\begin_layout Standard
First of all reading and compiling an instance of a dynamic model is the
 same as a steady state model except, as stated earlier, we must load 
\family typewriter
ivpsystem.a4l
\family default
 instead of 
\family typewriter
system.a4l
\family default
.
 The file containing 
\family typewriter
example.a4c
\family default
 in the first version of the code has 
\family typewriter
REQUIRE
\family default
 statements to load the right system file and the file 
\family typewriter
atoms.a4l
\family default
.
 
\end_layout

\begin_layout Standard
Now it is time to solve the model, and this is where things start to change.
 We must first solve the model for its initial conditions.
 We set the boolean variable 
\family typewriter
dynamic
\family default
 to 
\family typewriter
FALSE
\family default
 (in the 
\family typewriter
default_self
\family default
 method) and run the 
\family typewriter
reset
\family default
 method to get a well-posed steady-state model.
 We also need to run the 
\family typewriter
values
\family default
 method to set the fixed values of the initial conditions.
 Finally we are solve, getting as the solution the initial conditions for
 our model.
\end_layout

\begin_layout Standard
After solving for the initial conditions
\begin_inset LatexCommand \index{initial conditions}

\end_inset

, we set things up for the dynamic simulation.
 We set the boolean variable 
\family typewriter
dynamic
\family default
 to 
\family typewriter
TRUE
\family default
 and then run the 
\family typewriter
seqmod
\family default
 method to give a well-posed dynamic model.
 We now have to establish which variables are the independent variables,
 the state variables and their corresponding derivatives, and tell which
 variables we would like to observe; we run 
\family typewriter
set_ode
\family default
 and 
\family typewriter
set_obs
\family default
 methods described above.
\end_layout

\begin_layout Standard
In order for ASCEND and LSODE to know what step size and how many steps
 we want to observe, we must load a Tcl file that defines a new script command.
 The file we need to load is called 
\family typewriter
set_intervals.tcl
\family default
, and it is found in the models subdirectory of the ASCEND distribution.
 The command source comes from Tcl and is used to read and execute the a
 set of commands in a file.
 The file in this case is 
\family typewriter
set_intervals.tcl
\family default
 and the commands within it setup a new script command 
\family typewriter
set_int
\family default
.
 Once we have loaded this file, we can use the new command 
\family typewriter
set_int
\family default
 to set up the number of possible steps and their maximum size.
 Now we are ready to integrate.
 The way we do this is to use the 
\family typewriter
INTEGRATE
\family default
 command in the script.
 The syntax for these command is as follows.
\end_layout

\begin_layout Subsubsection*
Syntax for 
\family typewriter
set_int
\end_layout

\begin_layout LyX-Code
set_int number_of_steps step_size
\end_layout

\begin_layout LyX-Code
     {units of step size(time)};
\end_layout

\begin_layout Subsubsection*
Syntax for 
\family typewriter
INTEGRATE
\family default
 
\end_layout

\begin_layout LyX-Code
INTGRATE compiled_model_name 
\end_layout

\begin_layout LyX-Code
   FROM initial_step 
\end_layout

\begin_layout LyX-Code
   TO final_step 
\end_layout

\begin_layout LyX-Code
   WITH BLSODE;
\end_layout

\begin_layout Standard
The command is set up with the initial and final step so that you can integrate
 for a number of steps, then make step changes, and then continue to integrate
 another number of steps.
\end_layout

\begin_layout Section
Viewing Simulation Results
\end_layout

\begin_layout Standard
To view the simulation results, open the ASCPLOT
\begin_inset LatexCommand \index{ASCPLOT}

\end_inset

 window using the Tools menu on the Script window.
 To view a plot, first use the File menu to load the data using Load data
 set.
 Depending on what you want to look at, you can load the file containing
 the states or the file containing the variables you flagged for observation.
 Once the data file is loaded, you can double click on the file name in
 the top window to get a list of the variables in the file.
 This list will appear in the left window named Unused variables
\begin_inset LatexCommand \index{variables, unused}

\end_inset

 below where you just double clicked.
 As you will notice on the line below, the independent variable has already
 been set to time.
 The way we select the variables we want to plot vs.
 time is to highlight them from the list in the left window and, using the
 top arrow button, move them over to the plotted variables window on the
 right.
 We then use the View plot file command from the Execute menu to view the
 plot.
 
\end_layout

\begin_layout Standard
If we now want to plot something else, we simply highlight those variables
 that we do not want to plot in the plotted variables window, use the other
 arrow to move them back to the unused variable window and then move new
 variables to the plotted variables window.
 
\end_layout

\begin_layout Standard
If we want to change the independent variable, we select the variable we
 want to be the new independent variable from the list in either the unused
 variable window or the plotted variable window and then use the appropriate
 down arrow to move that variable down to become the independent variable.
\end_layout

\begin_layout Subsection
Graphing options
\end_layout

\begin_layout Standard
Now that you are able to view a plot, you might want to add titles or change
 the axis scale, line colors, and so forth.
 Adding titles can be done by selecting set 
\shape italic
titles
\shape default
 under the 
\shape italic
Display
\shape default
 menu, a new window will open in which you will have the option to add a
 plot title and axis labels.
 To change the axis scale, line color and many other features select see
 options from the 
\shape italic
Options
\shape default
 menu.
\end_layout

\begin_layout Subsubsection*
Graphing in Windows
\end_layout

\begin_layout Standard
Under MS Windows
\begin_inset LatexCommand \index{MS Windows}

\end_inset

 the default graph program Tkxgraph
\begin_inset LatexCommand \index{Tkxgraph}

\end_inset

 gives you full control of the options without having to go through the
 ASCPLOT Options menu.
 Tkxgraph is also available for UNIX, but xgraph
\begin_inset LatexCommand \index{xgraph}

\end_inset

 does a much better job drawing dashed lines with X11 than Tkxgraph does.
\end_layout

\begin_layout Standard
If you decide you do not like the plotting tools described above, you have
 two more options, and they are to convert the ASCEND output data files
 so that they can be loaded by Matlab or a spreadsheet.
 To convert the data files a new script command needs to be introduced and
 the command is 
\family typewriter
asc_merge_data_file
\family default

\begin_inset LatexCommand \index{asc\_merge\_data\_file}

\end_inset

.
 
\end_layout

\begin_layout Subsubsection*
Syntax for 
\family typewriter
asc_merge_data_file
\family default
 command
\end_layout

\begin_layout LyX-Code
asc_merge_data_file convert_to 
\backslash

\end_layout

\begin_layout LyX-Code
   output_file_name input_file_names
\end_layout

\begin_layout Standard
The syntax for the 
\family typewriter
asc_merge_data_file
\family default
 command is as follows.
 First of all the 
\family typewriter
convert_to
\family default
 is the format you want the data converted to.
 There are three options matlab, excel or ascend.
 The 
\family typewriter
output_file_name
\family default
 is exactly that, the name of the file in which you want the converted data
 to be put.
 The 
\family typewriter
input_file_names
\family default
 is also exactly that, the file name or names that you want converted.
 If more than one input file is given the data is combined into one output
 file.
\end_layout

\begin_layout Standard
If the matlab
\begin_inset LatexCommand \index{matlab}

\end_inset

 option is used the output file extension should be 
\family typewriter
m
\family default
, if excel is used the extension should be 
\family typewriter
txt
\family default
 as it is a tab delimited text file and for ascend the extension should
 be 
\family typewriter
dat
\family default
 for use with ASCPLOT.
\end_layout

\begin_layout Standard
You maybe wondering what exactly is this 
\family typewriter
asc_merge_data_file
\family default
 command doing.
 In the next three paragraphs we will give a brief explanation of each of
 the options.
\end_layout

\begin_layout Subsubsection*
Matlab conversion
\end_layout

\begin_layout Standard
When the data is converted to be used in matlab the first thing that is
 done is the header of the ascend data file is placed in the output file
 but is commented out.
 This is so the user can still tell when the data was created.
 The next thing is does is put all the data into a matrix that has the same
 name as the output file with var added to the end.
 All variable names from the ascend data file are then converted to matlab
 legal names by replacing the all dots and brackets with underscores(_).
 The new variable names are then set equal to there corresponding column
 of data in the matrix.
 Each variable then becomes a vector.
 When the file is run all the data is loaded and set equal to the new variable
 names and can easily be plotted using matlab commands.
\end_layout

\begin_layout Subsubsection*
Excel
\begin_inset LatexCommand \index{Excel}

\end_inset

 conversion
\end_layout

\begin_layout Standard
When the data is converted to be used in Excel the only thing that happens
 is instead of the list of variables and units being a column it is turn
 into rows.
 When the data is loaded into Excel as a tab delimited text file all the
 data will be in columns with the first row being the units of the data
 and the second being the ascend variable name.
 The data is then easily plotted using the Excel graphing package.
\end_layout

\begin_layout Subsubsection*
Ascend conversion
\end_layout

\begin_layout Standard
This is not so much a conversion as a merge and is the origin of the command.
 It is only useful if there are multiple headers in a file or more than
 one input file is given.
 Multiple headers in the file occur when stopping and starting integrations
 with the overwrite option turned off.
 This conversion removes all subsequent headers that are the same as the
 first, whether in one file or multiple, to leave one output file with what
 looks like one data set for plotting.
 If the headers are different the data will just be combined into one file
 and when loaded in ASCPLOT will still look like different data sets.
\end_layout

\begin_layout Section
Preparing a model for reuse
\begin_inset LatexCommand \index{reuse, model}

\end_inset


\end_layout

\begin_layout Standard
There are four major ways to prepare a model for reuse as described in Chapter\InsetSpace ~

\begin_inset LatexCommand \ref{cha:model2}

\end_inset

.
 All of what is said there about reusable models applies to dynamic models.
 However, there is one thing that we think should be repeated to make clear
 for dynamic models, and that is parameterizing a model.
\end_layout

\begin_layout Subsection
Parameterizing
\begin_inset LatexCommand \index{parameterizing}

\end_inset

 the tank model
\end_layout

\begin_layout Standard
As stated in Section\InsetSpace ~

\begin_inset LatexCommand \vref{sec:model2.parameterizingVessel}

\end_inset


\color none
, parameterizing a model type definition alerts a future user as to which
 parts of this model you deem to be the most likely to be shared.
 An instance of a parameterized model is then created from previously defined
 types.
\end_layout

\begin_layout Standard
The new thing that needs to be repeated is that the 
\family typewriter
ode_id
\family default
's of derivative and state pairs must be different even if they are in different
 part of a larger model.
 If for instance we wanted to have two tanks in series we could parameterize
 the tank model and connect the two tanks together with the outlet of the
 first tank being the feed to the second tank.
 However, with the 
\family typewriter
set_ode
\family default

\begin_inset LatexCommand \index{set\_ode}

\end_inset

 method, as we have currently written it, the derivative and state pairs
 for both tanks would have the same 
\family typewriter
ode_id
\family default
's.
 Our way around this is to introduce an 
\family typewriter
ode_counter
\family default
 that is used to set the 
\family typewriter
ode_id
\family default
's and is incremented after each derivative and state pair is set.
 The 
\family typewriter
ode_counter
\family default
 becomes one of the model parameters and is, therefore, the same in all
 models.
 We will now give an example of this to help explain.
\end_layout

\begin_layout Subsubsection*

\family typewriter
set_ode
\family default
 method for parameterized tank model
\end_layout

\begin_layout LyX-Code
METHOD set_ode;
\end_layout

\begin_layout LyX-Code
(* set ODE_TYPE -1=independent variable,
\end_layout

\begin_layout LyX-Code
0=algebraic variable, 1=state variable,
\end_layout

\begin_layout LyX-Code
2=derivative *)
\end_layout

\begin_layout LyX-Code
t.ode_type :=-1;
\end_layout

\begin_layout LyX-Code
dM_dt.ode_type :=2;
\end_layout

\begin_layout LyX-Code
M.ode_type :=1;
\end_layout

\begin_layout LyX-Code
(* Set ODE_ID *)
\end_layout

\begin_layout LyX-Code
dM_dt.ode_id := ode_offset;
\end_layout

\begin_layout LyX-Code
M.ode_id := ode_offset;
\end_layout

\begin_layout LyX-Code
ode_offset := ode_offset+1;
\end_layout

\begin_layout LyX-Code
END set_ode;
\end_layout

\begin_layout LyX-Code

\end_layout

\begin_layout Subsubsection*

\family typewriter
set_ode
\family default
 method for larger model with two tank models being used as parts
\end_layout

\begin_layout LyX-Code

\end_layout

\begin_layout LyX-Code
METHOD set_ode;
\end_layout

\begin_layout LyX-Code
RUN tank_1.set_ode;
\end_layout

\begin_layout LyX-Code
RUN tank_2.set_ode;
\end_layout

\begin_layout LyX-Code
END set_ode;
\end_layout

\begin_layout Standard
The parameterized tank 
\family typewriter
set_ode
\family default
 method is almost the same as the original one we wrote except it now uses
 
\family typewriter
ode_offset
\family default
, an 
\family typewriter
ode_counter
\family default
, to set the 
\family typewriter
ode_id
\family default
s.
 It may be obvious, but this is how it works.
 When the larger model 
\family typewriter
set_ode
\family default
 is run, the 
\family typewriter
set_ode
\family default
 for 
\family typewriter
tank_1
\family default
 is run, the
\family typewriter
 ode_id
\family default
s are set to the current value of 
\family typewriter
ode_offset
\family default
, the counter is then incremented and 
\family typewriter
set_ode
\family default
 is run for 
\family typewriter
tank_2
\family default
 which then gets the incremented 
\family typewriter
ode_offset
\family default
 so the values are now different.
 You can now hopefully see that we can string as may tanks together as we
 like, and all the derivative and state pairs 
\family typewriter
ode_id
\family default
 will be different.
\end_layout

\begin_layout Standard
This same idea can be applies to setting the observed variables.
 The reason this is a good idea is that the variables are placed in the
 output files in order of there 
\family typewriter
obs_id
\family default
 value.
 This way we can keep all variables flagged for observation from one part
 of a model together.
\end_layout

\begin_layout Standard
The important thing that needs to be stressed for a dynamic system is that
 the time variable, dynamic boolean, and ode and obs counters must be in
 the parameter list.
 All these variable need to be the same in each model to be consistent and
 to make sure the model gets setup correctly when the 
\family typewriter
set_ode
\family default
 method is executed.
\end_layout

\begin_layout Section
In conclusion
\end_layout

\begin_layout Standard
We have just led you step by step through the process of creating a small
 dynamic ASCEND model and the basics on how to view the results.
\end_layout

\end_body
\end_document