Dynamic models - 2014

Class date(s):	13 to 17 January 2014
Download video: Link (plays in Google Chrome) [356 M]

Readings and preparation for class; video and audio files

Date	Class number	Reading (Marlin)	Reading (Seborg*)	Reading (other)	Handout	Video and audio files
13 January	02A	Chapter 3 and Appendix B	Chapter 2	Your 3E4 notes on dynamic models and ODEs. Any math textbook on the Integrating Factor (or Appendix B in Marlin) MATLAB software for numerical integration	None	Video (361M)	Audio (42M)
15 January	02B	Chapter 3	Chapter 2		None
17 January	02C	Chapter 3	Chapter 2

* The book by Seborg et al. is easily available new or second hand, as it was the prescribed textbook in 2013 (Marlin's book was prescribed in 2012). I will make reference to the chapters from Seborg on the website as well.

Test your understanding before and after class with these resources from Dr. Thomas Marlin. This website also contains full Powerpoint slides for each chapter from his textbook. Use this as a resource if you are still waiting for your copy of the Marlin textbook to arrive.

Computer code: class 02B, 15 January

In a file called cstr_height.m:

function d_depnt__d_indep = cstr_height(indep, depnt)
 
% Dynamic balance for the CSTR height

%    indep: the independent ODE variable, such as time or length or the reactor
%    depnt: a VECTOR of dependent variables
% 
%    Returns:
%
%    d(depnt)
%   ---------- = a vector of ODEs
%    d(indep)
 
% Assign some variables for convenience of notation: one row per DEPENDENT variable
h = depnt(1);
 
% Constant and other equations
A = 0.5;      % m^2
F_i = 0.8;    % m^3/min
R   = 15;     % min/m^2
F_o = h/R;    % m^3/min

% Output from this ODE function must be a COLUMN vector, with n rows
% n = how many ODEs in this system?
n = numel(depnt); d_depnt__d_indep = zeros(n,1);

% Specify every element in the vector below: 1, 2, ... n
d_depnt__d_indep(1) = 1/A * (F_i - F_o);

The call the above model file from the "driver"; you can call this file anything, e.g. ODE_driver.m:

% The independent variable always requires an initial and final value:
indep_start = 0.0;  % s
indep_final = 50.0; % s
 
% Set initial condition(s): for integrating variables (dependent variables)
h_depnt_zero = 4.0;    % i.e. h(t=0) = 3.0
 
IC = [h_depnt_zero];
  
% Integrate the ODE(s):
[indep, depnt] = ode45(@c02B_linear, [indep_start, indep_final], IC);
 % Plot the results:
clf;
plot(indep, depnt(:,1))
grid('on')
hold('on')

xlabel('Time [min]')
ylabel('Tank height')
legend('h')
title('Tank height with time')

% Does it match the analytical equation?
height = 12 -8.*exp(-indep/7.5);
hold on
plot(indep, height, 'r.')