genrdemo.m

控制系统计算机辅助设计——MATLAB语言与应用(源代码）

% GENRDEMO MVFR Generation and Display Demonstration for MFD Toolbox.

echo off
%       J.M Boyle 30th August 1987
% Copyright (c) 1987 by GEC Engineering Research Centre & Cambridge Control Ltd
% History:
%       `more on' added, comment about zeros changed, remark
%       about CTRL-S removed, 12.7.93, JMM.
% 8/2/88 TSM names of arrays 'poles zeros' changed to 'crpoles crzeros'
% MRN0016
% MRN0017
% MRN0023
clc
echo on

% This demo shows how MultiVariable Frequency Response (MVFR) 
% matrices can be generated and displayed.

% A system with n inputs and m outputs, has a frequency response 
% matrix represented by a single complex matrix.

% To store the response of a system over a frequency range, the 
% matrices for each frequency are stacked on top of each other.
% The associated frequency vector 'w' specifies the frequencies at
% which the MVFR matrix has been evaluated.

% For example, a system with m outputs and n inputs
% is defined at 10 frequency points by:

%      -   a frequency vector of dimensions:     1 by 10.
% plus,
%      -   a complex matrix of dimensions:       10*m by n

pause  % Strike any key to continue.
clc

%   An MVFR matrix can be calculated from either:

%    - A Transfer Function Matrix description:
%            G(s) = NUM(s)/Comden(s)
%                    or
%    - The A,B,C,D matrices of a State Space description.

pause % Strike any key to continue.
clc

% We start by entering our A,B,C & D matrices for the state 
% space description of a 2 input - 2 output open-loop unstable 
% Chemical Reactor (Ref: [2] in the MFD Tutorial)

a=[ 1.3800 -0.2077  6.7150 -5.6760
   -0.5814 -4.2900  0.0000  0.6750
    1.0670  4.2730 -6.6540  5.8930
    0.0480  4.2730  1.3430 -2.1040];

b=[0.000  0.000
   5.679  0.000
   1.136 -3.146
   1.136  0.000];

c=[1  0  1 -1
   0  1  0  0];

d=[0 0
   0 0];

pause % Strike any key to continue.
format short e
clc

% The Chemical Reactor has two right-half plane poles and is
% therefore open loop unstable.
% The finite zeros are both in the left-half plane.

% Poles are found by calculating the eigenvalues of the A matrix

crpoles = eig(a)'
% Transmission zeros are found using the Control System
% Toolbox function TZERO.

crzeros = tzero(a,b,c,d)'


pause % Strike any key to continue.
format
clc

% Now generate a vector w, containing the frequencies, 
% in radians/(time unit), at which the MVFR matrix is 
% to be evaluated:

w = logspace(-2,2,9);

% Then to generate the MVFR matrix we use

mvfr = mv2fr(a,b,c,d,w);

% To display the component matrices use, FDISP(w,mvfr). FDISP displays
% an MVFR matrix together with the associated frequency vector.
% First the frequency is displayed then the associated response matrix.

pause % Strike any key to display the MVFR matrix
more on  % Added 12.7.93, JMM

fdisp(w,mvfr)

pause % Strike any key to continue
more off  % Added 12.7.93, JMM
clc

% To establish the size of the component matrices, use:

fsize(w,mvfr)

pause % Strike any key to continue.
clc

% To speed-up computations, you might wish to work with a 
% subset of the frequency points. FCOMP returns the first 
% component matrix of the MVFR matrix, and every Nth + 1 
% component matrix thereafter. Here we take every fourth point.

[mvfrs,ws] = fcomp(w,mvfr,4);

pause % Strike any key to display the subset of MVFR matrices.
clc

fdisp(ws,mvfrs)

pause % Strike any key to continue.
clc

% The MFD TOOLBOX can also handle systems with time delays using
% the function FDLY.

% End of Demo
% The MVFR matrix will be saved in the .mat file genrdata
% for use by future demos.
save genrdata

pause % Strike any key to return to the Main Menu.
echo off