MATLAB and Simulink Files

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MATLAB and Simulink files for textbook Nise/Controls 6e.

ch3p4.m
% Nise, N.S. 
% Control Systems Engineering, 6th ed. 
% John Wiley & Sons, Hoboken, NJ, 07030
%
% Control Systems Engineering Toolbox Version 6.0 
% Copyright  2011 by John Wiley & Sons, Inc.
%
% (ch3p4) Example 3.4: Transfer functions represented either by numerator and 
% denominator or an LTI object can be converted to state space. For numerator
% and denominator representation, the conversion can be implemented using
% [A,B,C,D] = tf2ss(num,den). The A matrix is returned in a form called the 
% controller canonical form, which will be explained in Chapter 5 in the text. To 
% obtain the phase-variable form, [Ap, Bp, Cp, Dp], we perform the following 
% operations: Ap = inv(P)*A*P; Bp = inv(P)*B; Cp = C*P, Dp  = D, where P is a matrix
% with 1's along the anti-diagonal and 0's elsewhere. These transformations will be 
% explained in Chapter 5. The command inv(X) finds the inverse of a square 
% matrix. The symbol * signifies multiplication. For systems represented as LTI 
% objects, the command ss(F), where F is an LTI transfer-function object, can be used
% to convert F to a state-space object. Let us look at Example 3.4 in the text. For the 
% numerator-denominator representation, notice that the MATLAB response associates 
% the gain, 24, with the vector C rather than the vector B as in the example in the text. 
% Both representations are equivalent. For the LTI transfer-function object, the
% conversion to state space does not yield the phase-variable form. The result is
% a balanced model that improves the accuracy of calculating eigenvalues, which are
% covered in Chapter 4. Since ss(F) does not yield familiar forms of the state
% equations (nor is it possible to easily convert to familiar forms), we will have 
% limited use for that transformation at this time.

'(ch3p4) Example 3.4'               % Display label.
'Numerator-denominator representation conversion' 	
                                    % Display label.
'Controller canonical form'         % Display label.
num=24;                             % Define numerator of G(s)=C(s)/R(s).
den=[1 9 26 24];                    % Define denominator of G(s).
[A,B,C,D]=tf2ss(num,den)            % Convert G(s) to controller 
                                    % canonical form,  
                                    % store matrices A, B, C, D, and 
                                    % display.
'Phase-variable form'               % Display label.
P=[0 0 1;0 1 0;1 0 0];              % Form transformation matrix.
Ap=inv(P)*A*P                       % Form A matrix, phase-variable form.
Bp=inv(P)*B                         % Form B vector, phase-variable form.
Cp=C*P                              % Form C vector, phase-variable form.
Dp=D                                % Form D phase-variable form.
'LTI object representation'         % Display label.
T=tf(num,den)                       % Represent T(s)=24/(s^3+9s^2+26s+24)
                                    % as an LTI transfer-function object.
Tss=ss(T)                           % Convert T(s) to state space.

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