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Process Control: Modeling, Design, and Simulation by B. Wayne Bequette

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14.8. MATLAB tzero, svd, and LTI Functions

The MATLAB Control Toolbox has a routine (tzero) for calculating the transmission zeros of a multivariable model. MATLAB can also be used to perform a SVD analysis (using the function svd).

Transmission Zero Calculation

Here we illustrate the use of tzero by way of an example.

Example 4.2, continued

Operating Point 1 (minimum phase)

Consider first the minimum-phase operating point. First, set all of the individual matrix elements as follows:

g11 = tf([2.6],[62 1]);
g12 = tf([1.5],conv([62 1],[23 1]));
g21 = tf([1.4],conv([30 1],[90 1]));
g22 = tf([2.8],[90 1]);

Then define the transfer function matrix

 G = [g11 g12;g21 g22] Transfer function from input 1 to output... 2.6 #1: -------- 62 s + 1 1.4 #2: ...

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