Question 13.13: Develop a flowchart for the digital compensator defined by E...

Control Systems Engineering

Develop a flowchart for the digital compensator defined by Eq. (13.100).

$G_{c} (z) = \frac{X (z)}{E (z)} = \frac{z + 0.5}{z² − 0.5z + 0.7}$ (13.100)

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Cross-multiply and obtain

(z² − 0.5z + 0.7) X (z) = (z + 0.5) E (z) (13.101)

Solve for the highest power of z operating on the output, X(z),

z² X (z) = (z + 0.5) E (z) − (−0.5z + 0.7) X (z) (13.102)

Solving for X(z) on the left-hand side,

X (z) = (z $^{-1}$ + 0.5z $^{-2}$ ) E (z) − (−0.5z $^{-1}$ + 0.7z $^{-2}$ ) X (z) (13.103)

Implementing Eq. (13.103) with the flowchart of Figure 13.29 completes the design.

13.29

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