New answers tagged control-systems
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You need to solve (6.3) for $G_R$, here is the step-by-step:
$G_w = \frac{G_R(z) G_P(z)}{1 + G_R(z) G_P(z)}$, multiply both sides by $1 + G_R(z) G_P(z)$ to get:
$G_R(z)G_w(z)G_P(z) - G_R(z)G_P(z) = -G_w$, now solve for $G_R(z)$:
$G_R(z) = -\frac{G_w(z)}{G_w(z)G_P(z) - G_P(z)} = -\frac{G_w(z)}{G_P(z)(G_w(z) -1)} = \frac{1}{G_P(z)}\frac{G_w(z)}{1 - G_w(z)}$
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