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4 Qualifying Exam/2 Writing/2. QE State of the Art.md
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@ -22,7 +22,12 @@ Robustness is dependent on two features: the characteristic to be guaranteed, an
Suppose a plant representing a spring-mass-damper system is described as follows @controltutorialsformatlab&simulinkInvertedPendulumSystem: Suppose a plant representing a spring-mass-damper system is described as follows @controltutorialsformatlab&simulinkInvertedPendulumSystem:
$$ P = \frac{X(s)}{F(s)} = \frac{1}{ms^2 + bs +k}$$ $$ P = \frac{X(s)}{F(s)} = \frac{1}{ms^2 + bs +k}$$
A structured perturbation might A structured perturbation might take each of these physical parameters $m$, $b$, and $k$ and attribute a likely range or tolerance to their value:
$$ \mathcal{P} = \left\{ \frac{1}{(m+e_m)s^2 + (b+e_b)s + (k + e_k)} \right\} \text{ : }
\matrix{m_{min} \leq m+e_m \leq m_{max} \\
b_{min} \leq b +e_b \leq b_{max} \\
k_{min} \leq k +e_k \leq k_{max}} $$
where $e_i$ is the difference between the nominal value of $i$, and the real value on the actual plant.
(The disk multiplicative perturbation) (The disk multiplicative perturbation)
(Explain how actually getting to W_2 isn't really trivial). (Explain how actually getting to W_2 isn't really trivial).