diff --git a/4 Qualifying Exam/2 Writing/2. QE State of the Art.md b/4 Qualifying Exam/2 Writing/2. QE State of the Art.md index a8f44bf0..89c3f1e0 100644 --- a/4 Qualifying Exam/2 Writing/2. QE State of the Art.md +++ b/4 Qualifying Exam/2 Writing/2. QE State of the Art.md @@ -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: $$ P = \frac{X(s)}{F(s)} = \frac{1}{ms^2 + bs +k}$$ -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) (Explain how actually getting to W_2 isn't really trivial). \ No newline at end of file