# Classes - Beard

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As an introduction to use doku-wiki you must have double backslashes (\\) to indicate a newline. To have a space between entries leave an empty line in the code. To edit a section please select the “edit” button after the section not before. A quick tutorial on additional syntax is available here. You can enter equations by using latex syntax like

• <latex>
\dot{x}=f(x,u) \\
\frac{3}{4 \pi}   \sqrt{4 \cdot x^2   12}\\
\lim_{n \to \infty}
\sum_{k=1}^n \frac{1}{k^2} = \frac{\pi^2}{6}\\
\it{f}(x) = \frac{1}{\sqrt{x} x^2}\\
e^{j \pi} + 1 = 0}\;
</latex> ## 4. Forces and Moments

On page 43 in the description for Figure 4.2, it says “draft force” instead of “drag force”. -Brandon Carroll

On page 50 in note 1 at the bottom of the page, the reference to “Equation (4.3)” should be a reference to “Equation (4.4)”. There is no C_D_0 term in Eq 4.3, but there is in Eq 4.4. -Brandon Carroll

On page 58, a reference to Equation 2.8 is made and the equation is shown again. However, the equation shown on this page is not the same as Equation 2.8 on page 21. The version on page 21 has the magnitude of Va in the denominator, while the version on page 58 has the magnitude of Va projected onto the xz plane. Which one is correct? According to Figure 2.9, it should be the one that uses full magnitude of Va (on page 21). -Brandon Carroll

## 5. Linear Design Models

On page 92 on the 8th line under the “5.6 Chapter Summary” heading, the word “dominate” should be “dominant”. -Brandon Carroll

On page 94, Exercise 5.6 tells us to “create the transfer functions listed in Section 5.6”. However, the section that lists the transfer functions is 5.4. -Brandon Carroll

## 6. Autopilot Design using Successive Loop Closure

Page 99 - While explaining the successive loop closure, it reads “it is a factor of 5 to 10 times slower than the preceding loop.” The word “slower” should be replaced with “smaller”.
- Everett Bryan

Page 102 - When the following equation is mentioned:
<latex> |\$\mathcal{k}_{p_\phi}| = \frac{\big\delta^{max}_\big{a}}{(\big\phi^c-\big\phi)^{max}} </latex>
It might be useful to reference equation 6.2 from page 100.
- Everett Bryan

Page 104 - There is a typo in the following equation:
<latex> s^3 + (a_{\phi_1}+a_{\phi_2}k_{d_\phi})s^2+a_{\phi_2}k_{d_\phi}s+a_{\phi_2}k_{i_\phi} = 0,</latex>
It should be written as:
<latex> s^3 + (a_{\phi_1}+a_{\phi_2}k_{d_\phi})s^2+a_{\phi_2}k_{p_\phi}s+a_{\phi_2}k_{i_\phi} = 0, </latex>
- Everett Bryan

Page 104 - The above typo was carried through to the next line. The next equation should be:
<latex> 1+k_{i_\phi} \bigg{(}\frac{\big{a_{\phi_2}}}{\big{s(s^2+(a_{\phi_1}+a_{\phi_2}k_{d_\phi})s+a_{\phi_2}k_{p_\phi})}}\bigg{)}=0. </latex>
- Everett Bryan

Page 106 - The equation near the bottom: <latex> \omega_{n_\phi}>5\omega_{n_\chi}. </latex>
should probably be written as: <latex> \frac{\big{\omega_{n_\phi}}}{\big{5}}>\omega_{n_\chi}. </latex>
- Everett Bryan

## 7. Sensors for Small and Miniature UAVs

On page 124, the gravity terms got dropped out of Eq 7.2, but are present in 7.1 and 7.3. -Brandon Carroll - I think that Eq 7.2 is correct. -RB

On page 124, the force terms in Equation 7.3 should all be divided by the mass to convert them to acceleration. Otherwise, you're adding forces to accelerations. Note that the division by mass is present in Equation 7.2. -Brandon Carroll

In the last paragraph on page 129, you say that the volume on the left is closed and at a constant reference pressure and the volume on the right is open to the ambient air. However, in the figure at the top of the next page it is reversed - the volume on the right is closed and at a constant reference pressure and the left is open. -Brandon Carroll

On page 143 in exercise 7.2, the reference for the accelerometer equation should be Eq 7.3 instead of Eq 7.2 to match the inputs for the sensors.m file you provide on the website. -Brandon Carroll

## 9. Nonlinear Design Models

TWM: The first paragraph of section 9.3 is a little confusing. The last sentence says “Equations 2.10 through 2.12 will be used to obtain the missing variables.” What are the missing variables? We need to be a little more specific.

## 10. Waypoint and Orbit Following

RWB: path following doesn't work well, especially for estimated states. One of the problems is that the estimated GPS location has a bias and the commanded orbit/line does not have the same bias. Two solutions: (1) remove the Gauss-Markov bias generation from GPS (retaining only zero mean noise), (2) do what happens in field: draw the desired orbit/line using the estimated GPS location, i.e., with same bias (not sure how to do this simply).

## 11. Path Manager

Figure 11.7 - Case four has listed “Case IV: L-S-V” which should be “Case IV: L-S-L” - Everett Bryan

In path_manager_line.m, on line 6, “5 by P.size_waypoint_array” should read “P.size_waypoint_array by 5” - It was correct as it was.

There is a typo at the end of line 1 in Algorithm 11. There should not be any “r” in there.

RWB: In the algorithm for Dubins paths, describe why 5 states are needed, and add five states to the algorithm description (initial conditions may be on wrong side of half plane).

RWB: Figure 11.5 is wrong. The center circle should have a “+” instead of “-”. Do on mac.

Algorithm 12 contains a 3 state algorithm while the path_manager_dubins.m contains a 5 state algorithm. This may not be an error but perhaps the project and the algorithm should be consistent. - Everett Bryan

## A. Notation

On page 273 in the rotate function code block, the semicolon at the end of line 1 is unnecessary. -Brandon Carroll

On page 274 in the drawSpacecraftBody function code block, the comma at the end of line 16 is unnecessary. -Brandon Carroll

On page 277 in the drawSpacecraftBody function code block, the comma at the end of line 11 is unnecessary and lines 12 through 15 should be indented one more time. -Brandon Carroll

On pg 279 in the beginning of the third sentence, there should be a comma before the word “essentially” (as well as after). -Brandon Carroll

## F. Sensor Parameters 