Helicopter Lab Day 3

In all of the test matrices we have a travel offset of $180$ degrees, and a pitch offset of $-7.5$ degrees.

Need for report

Good tune

Has the following values

$$\begin{array}{rl}Q& =\left[\begin{array}{cccc}3& 0& 0& 0\\ 0& 2& 0& 0\\ 0& 0& 0.1& 0\\ 0& 0& 0& 0.5\end{array}\right]\\ R& =0.1\end{array}$$

We also added a disturbance for the travel ($30$ degrees) at $15$ second that lasted $1$ second

In another test we did the same thing, but for pitch (still $30$ degrees and $15-16$s).

Unit tune

Has the following values

$$\begin{array}{rl}Q& =\text{diag}(1,1,1,1)\\ R& =1\end{array}$$

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OPTIONAL tunes

State prioritized tune

Has the following values

$$\begin{array}{rl}Q& =\text{diag}(100,100,100,100)\\ R& =1\end{array}$$

Prioritize pitch (same for travel)

$$\begin{array}{rl}Q& =\text{diag}(1,1,15,1)\\ R& =1\end{array}$$

Input prioritized tune

Has the following values

$$\begin{array}{rl}Q& =\text{diag}(1,1,1,1)\\ R& =100\end{array}$$

MPC vs LQR

MPC is likely more accurate due to feedback in the optimization problem, contrary to LQR where we only solve the optimization problem once.

MPC is however more computationally heavy and takes longer time to compute (duh).

Row vs data

1. Time
2. Travel
3. Travel rate
4. Pitch
5. Pitch rate
6. Elevation
7. Elevation rate
8. Pitch reference
9. Elevation reference
10. V_d
11. V_s 12-16. x_star (row 13-17)