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20 | 20 | "## System Description\n", |
21 | 21 | "This example uses a simplified model for a (planar) vertical takeoff and landing aircraft (PVTOL), as shown below:\n", |
22 | 22 | "\n", |
23 | | - "\n", |
| 23 | + "\n", |
24 | 24 | "\n", |
25 | | - "\n", |
| 25 | + "\n", |
26 | 26 | "\n", |
27 | 27 | "The position and orientation of the center of mass of the aircraft is denoted by $(x,y,\\theta)$, $m$ is the mass of the vehicle, $J$ the moment of inertia, $g$ the gravitational constant and $c$ the damping coefficient. The forces generated by the main downward thruster and the maneuvering thrusters are modeled as a pair of forces $F_1$ and $F_2$ acting at a distance $r$ below the aircraft (determined by the geometry of the thrusters).\n", |
28 | 28 | "\n", |
|
307 | 307 | "\n", |
308 | 308 | "To design a controller for the lateral dynamics of the vectored thrust aircraft, we make use of a \"inner/outer\" loop design methodology. We begin by representing the dynamics using the block diagram\n", |
309 | 309 | "\n", |
310 | | - "<img src=http://www.cds.caltech.edu/~murray/wiki/images/3/3f/Pvtol-lateraltf.png>\n", |
311 | | - "where\n", |
312 | | - "<img src=http://www.cds.caltech.edu/~murray/wiki/images/math/3/6/4/364e56f7893637e12edb0e0ac6c45722.png> \n", |
| 310 | + "<img src=https://murray.cds.caltech.edu/images/murray.cds/3/3f/Pvtol-lateraltf.png>\n", |
| 311 | + "\n", |
313 | 312 | "The controller is constructed by splitting the process dynamics and controller into two components: an inner loop consisting of the roll dynamics $P_i$ and control $C_i$ and an outer loop consisting of the lateral position dynamics $P_o$ and controller $C_o$.\n", |
314 | | - "<img src=http://www.cds.caltech.edu/~murray/wiki/images/f/f1/Pvtol-nested-1.png>\n", |
| 313 | + "<img src=https://murray.cds.caltech.edu/images/murray.cds/f/f1/Pvtol-nested-1.png>\n", |
315 | 314 | "The closed inner loop dynamics $H_i$ control the roll angle of the aircraft using the vectored thrust while the outer loop controller $C_o$ commands the roll angle to regulate the lateral position.\n", |
316 | 315 | "\n", |
317 | 316 | "The following code imports the libraries that are required and defines the dynamics:" |
|
547 | 546 | "name": "python", |
548 | 547 | "nbconvert_exporter": "python", |
549 | 548 | "pygments_lexer": "ipython3", |
550 | | - "version": "3.7.9" |
| 549 | + "version": "3.9.1" |
551 | 550 | } |
552 | 551 | }, |
553 | 552 | "nbformat": 4, |
|
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