## Controls System

I am identifying the three fans as motors “a”, “b”, “c”. Each motor has a calibration coefficient of α, β, and γ, respectively. The purpose of the correction coefficient is to compensate for factors that would effect the net thrust of each fan. The factors include lubrication, wear, heat, and dirt among other factors.

Values x, y, and z are decimal inputs between -1 and 1. These values will be sent to a speed controller where it will be parsed and turned into a vector where current is the magnitude and + or – is the direction. These values are based on the position of the joystick. Our inputs are *x* is forward and reverse, y is up and down, and *z* is left and right.

The equations that control the calibration are:

*A=(-(αxsinӨ) /2 i, (αcosӨy/2) j, αz k)*

*B=(-(βxsinӨ)*

**/2 i,**(βycosӨ/2)**j**, -βz**k**)*C=(γx*

**i,**γycosӨ**j**, 0**k**)The range of y is 0 to 1, it cannot accelerate downward at a rate higher than free fall.

Simplifying the equation for *Ө*=0 yields;

A=(0* i*, *α*y * j, αz k*)

B=(0

*i*,*β*y

*)*

**j**, βz**k**C=(

*γx*

**y**

*i*, γ*0*

**j**,*)*

**k**Simplifying for x=0, z=0 the equations yield:

A=(0* i*, *α*y * j, 0 k*)

B=(0

*i*,*β*y

*)*

**j**,**0 k**C=(

*o*

**y**

*i*, γ*0*

**j**,*)*

**k**Our unit vectors are * i* is forward and reverse,

**is up and down, and**

*j**is left and right.*

**k**So in order to hover in place, this equation must be true: A+B+C=(0,n,0) where *n* is the amount of current required to keep Sirrus one foot off the ground.