I want to model aerodynamic forces such as thrust on all motors of quadcopter in simulink.But equations for thrust involves density of air , but then we have to include model air in simulink . So what would be the way to model thrust forces on quadcopter .

Control design

I made the control design using PID controllers for Height , Roll , Pitch and Yaw for getting \begin{bmatrix} U_1 & U_2 & U_3 & U_4 \\ \end{bmatrix} control input vector . Using the equation : $$ \begin{bmatrix} U_1 \\ U_2 \\ U_3 \\ U_4 \\ \end{bmatrix} =\begin{bmatrix} K_T & K_T & K_T & K_T\\ 0 & -K_T & 0 & K_T\\ K_T & 0 & -K_T & 0\\ K_H & -K_H & K_H & -K_H\\ \end{bmatrix} \begin{bmatrix} \omega_1^2\\ \omega_2^2\\ \omega_3^2\\ \omega_4^2\\ \end{bmatrix} $$

We get values for $\begin{bmatrix} \omega_1^2 & \omega_2^2 & \omega_3^2 & \omega_4^2 \\ \end{bmatrix}$ by multyiplying $\begin{bmatrix} U \\ \end{bmatrix}$ with inverse matrix [C] .

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Now how should I model thrust force using calculated values of ${\omega^2}$. Given values of thrust are $T = K_T . \omega^2 . $ and hub torque $T = K_H . \omega^2$ . Where Kt and Kh are 0.82 × 10^−5 and 1.4 × 10^−7 .

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    $\begingroup$ Welcome. Please clarify, what is your actual question? $\endgroup$ Commented Dec 25, 2023 at 22:40
  • $\begingroup$ To clarify , after getting values of $\omega^2$ , which blocks should be used to model thrust force on quadcopter that lifts it up . $\endgroup$ Commented Dec 26, 2023 at 6:26

1 Answer 1


You already give the thrust and torque equations with the respective parameters, why you don't just use them?

Of course, there will be a dependence on the air density. But this might not change a lot during your flight with the quadcopter. A more severe influence will come from the ground effect, or at higher air speed the airstream at the rotor disc. But these effects are more difficult to parameterize without extensive test equipment or CFD analysis.

My suggestion: Use your simple rotor model and parameterize a robust attitude controller, which copes with the neglected effects.


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