3.1.3. Angular Velocity Control

This controller performs angular velocity control, the main task of the controller is the minimization of error between desired and measured angular velocity components. The angular velocity control is denoted as:

$$u\_2(t) = K\_{PP}e\_p(t) + K\_{IP} \int\_0^t e\_p(\tau)d\tau + K\_{DP} \frac{de\_p(t)}{d\_I} \tag{16}$$

$$
\mu\_3(t) = K\_{PQ} \varepsilon\_q(t) + K\_{IQ} \int\_0^t \varepsilon\_q(\tau) d\tau + K\_{DQ} \frac{d\varepsilon\_q(t)}{dt} \tag{17}
$$

$$u\_4(t) = K\_{PR}e\_7(t) + K\_{IR} \int\_0^t e\_r(\tau)d\tau + K\_{DR} \frac{de\_r(t)}{dt} \tag{18}$$

where *KPP*, *KIP*, *KDP* express PID gains that control the angular velocity along *xb*; *KPQ*, *KIQ*, *KDQ* indicate PID gains that control the angular velocity along *yb*; and *KPR*, *KIR*, *KDR* refer to PID gains that control the angular velocity along *zb*. The outputs of controller constitute the orientation control variables (*u*2, *u*3, *u*4) of the quadcopter [38].
