wn.2 Actar h s2 +2*z'wnstwn'2 Actuator Actator Transfer Fcn Rate Limiter Figure 2-3: Actuator models used the Cloud Cap Hardware-in-the-loop sim- ulation n-the-loop simulator. As shown in Ref. 26, the actuator transfer function, Gact(s) is given by specifying the bandwidth limit, Bw 2丌B1w 8) =c=0.707 (29) where the damping ratio, S, is selected at the critical value to set the actuator band width equal to the natural frequency (wb Wn). The aileron, elevator, and rudder channels all respond with approximately the same characteristics(Bw= 10 Hz),but the throttle is modeled with less dynamic range(Bw= 2 Hz) as the engine RPM equires added time to ramp up to produce thrust. The input/output saturation and slew rate limits are determined as per manufacturer specifications(++60, 2 Hz respectively), and applied as shown in Figure 2-3 2.1. 3 Sensor noises The Cloud Cap hardware-in-the-loop simulator includes detailed sensor models based on information from the manufacturer to corrupt the simulation measurements. For the purposes of simulation, noises on the pressure, rate gyros and accelerometers onboard the aircraft are modeled using band-limited white noise and specified drift rates26. Although the same noise and drift models could be applied to GPS position and velocity measurements, this information is typically assumed to be perfect in the HWIL tests. The values used to parameterize the Piccolo pressure sensors, the CristaTM IMu angle-rate sensors. and the accelerometers are shown in Table 2.3Figure 2­3: Actuator models used the Cloud Cap Hardware­in­the­lo op sim￾ulations in­the­loop simulator. As shown in Ref. [26], the actuator transfer function, Gact(s), is given by specifying the bandwidth limit, BW Gact(s)= ω2 n s2 + 2ζωns + ω2 n (2.7) ωn = 2πBW (2.8) ζ = ζc = 0.707 (2.9) where the damping ratio, ζ, is selected at the critical value to set the actuator band￾width equal to the natural frequency (ωb = ωn) . The aileron, elevator, and rudder channels all respond with approximately the same characteristics (BW = 10 Hz), but the throttle is modeled with less dynamic range (BW = 2 Hz) as the engine RPM requires added time to ramp up to produce thrust. The input/output saturation and slew rate limits are determined as per manufacturer specifications (±60◦, 2 Hz respectively), and applied as shown in Figure 2­3. 2.1.3 Sensor Noises The Cloud Cap hardware­in­the­lo op simulator includes detailed sensor models based on information from the manufacturer to corrupt the simulation measurements. For the purposes of simulation, noises on the pressure, rate gyros and accelerometers onboard the aircraft are modeled using band­limited white noise and specified drift rates [26]. Although the same noise and drift models could be applied to GPS position and velocity measurements, this information is typically assumed to be perfect in the HWIL tests. The values used to parameterize the PiccoloTM pressure sensors, the CristaTM IMU angle­rate sensors, and the accelerometers are shown in Table 2.3. 36