Where is the Natural Frequency and is the Damping Factor. Once the desired response of the general second-order system G(s) is found, the Angle Tracking Observer coefficients can be calculated using these expressions: The Angle Tracking Observer transfer function is a second order and has one zero. This zero affects the residue, or amplitude, of a response component but does not affect the nature of the response - exponential damped sine. It can be proven that the closer the zero is to the dominant poles, the greater its effect is on the transient response. As the zero moves away from the dominant poles the transient response approaches that of the two-pole system. Example To better understanding, we propose to take an example: Let take 3.7 inch size one has got 360 poles. At 1600 rpm (27 rps) we have a mechanical frequency to about 10 kHz (27 rps*360 poles). We take a frequency excitation to 100 kHz. For this configuration the relation becomes: We have the following signal on out of sensor:
Where is the Natural Frequency and is the Damping Factor. Once the desired response of the general second-order system G(s) is found, the Angle Tracking Observer coefficients can be calculated using these expressions: The Angle Tracking Observer transfer function is a second order and has one zero. This zero affects the residue, or amplitude, of a response component but does not affect the nature of the response - exponential damped sine. It can be proven that the closer the zero is to the dominant poles, the greater its effect is on the transient response. As the zero moves away from the dominant poles the transient response approaches that of the two-pole system. Example To better understanding, we propose to take an example: Let take 3.7 inch size one has got 360 poles. At 1600 rpm (27 rps) we have a mechanical frequency to about 10 kHz (27 rps*360 poles). We take a frequency excitation to 100 kHz. For this configuration the relation becomes: We have the following signal on out of sensor:
rapport_inductosyn.docx