As can be seen from the previous article, the transfer function block diagram of the speed loop is known, but it is actually worth studying why the previous part of the block diagram is written like that .
2 The source of the transfer function of each link of the speed loop
The block diagram of the speed loop transfer function is shown in the figure below:
Let's explain one by one where each link in the picture comes from.
The first one: Speed loop PI regulator. The transfer function of the speed loop PI regulator is traditional PI. In the basic double closed-loop control system, linear traditional PI is generally used, because linear traditional PI can satisfy basic control. Performance requirements are up. But one thing to note here is that the input of the speed regulator ASR is the difference between the feedback speed and the given speed, and the output of the speed regulator ASR is the given value of the current loop, generally the given value of iq .
Second: the equivalent transfer function of the current inner loop. Generally, when studying the outer loop, the inner loop closed loop transfer function is regarded as a first-order inertial link. The specific derivation is shown in the figure below. Generally, the current inner loop is designed according to the damping ratio equal to 0.707, so the transfer function of the current inner loop at this time is 1/3Ts*s+1. Some students asked here, should the input of the current loop be iq and the output shouldn’t be Uq? How come there is neither an input mark nor an output mark? In fact, the approximation of the current inner loop is purely considering its control time The delay effect is not input and output, and it is only defined as a first-order inertia link.
Third: the delay link caused by the one-shot delay of the controller. This link comes from the control delay caused by the digital control itself, because the controller can calculate the duty cycle after the sampling is completed, and the calculated duty cycle must be effective on the inverter in the next sampling period. Therefore, the digital controller has a one-shot delay . In the double-sampling and double-update modulation strategy, the digital delay can be reduced to half a beat, but here we calculate the delay according to our usual regular sampling method. The transfer function is a first-order inertia link, and the delay time is a sampling period. As shown below:
Fourth: the conversion of torque and current. Only in this place, the conversion of specific physical quantities is involved, so the source of the transfer function no longer comes from the influence of the calculation time, but from the specific mathematical model, that is, the magnitude of the torque and the magnitude of the current. The relational formula is shown in the figure below. According to this formula, the transfer function can be derived as a pure gain link , as shown in the right figure below.
After the specific reasons for each link are explained, it is necessary to conduct specific time-domain and frequency-domain analysis of the open-loop transfer function characteristics of the outer speed loop. Please see the follow-up article.
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