Vector Control of Permanent Magnet Synchronous Motor (3)-Parameter tuning of current loop speed loop regulator

3. Design of current loop speed loop

3.1 Design of current inner loop regulator

The current loop of the vector control system $\small i_{q}$ controls the stator current, which in turn controls the motor torque.

The function of the current inner loop is to be able to start with the maximum current during the start of the motor, and to recover quickly when external disturbances occur, speed up the dynamic tracking response speed, and improve the stability of the system.

The figure above is the flow chart of the current inner loop, the error value of the input bit current signal of the current inner loop, the output bit reference voltage, and the control motor torque. The first link is the PI regulator, the second link is the delay link, and the third link is the PWM link. The motor transfer function can be approximated as:

$\small G_{p}\left ( s \right )=\frac{i_{q}}{u_{q}}=\frac{1}{L_{q}s+R}$

When the switching frequency is 10KHz, due to the higher switching frequency, the delay link and the PWM link can be combined for processing, remember $\small t_{d}=T_{s}$ , and treat it $\small K_{pwm}$ as 1 to get the following flow chart:

Based on the above flow chart analysis, the current loop is set according to a typical I-type system.

Then the open loop transfer function:

$\small \frac{K_{p}\left ( T_{i}s+1 \right )}{T_{i}s}\cdot \frac{1}{L_{q}s+R}\cdot \frac{1}{1+1.5T_{s}s}$

If it is $\tiny T_{i}=\frac{L_{q}}{R}$ possible to get the open-loop transmission after setting:

$\small G\left ( s \right )=\frac{K_{p}}{R_{s}\ast T_{i}\ast\left ( 1.5T_{s}+1 \right ) }=\frac{K_{p}}{L_{q}(1.5T_{s}+1)}$

Compared with a typical first-order system,

$\small G\left ( s \right )=\frac{K}{s\left ( T_{s}+1 \right )}$

get

$\small K=\frac{K_{p}}{L_{q}}$

$\small T=1.5T_{s}$

The first-order system is $\tiny K_{T }=0.5$ calculated

$\small K_{p}=\frac{L_{q}}{3T_{s}}$

$\small K_{i}=\frac{K_{p}}{T_{i}}=\frac{K_{p}\ast R_{s}}{L_{q}}=\frac{R_{s}}{3T_{s}}$

3.2 Design of speed outer loop regulator

If the design of the outer speed ring is reasonable, it can reduce the influence of disturbance on the system, reduce speed fluctuation, and make the system work in a stable state.

When studying the outer speed loop, consider the current loop as a link:

From the performance of the second-order system itself, the best performance when the damping ratio is 0.707, you can infer:

$\small \xi =0.707=>G\left ( s \right )acr=\frac{1}{3T_{s}+1}$

Same as the current loop, combining the delay link and the simplified current loop to get

$\small T_{s2}=4\ast T_{s}$

The flowchart is further simplified as

Set the speed loop according to the second-order typical link, and set the speed loop PI regulator as:

$\small \frac{Kn\left ( \tau n\ast s+1 \right )}{\tau n\ast s}$

The following open-loop transmission letters are available:

$\small G\left ( s \right )=\frac{Kn\left ( \tau n\ast s+1 \right )}{\tau n\ast s}\ast \frac{1}{T_{s2}+1}\ast \frac{90\ast Pn\ast \varphi f}{2\pi Js}$

After finishing:

$\small G\left ( s \right )=\frac{Kn\left ( \tau n\ast s+1 \right )}{s^{2}\left ( T_{s2}\ast s+1 \right )}$

According to the parameter relationship of a typical Type 2 system, there should be

$\small \tau n=h\ast T_{s2}$

$\small K_{N}=\frac{h+1}{2h^{2}\ast T_{s2}^{2}}$

According to the typical second-order system tuning theory, the system performance is best when h=5.

After sorting out:

$\small K_{n}=\frac{\pi J}{75\ast P\ast \varphi f\ast T_{s2}}$

The PI regulator parameters can be obtained as

$\small K_{p}=K_{n}=\frac{\pi J}{300\ast P\ast \varphi f\ast T_{s}}$

$\small K_{i}=\frac{K_{p}}{\tau _{n}}=\frac{\pi J}{6000\ast P_{n}\ast \varphi f\ast T_{s}^{2}}$