Pulsating High Freq Observer

Estimate initial rotor electrical position of interior PMSM using PHF injection

• Library:

• Motor Control Blockset / Sensorless Estimators

• 

Description

The PHF Observer block estimates the initial position (in electrical radians) of a stationary interior PMSM by using pulsating-high-frequency (PHF) injection and dual-pulse (DP) techniques. In addition, the block also detects real-time position when the rotor runs using (low-speed) closed-loop control.

Ports

Input

Iab hf — PHF current response

vector

The high-frequency (phase a and b) current feedback from motor in response to the PHF voltage injection, in Amperes or per-unit.

Data Types: single | double | fixed point

Enable — Enable block

scalar

Signal to enable block. The port supports one of the following input signals:

• 1 — Enable block operation

• 0 — Disable the block

Data Types: Boolean

θin — Initial rotor position

scalar

Initial rotor position input when the block skips the stage 1 IPE operation, in radians, degrees, or per-unit.

The unit depends on the Position unit parameter.

Data Types: single | double | fixed point

IPEEn — Enable stage 1 IPE operation

scalar

Signal to enable stage 1 IPE operation. The port supports one of the following input signals:

• 1 — Enable the block to run stage 1 IPE followed by stage 2 closed-loop PHF injection.

• 0 — Enable the block to skip stage 1 IPE and directly run stage 2 closed-loop PHF injection.

Data Types: Boolean

Output

Vαβ hf — PHF output

scalar

Pulsating high-frequency voltage (in αβ reference frame) output, in per-unit.

Data Types: single | double | fixed point

θest — Estimated rotor position

scalar

The rotor position estimated by the block, in radians, degrees, or per-unit.

The unit depends on the Position unit parameter.

Data Types: single | double | fixed point

PosEn — Status of θ_est port

scalar

The port provides one of the following outputs:

• 1 — Indicates that stage 1 IPE is successfully complete and the θ_est port output is accurate.

• 0 — Indicates that stage 1 IPE is in progress (θ_est port output is not accurate as yet) or estimation has failed.

Data Types: single | double | fixed point

Info — Bus signal

bus

The bus signal contains these block calculations.

Signal				Description	Units
Sin θest and cos θest				Sine and cosine of estimated rotor position	-
Id and Iq				Stator direct axis and quadrature axis currents	A
Convergence				Difference between current and previous sample of θest output. A value closer to zero indicates saturation of θest.	rad
Status			0	Block is not enabled (Enable input port is 0)	-
			1	Block is finding the best possible initial estimate (Stage 1 Part A)	-
			2	Block is running the PHF method (Stage 1 Part B)	-
			3	Block is running Dual-Pulse (DP) Method (Stage 1 Part C)	-
			4	Block has successfully completed stage 1 and has started stage 2 closed-loop PHF injection	-
			5	Stage 1 Part B failed due to a large error in the estimated rotor position	-

Parameters

Discrete step size (s) — Sample time after which block executes again

50e-6 (default) | scalar

The time between two consecutive instances of block execution.

Position unit — Unit of position input and output

Radians (default) | Degrees | Per-unit

Units for the θ_in input and θ_est output.

Datatype — Input and output data type

single (default) | double | fixdt(1,16) | fixdt(1,16,0) | fixdt(1,16,2^0,0) | <data type expression>

Data type of the block inputs and outputs.

PHF Parameters

PHF peak voltage (PU) — Peak voltage of PHF

0.2 (default) | scalar

Peak amplitude of the PHF voltage applied by the block, in Volts.

PHF frequency (Hz) — PHF voltage frequency

2000 (default) | scalar

Frequency of the PHF voltage applied by the block, in Hz.

Proportional gain — Proportional gain for PI controller of PHF

3000 (default) | scalar

Proportional PI controller gain K_p for the PHF applied by the block.

Integral gain — Integral gain for PI controller of PHF

4000 (default) | scalar

Integral PI controller gain K_i for the PHF applied by the block.

Cutoff frequency (Hz) — Cutoff frequency for lowpass filter of PHF

500 (default) | scalar

Cutoff frequency of the lowpass filter for the PHF applied by the block, in Hz.

Open loop duration (s) — Duration of open-loop PHF injection during stage 1 part A

5e-3 (default) | scalar

Duration of the open-loop PHF injection during stage 1 part A, in seconds.

Close loop duration (s) — Duration of closed-loop PHF injection during stage 1 part B

0.2 (default) | scalar

Duration of the closed-loop PHF injection during stage 1 part B, in seconds.

Idle time (s) — Duration between algorithm steps

5e-3 (default) | scalar

Duration (in seconds) between steps in the algorithm related to stage 1 part A and stage 1 part B that allow for fading of transient dynamics. For example, this block stops operating for this duration between each PHF injection (open-loop or closed-loop).

DP Parameters

Pulse voltage (s) — Amplitude of injected pulses

0.4 (default) | scalar

Voltage amplitude of the injected pulses, in Volts.

Pulse duration (s) — Duration of injected pulses

750e-6 (default) | scalar

Duration of the injected pulses, in seconds.

Idle time (s) — Duration between two pulses during dual-pulse injection

5e-3 (default) | scalar

Duration (in seconds) between two pulses during dual-pulse injection (stage 1 part C).

Model Examples

Estimate Initial Rotor Position Using Pulsating High-Frequency and Dual-Pulse Methods

Estimates initial position (in electrical radians) of a stationary interior PMSM by using pulsating high frequency (PHF) injection and dual pulse (DP) techniques.

Open Example

Algorithms

The block determines the best possible initial estimation for the rotor position using open-loop PHF injection, which it uses to run closed-loop PHF.

The block executes closed-loop PHF by injecting a high-frequency signal into the estimated rotor position to determine the actual rotor position without spinning the motor. This technique works when the motor saliency ratio (L_q/L_d) is greater than 1. Due to a limitation in the PHF method, the estimated position can show ambiguity equal to the value of π (pi). The dual-pulse (DP) method uses polarity detection to resolve the ambiguity of π and applies a compensation of π if there is an error. The estimated rotor position ranges from 0 to 2π electrical radians.

The block can run in these 2 stages:

1. Stage 1 – Initial position estimation (IPE), which includes three parts.

2. Stage 2 – Closed-loop pulsating-high-frequency (PHF) injection.

Stage 1 focuses on determining the initial position of the rotor when it is stationary. This stage includes the following three parts:

Part A: Find Best Possible Initial Estimation

The block uses the PHF injection technique. PHF injection needs initial estimation to start the algorithm.

If you use only one initial estimation, θ_{i_est}, (for PHF) for all possible actual rotor positions, the block algorithm might not work accurately for certain actual rotor positions when the motor has low saliency. These ambiguous positions are when:

1. θ_actual lies in the range $$\left[\left({\theta }_{i\_est}+ \frac{\pi }{2}-0.1\right),\left({\theta }_{i\_est}+ \frac{\pi }{2}+0.1\right)\right]$$

2. θ_actual lies in the range $$\left[\left({\theta }_{i\_est}- \frac{\pi }{2}-0.1\right),\left({\theta }_{i\_est}- \frac{\pi }{2}+0.1\right)\right]$$

3. θ_actual lies in the range $$\left[\left({\theta }_{i\_est}+\pi -0.1\right),\left({\theta }_{i\_est}+ \pi +0.1\right)\right]$$

To make PHF work for motors with low saliency, the block picks different initial estimation for different actual rotor positions.

When executing this part, the block picks the best possible initial estimation from these three alternatives:

1. θ_{i_est} = 0

2. θ_{i_est} = 2π/3

3. θ_{i_est} = -2π/3

Therefore, the block injects three high-frequency voltage signals (approximately 2000 KHz) across the preceding three θ_est values and measures the resulting i_q currents. For each i_q:

$$iq\propto PHF\_signal\times \sin \left(2{\theta }_{err}\right)$$

Therefore, $i_q\propto \left|sin\left(2{\theta }_{err}\right)\right|\text{ or }{i}_q\propto \left|sin\left(2({\theta }_{actual}-{\theta }_{i\_est})\right)\right|$

where:

θ_{i_est} — Initial estimation of rotor position (which can be either 0, 2π/3, or -2π/3) (in degrees, per-unit, or radians)

θ_actual — Actual rotor position (in degrees, per-unit, or radians)

θ_err = θ_actual-θ_{i_est} (in degrees, per-unit, or radians)

The block uses these definitions:

i_q1 = i_q for θ_{i_est} = 0

i_q2 = i_q for θ_{i_est} = 2π/3

i_q3 = i_q for θ_{i_est} = -2π/3

For θ_{i_est} = 0, when varying θ_actual from 0 to 2π, $i_{q1}\propto \left|sin 2({\theta }_{actual}-0)\right|$ is the maximum among the preceding three i_q currents when the rotor lies in the following four highlighted regions.

If θ_{i_est} = 0 is used for all θ_actual = 0 to 2π, the algorithm fails for the following ambiguous regions (when motor saliency is low):

1. θ_actual lies in the range $$\left[\left(0+ \frac{\pi }{2}-0.1\right),\left(0+ \frac{\pi }{2}+0.1\right)\right]$$

2. θ_actual lies in the range $$\left[\left(0- \frac{\pi }{2}-0.1\right),\left(0- \frac{\pi }{2}+0.1\right)\right]$$

3. θ_actual lies in the range $$\left[\left(0+\pi -0.1\right),\left(0+ \pi +0.1\right)\right]$$

Because these ambiguous regions are not present in the preceding four regions, you eliminate the regions where the algorithm might fail.

For θ_{i_est} = (2π/3), when varying θ_actual from 0 to 2π, $i_{q2}\propto \left|sin 2({\theta }_{actual}-\frac{2\pi }{3})\right|$ is the maximum among the three i_q currents when the rotor lies in the following four highlighted regions.

If θ_{i_est} = (2π/3) is used for all θ_actual = 0 to 2π, the algorithm fails for following ambiguous regions (when motor saliency is low):

1. θ_actual lies in the range $$\left[\left(\frac{2\pi }{3}+ \frac{\pi }{2}-0.1\right),\left(\frac{2\pi }{3}+ \frac{\pi }{2}+0.1\right)\right]$$

2. θ_actual lies in the range $$\left[\left(\frac{2\pi }{3}- \frac{\pi }{2}-0.1\right),\left(\frac{2\pi }{3}- \frac{\pi }{2}+0.1\right)\right]$$

3. θ_actual lies in the range $$\left[\left(\frac{2\pi }{3}+\pi -0.1\right),\left(\frac{2\pi }{3}+ \pi +0.1\right)\right]$$

Because these ambiguous regions are not present in the preceding four regions, you eliminate the regions where the algorithm might fail.

For θ_{i_est} = -(2π/3), when varying θ_actual from 0 to 2π, $i_{q3}\propto \left|sin 2({\theta }_{actual}-\left(-\frac{2\pi }{3}\right))\right|$ is the maximum among the three i_q currents when the rotor lies in the following four highlighted regions.

If θ_{i_est} = -(2π/3) is used for all θ_actual = 0 to 2π, the algorithm fails for following ambiguous regions (when motor saliency is low):

1. θ_actual lies in the range $$\left[\left(-\frac{2\pi }{3}+ \frac{\pi }{2}-0.1\right),\left(-\frac{2\pi }{3}+ \frac{\pi }{2}+0.1\right)\right]$$

2. θ_actual lies in the range $$\left[\left(-\frac{2\pi }{3}- \frac{\pi }{2}-0.1\right),\left(-\frac{2\pi }{3}- \frac{\pi }{2}+0.1\right)\right]$$

3. θ_actual lies in the range $$\left[\left(-\frac{2\pi }{3}+\pi -0.1\right),\left(-\frac{2\pi }{3}+ \pi +0.1\right)\right]$$

Because these ambiguous regions are not present in the preceding four regions, you eliminate the regions where the algorithm might fail.

Therefore, using this approach you have three sets of regions corresponding to three different initial estimates. These three sets or regions cover all the motor sectors where the rotor can lie:

In part A, the block picks the θ_{i_est} corresponding to the maximum I_q current value between i_q1, i_q2, and i_q3 for Part B.

Part B: Pulsating High-Frequency (PHF) Method

After determining the best possible initial estimate θ_{i_est}, the block injects a sinusoidal high-frequency voltage along the finalized (θ_est | t = 0) = θ_{i_est} (resulting in an unbalanced three-phase voltage in the motor) and reads the current response from the motor. The block then performs numerical analysis of the resulting stator current response to compute the initial position of the stationary rotor (in electrical radians) by making corrections to θ_est.

The block performs iterative tests on the motor. Therefore, when the block executes, the estimated position is initially θ_{i_est}, but rises steadily to saturate at the actual rotor angle (with respect to a-axis).

The PHF method has a limitation due to which it might compute the rotor position with an ambiguity of π. If the rotor lies in the range $${\theta }_{actual}=\left(0,\frac{\pi }{2}\right]\cup \left[\frac{3\pi }{2},2\pi \right)$$ electrical radians (region 1), the estimated position is accurate (π compensation is not required).

If the rotor lies in the range $${\theta }_{actual}=\left(\frac{\pi }{2},\frac{3\pi }{2}\right)$$ electrical radians (region 2), the estimated position shows an ambiguity of π (π compensation is required).

Therefore, the block uses the dual-pulse method to determine if the estimated position needs π compensation.

Part C: Dual-Pulse (DP) Method

The block injects two very short duration voltage pulses (with the same width and magnitude) in the following positions:

• Pulse 1 at the rotor position estimated in Part B

• Pulse 2 at the rotor position estimated in Part B + π

Because pulse width is very short, the motor does not run, and the rotor remains stationary after pulse injection.

The interaction between the resulting stator magnetic flux and the rotor permanent magnets results in two current impulses along the d-axis of the rotor that rise and fall quickly.

Because the stator core is saturated, it shows nonlinear behaviour. A small L_d results in higher current I_d, and a high L_d results in smaller current I_d. Therefore, the I_d current impulses generated by Pulse 1 and Pulse 2 show different peak values.

Note

The pulse duration of the injected voltage pulses is large enough to obtain a measurable difference between the peak current values. At the same time, the duration is not too high, that is, when the pulse duration exceeds a certain limit, the rotor can start spinning.

The block computes the difference between the peak values of the two current impulses ΔI_d to determine if the position estimated in Part A needs π compensation.

ΔI_d = |I_d1| - |I_d2|

PHF injection benefits use cases that require the rotor to remain stationary or that require position estimation without starting the motor. The PHF injection technique also benefits use cases where you need to avoid open-loop runs to estimate position (before transitioning to closed-loop speed control) or where you require the motor to start directly in the closed-loop mode. The block algorithm in stage 1 addresses these use cases by estimating the position while keeping the rotor stationary and avoiding an open-loop run.

After the block completes stage 1, you can continue to run the block in stage 2 where it computes the rotor position while the motor runs using closed-loop control (for example, field-oriented control). Using the Stage 2 algorithm (closed-loop PHF injection), the block can continue to inject pulsating high-frequency signal (as described in Part B) and performs numerical analysis of the resulting stator-current response to compute and track the rotor position during closed-loop operation.

Version History

Introduced in R2022b