A position sensorless control method in low-speed region of a fault-tolerant permanent magnet motor system based on envelope detection and a non-orthogonal phase-locked loop, wherein the fault-tolerant permanent magnet motor system comprises a fault-tolerant permanent magnet motor, a signal detection circuit, an isolation drive circuit, a fault-tolerant power drive circuit, a DSP system and an FPGA system;
- the DSP system comprises a speed loop controller, a fault-tolerant controller and a sensorless resolving module, and the DSP system is configured for speed loop control, the calculation of a fault-tolerant current given instruction, the conditioning of an estimated inductance signal, and the resolving of a rotor position and a speed based on differential mode inductance of two phase windings of the system;
- wherein the FPGA system comprises a current A/D sampling control module, a current loop controller, a PWM generator module, a high-frequency signal generator, a digital bandpass filter, a digital notch filter, an envelope detection algorithm module, a data transmission module and a fault diagnosis module, and the FPGA system is configured for the A/D sampling control, the current loop control, the high-frequency voltage signal injection and the corresponding signal processing for sensorless control, PWM signal generation and system fault diagnosis;
- the sensorless control method in low-speed region comprises the following steps:
- step 1:
- injecting the high-frequency sinusoidal voltage signals;
- the high-frequency sinusoidal voltages are injected into any two non-faulty phase windings of the motor by superimposing digital high-frequency sinusoidal signals onto given voltages of two corresponding phases acquired by a current loop, wherein the high-frequency voltages applied on the two phase windings are expressed as follows:
- {
- U
- A
-
- h
- =
- V
- h
-
- sin
-
- (
- ω
- h
-
- t
- +
- φ
- A
- )
- U
- B
-
- h
- =
- V
- h
-
- sin
-
- (
- ω
- h
-
- t
- +
- φ
- B
- )
- ,
- (
- 1
- )
- where UAh, UBh respectively represent the high-frequency voltages applied on terminals of non-faulty phase windings A and B of the motor, Vh is the amplitude of the injected high-frequency voltage, ωh is the frequency of the injected high-frequency voltage, and φA, φB represent the initial phase of the injected high-frequency voltage;
- according to the high-frequency approximate voltage model of the fault-tolerant permanent magnet motor, the high-frequency voltages are expressed as follows:
- {
- U
- A
-
- h
- =
- L
- A
-
- (
- θ
- r
- )
-
- d
-
-
- i
- A
-
- h
- d
-
-
- t
- U
- B
-
- h
- =
- L
- B
-
- (
- θ
- r
- )
-
- d
-
-
- i
- B
-
- h
- d
-
-
- t
- ,
- (
- 2
- )
- where LA(θr), LB(θr) respectively represent the self-inductances of the winding A and the winding B, θr represents the electrical angle of the rotor, and iAh, iBh represent the high-frequency response currents of the winding A and the winding B, respectively;
- from equations (1) and (2), the high-frequency response currents are solved and expressed as follows:
- {
- i
- Ah
- =
- F
- A
-
- (
- 2
-
-
- ω
- r
-
- t
- )
-
-
- sin
-
-
- (
- ω
- h
-
- t
- +
- φ
- 1
-
- (
- ω
- r
- )
- )
- i
- B
-
-
- h
- =
- F
- B
-
- (
- 2
-
-
- ω
- r
-
- t
- )
-
-
- sin
-
-
- (
- ω
- h
-
- t
- +
- φ
- 2
-
- (
- ω
- r
- )
- )
- ,
- (
- 3
- )
- where FA(2ωrt) and FB(2ωrt) respectively represent the amplitudes of the high-frequency response currents of phase A and phase B, ωr is the electrical angular velocity of the rotor, and these parameters have the following approximate relationship with the self-inductances of the winding A and the winding B:
- {
- 1
- F
- A
-
- (
- 2
-
- ω
- r
-
- t
- )
- =
- ω
- h
- V
- h
-
- L
- A
-
- (
- 2
-
- ω
- r
-
- t
- )
- 1
- F
- B
-
- (
- 2
-
- ω
- r
-
- t
- )
- =
- ω
- h
- V
- h
-
- L
- B
-
- (
- 2
-
- ω
- r
-
- t
- )
- ;
- (
- 4
- )
- step 2:
- designing the digital notch filter and the digital bandpass filter in the FPGA system according to the frequency of the injected high-frequency voltage signal;
- the designed digital notch filter is configured to filter out the high-frequency current response components in the current loop control signal and is designed according to the frequency of the injected high-frequency voltage signal;
- and the digital notch filter has a stop band in a very small frequency band near ωh and the amplitude attenuation greater than 50 dB at ωh, and has almost no amplitude attenuation in other frequency bands and no phase lag;
- the designed digital bandpass filter is configured to extract the high-frequency response currents, and has a pass-band in the frequency band near ωh and a sufficiently high order for ensuring sufficient attenuation of the stop band;
- both the digital notch filter and the digital bandpass filter have the sufficient bandwidth and have the sampling frequency fs meeting the following condition:
- fs>2fPWM (5),
- where fPWM is the PWM chopping frequency;
- step 3:
- detecting the actual currents of the winding A and the winding B by the signal detection circuit, and acquiring the high-frequency response currents iAh and iBh of the winding A and the winding B by the digital bandpass filter;
- step 4:
- extracting the amplitude signals FA(2ωrt) and FB(2ωrt) of the high-frequency response current signals iAh and iBh by performing the envelope detection thereon respectively, specifically as follows:
- in a digital system, the high-frequency response current signal input in the envelope detection is expressed as follows:
- f(nTs)=F(nTs)cos(ωhnTs+φ(nTs))=FI(nTs)cos(ωhnTs)−FQ(nTs)sin(ωhnTs) (6),
- where F(nTs) represents the amplitude signal of the high-frequency response current, FI(nTs) is the in-phase component, FQ(nTs) is the quadrature component, n represents the nth sampling point, and Ts represents the sampling period;
- a mixing process is performed, in which the sine and cosine signals with amplitude 2 and frequency ωh generated by a digitally controlled oscillator are respectively multiplied with the input high-frequency response current signal, and a low-pass filtering process is performed, in which a product signal resulted in the mixing process is processed by a low-pass filter;
- after the mixing process and the low-pass filtering process, the following results are acquired:
- {
- I
- =
- LP
-
- F
-
- (
- f
-
- (
- n
-
- T
- s
- )
- ·
- 2
-
- cos
-
- (
- ω
- h
-
- n
-
- T
- s
- )
- )
- =
- F
- I
-
- (
- n
-
- T
- s
- )
- Q
- =
- L
-
- P
-
- F
-
- (
- f
-
- (
- n
-
- T
- s
- )
- ·
- 2
-
- sin
-
- (
- ω
- h
-
- n
-
- T
- s
- )
- )
- =
- F
- Q
-
- (
- n
-
- T
- s
- )
- ,
- (
- 7
- )
- where I represents the in-phase component of the amplitude signal F(nTs), Q represents the quadrature component of the amplitude signal F(nTs), and LPF ( ) represents the process by a low-pass filter;
- the processed signal is then subjected to square sum and square root operations and the following result is acquired:
- √{square root over (I2+Q2)}=√{square root over (FI(nTs)2+FQ(nTs)2)}=F(nTs) (8);
- consequently, the amplitude information of the input signal is extracted after the process with the envelope detection algorithm;
- step 5:
- acquiring the estimated differential mode inductances and of the winding A and the winding B by conditioning the amplitude signals FA(2ωrt) and FB(2ωrt) of the high-frequency response current signals;
- by the equation (4), estimated the self-inductances of the winding A and the winding B are acquired by taking the inverse of FA(2ωrt) and FB(2ωrt) and multiplying the inverse by an appropriate gain, wherein the self-inductance comprises a common mode component and a differential mode component;
- then the estimated differential mode inductances are acquired by measuring the common mode component of the self-inductance and subtracting the common mode component from the self-inductance;
- and finally the estimated differential mode inductances are properly filtered to filter out the interference signals;
- step 6:
- resolving the estimated rotor electrical angular frequency and the double estimated electrical angle 2 by inputting the estimated differential mode inductances and of the non-fault phase windings A and B into the non-orthogonal phase-locked loop, which is composed of a phase detector, a loop filter and a voltage-controlled oscillator;
- wherein the estimated differential mode inductance signals and change at the double rotor angular frequency in one sine cycle, including the speed and position information of the fault-tolerant permanent magnet motor;
- and are non-orthogonal with a phase difference of 120°;
- the error related signal between the estimated phase of the input signal and the actual phase of the input signal, i.e., the rotor position estimation error related signal, is acquired by processing two input estimated inductance signals with the phase detector of the non-orthogonal phase-locked loop;
- and the following equation is satisfied for the phase detector output PLLerr and the rotor position estimation error signal θerr:
- PL
-
- L
- e
-
- r
-
- r
- =
- ·
- cos
-
- (
- 2
-
- θ
- ^
- -
- 2
-
- π
- 3
- )
- -
- ·
- cos
-
- (
- 2
-
- θ
- ^
- )
- =
- 3
- 2
-
- L
-
- sin
-
- (
- 2
-
- θ
- e
-
- r
-
- r
- )
- ≈
- 3
- 2
-
- L
- ·
- 2
-
- θ
- e
-
- r
-
- r
- ,
- (
- 9
- )
- where θerr represents the error between the estimated rotor position and the actual rotor position, L is a constant characterizing the amplitude of inductance signal;
- the loop filter of the non-orthogonal phase-locked loop uses a PI controller, the rotor position estimation error-related signal PLLerr input into the loop filter is PI-modulated, and the double estimated rotor electrical angular frequency 2 and thus are acquired after the modulating becomes stable;
- the double estimated electrical angle 2 is acquired by processing the 2 by an integrator of the voltage-controlled oscillator of the non-orthogonal phase-locked loop;
- and the PI parameters of the PI controller of the loop filter are the design parameters of the non-orthogonal phase-locked loop, and the PI parameters need the reasonable design and tuning for ensuring the stability and rapidity of the non-orthogonal phase-locked loop;
- step 7:
- discriminating the polarity of the rotor permanent magnet of the fault-tolerant permanent magnet motor based on the acceleration, resolving the estimated electrical angle of the rotor, and performing the fixed compensation for the estimated rotor position;
- it is necessary to discriminate the polarity of the rotor permanent magnet for determining , due to the possible presence of a deviation of 180° between the value acquired by dividing the double estimated electrical angle 2 resolved by the non-orthogonal phase-locked loop by 2 and the actual rotor position;
- the discrimination of the polarity of the rotor permanent magnet is performed only when the motor is started;
- the fixed compensation is performed on the estimated rotor inductance acquired from the phase-locked loop for ensuring control accuracy, since the phase of the estimated differential mode inductance signal lags behind the actual value due to the use of the filter.