Delay compensation for stable current regulation when using variable-delay random PWM switching

[0001] The present invention relates to power converters and, more particularly, relates to a current regulation system used to compensate for the delay introduced by variable-delay random pulse width modulation.

[0002] Random pulse width modulation (RPWM) is recognized as a desirable technique to reduce both electromagnetic and acoustic noise emissions from pulse width modulation (PWM) inverters. RPWM is generally characterized by random variations of the switching frequency. The random variations of the frequency alleviate undesirable characteristics in PWM electronic power converters. Specifically, the fundamental AC component harmonics remain unchanged. However, the spectral power, measured in Watts, is converted to continuous power density, measured in Watts per Hertz, instead of being concentrated in discrete harmonics. The power spectra of the output voltage and current from a RPWM power converter emulate the spectrum of white noise. Consequently, spurious phenomena are significantly mitigated.

[0003] Additionally, conventional variable-delay random pulse width modulation (VD-RPWM) may also be used for various applications to further alleviate undesirable characteristics. In fact, the variable-delay random PWM technique provides a number of significant advantages over other RPWM techniques.

[0004] Known prior art systems have demonstrated the excellent EMC performance of true random switching frequency modulation techniques where both the sampling and PWM periods are synchronized. However, these RSF systems suffer from a significant disadvantage, namely the maximum code size is limited by the minimum sample period. Furthermore, the random sample rate places a constraint on the minimum sample period based upon the required time to execute the application code. For complicated motor control algorithms, the length of code may not allow sufficiently high switching frequency to achieve good spectral spreading.

[0005] Fixed sample rate techniques, on the other hand, allow optimal use of the processor computational capability. For example, random zero vector, random center displacement, and random lead-lag techniques all maintain synchronous sample and PWM period, but suffer some form of limitation. For example, random zero vector and random center displacement lose effectiveness at high modulation indexes. Random lead-lag does not offer suitable performance with respect to reducing acoustic/EMI emissions and, further, suffers an increased current ripple. Additionally, both random lead-lag and random center displacement introduce an error in the fundamental component of current due to a per-cycle average value of the switching ripple.

[0006] The VD-RPWM technique allows a fixed sample rate for optimal usage of processor computational power, while providing quasi-random PWM output for good spectral spreading.

[0007] However, conventional VD-RPWM suffers from disadvantages when operated at high fundamental frequencies. For example, using a 4-pole induction machine with a maximum speed of 14 krpm, the highest fundamental electrical frequency is 467 Hz. In this situation, using a 12 kHz sample rate, conventional VD-RPWM techniques provide satisfactory control. On the other hand, when used with induction machines having eight or more poles, the highest fundamental electrical frequency may exceed 800 Hz. In these cases, the delay introduced by VD-RPWM may cause undesirable instability.

[0008] Accordingly, there exists a need in the relevant art to provide a modified VD-RPWM technique that is capable of overcoming the instability associated with the use of VD-RPWM with machines having high fundamental electrical frequencies (e.g. 500 Hz or higher) and limited sample rate (e.g. 12 kHz). Furthermore, there exists a need in the relevant art to provide a delay compensation technique to generate stable current regulation when using VD-RPWM. Still further, there exists a need in the relevant art to provide a modified VD-RPWM technique that overcomes the disadvantages of the prior art.

[0009] According to the principles of the present invention, a control system for an electric machine is provided having an advantageous construction. The control system includes a rotor position sensor that generates a rotor position signal, a velocity module that generates an electric angular velocity value based on the rotor position signal, a random pulse width modulation module that generates a switching period and a delay for a current cycle, and a phase angle compensation module that sums a sample rate, one half of the switching period, and the delay of a previous cycle and that outputs a delay time. The phase angle compensation module further multiplies the delay time and the electric angular velocity value and generates a compensating angle.

[0010] Further areas of applicability of the present invention will become apparent from the detailed description provided hereinafter. It should be understood that the detailed description and specific examples, while indicating the preferred embodiment of the invention, are intended for purposes of illustration only and are not intended to limit the scope of the invention.

[0018] The following description of the preferred embodiment is merely exemplary in nature and is in no way intended to limit the invention, its application, or uses. As used herein, the term “module” refers to an application specific integrated circuit (ASIC), an electronic circuit, a processor (shared, dedicated, or group) and memory that execute one or more software or firmware programs, a combinational logic circuit, and/or other suitable components that provide the described functionality.

[0019] As discussed above, conventional variable-delay random pulse width modulation (VD-RPWM) provides a number of significant advantages over other RPWM techniques. According to conventional VD-RPWM, the sample rate (input), T_samp, remains constant while the PWM output period, T_sw, is randomly varied from T_sw—min to 2*T_samp, where T_sw—min is the minimum PWM switching period to be allowed and T_samp is the sample rate. This wide range in PWM output period provides excellent spectral spreading in many cases for improved modulation.

[0020] However, in applications having high fundamental electrical frequency and limited sample rate (for example, fundamental electrical frequencies above about 500 Hz with 12 kHz sample rates), conventional VD-RPWM techniques may exhibit significant control problems. In other words, in these cases, the additional delay introduced by conventional VD-RPWM becomes more critical and can cause instability.

[0021] It is undesirable to vary the sample rate (input) T_samp, since maintaining a constant sample rate offers many advantages. For example, many of the coefficients used in digital controllers are sample time dependent. By maintaining fixed sample rates, the need to recalculate coefficients every time the PWM period is changed is eliminated. Additionally, by maintain fixed sample rates, the time required for software execution remains fixed. This permits predictable and optimized usage of the microprocessor's capability and capacity. In other techniques that have variable sample rates, the maximum code length is limited by the minimum sample period. This may be a significant drawback in many applications.

[0022] Therefore, according to the principles of the present invention, a control system or algorithm is used compensate for the delay introduced by the VD-RPWM algorithm on a cycle-by-cycle basis to alleviate such control instability. This control system or algorithm is based on a fixed sample rate (input). The algorithm introduces a random delay into the trailing edge of the next PWM output cycle. Therefore, because two consecutive edges determine the PWM output period, a quasi-random PWM output is created.

[0023] Referring to FIG. 1, a schematic representation of a fixed frequency PWM algorithm is illustrated. More particularly, a sample sequence is defined along timeline A having samples S₁, S₂, S₃, S₄, and S₅. Similarly, a PWM output sequence is defined along timeline B having cycle edges P₁, P₂, P₃, P₄, and P₅. A voltage command V₁* is calculated between samples S₁ and S₂ using the sample information obtained at S₁. The PWM output for the command V₁* is implemented during the next period, namely between P₂ and P₃. Conventionally, the average output voltage occurs in the center of the period between P₂ and P₃. Hence, the time from S₁ to the average output of V₁* is 1.5 sample periods, or 1.5 T_samp. In fixed frequency applications, such as that illustrated in FIG. 1, the delay compensation does not vary with time. For the waveforms produced in connection with the schematic of FIG. 1 with no delay (i.e. Δt₁=Δt₂=0), the usual phase angle compensation is given by equation (1):
Δθ_fixed—freq=1.5T_sampω_e  (1)

[0024] Turning now to FIG. 2, a schematic representation of a variable-delay random PWM algorithm is illustrated. More particularly, a sample sequence is defined along timeline A having samples S₁, S₂, S₃, S₄, and S₅. Similarly, a PWM output sequence is defined along timeline B having cycle edges P₁, P₂, P₃, P₄, and P₅. In this case, the PWM output periods are not of fixed length. As described above in connection with FIG. 1, the voltage command V₁* is calculated between samples S₁ and S₂ using the sample information obtained at S₁. The PWM output for the command V₁* is then implemented during the next period, namely between P₂ and P₃. However, in this case, P₂ and P₃ are shifted or delayed as shown.

[0025] With reference to the voltage command V₂* computed between S₂ and S₃, the corresponding PWM output occurs between P₃ and P₄. The delay, T_delay, from the sample time S₂ to the middle of the PWM switching period T_sw is given as:
T_delay=T_samp+Δt₁+0.5T_sw  (2)

[0026] The generic equation for the delay, T_delay, is:
T_delay=T_samp+Δt*Z⁻¹+0.5T_sw  (3)

[0027] The algorithm of the present invention is to be utilized as part of a synchronous frame current regulator for motor drive applications. According to the present invention, the PWM delay is changed every sample period. For this reason, the delay compensation must be updated based upon the next delay value and PWM period as follows:
Δθ_VDRPWM=(T_samp+Δt* Z⁺¹+0.5·T_sw)ω_e  (4)
The compensating angle Δθ VDRPWM given in equation (4) is added to the measured rotor position, θ_r, prior to performing the synchronous to stationary transformation on the voltage commands. This compensation accounts for the rotation of the machine from the time the position and current are sampled to the time the voltage command is implemented by the power inverter or control system.

[0028] As best seen in FIG. 3, a block diagram of a control system 10 according to the present invention is illustrated. The input to control system 10 includes synchronous reference frame current commands, i_dqs^e* 42. Current commands 42 are compared to measured synchronous reference frame currents i_dqs^e* 44 using a summer 12. Summer 12 outputs an error signal 46, which is passed to a synchronous frame PI current regulator 14. The output of current regulator 14 is a synchronous reference frame voltage command V_dqs^e* 48. A synchronous to stationary reference frame transformation block 16 then uses the output of summer 30 for the transformation angle to generate stationary frame voltage commands V_dqs^s* 50. A random PWM block 20 generates a delay time, Δt, and switching period, T_sw, needed to implement the variable-delay random PWM technique.

[0029] A PWM inverter 18 processes the stationary frame voltage commands and the delay and switching period from random PWM block 20 to generate a PWM voltage output 52 to be applied to a motor 22. A sensor 24 measures the rotor position θ_r of motor 22. However, it should be understood that in addition to measuring, rotor position θ_r may be estimated. Sensor 24 may be a rotor position sensor that, when used in synchronous machine, outputs a measured position. A derivative of the measure position may be used to determine the corresponding speed or angular velocity. Similarly, sensor 24 may be a position sensor as described or an angular velocity sensor, which is used to integrate to determine the corresponding speed.

[0030] As can be seen, only two phase currents are measured, while a third is calculated from the two measured quantities. A 3-to-2 transformation block 26 is used to convert the phase a, b, c currents to equivalent two-phase components i_dqs^s 54. A transformation module 28 uses the rotor position and converts the stationary reference frame currents i_dqs^s to the synchronous reference frame currents i_dqs^e 44. Block 32 represents the phase angle compensation block, which implements the phase angle compensation computed in equation (3). More particularly, block 34 is a unit delay (delay of T_samp). A gain block 36 scales the switching period T_sw by ½. The summer 38 is used to compute the delay time 39, T_delay. The output of summer 38 is multiplied by the electrical angular velocity ω_e 41 to determine the phase angle compensation. The output of block 32, namely a compensating angle Δθ _VDRPWM 58, is added to the rotor position, θ_r by summer 30. The output of summer 30, namely a transformation angle 56, is then used in the synchronous-to-stationary transformation of the voltage commands at synchronous to stationary reference frame transformation block 16.

[0031] While the block diagram is shown for synchronous type machines, a similar diagram can be obtained for asynchronous machines by including the slip angle calculation. In this case, the delay compensation is still added to the angle used in the synchronous-to-stationary transformation.

[0032] To demonstrate the effectiveness of the present invention, laboratory tests were conducted utilizing a 600 V/600 A power inverter with floating point processor and an inductive load. VD-RPWM was implemented in the software. The sample rate was set to 11.1 kHz (90 usec). The fundamental electrical frequency was set to 800 Hz. To test the dynamic response, the q-axis current command was given a step input of 20→40 A. Ideally, the q-axis current would respond quickly with no overshoot, and there would be no cross-coupling into the d-axis. It should be noted that the PI regulators had the appropriate decoupling for the inductive load. Current regulator bandwidth was set to 4600 rad/sec. Referring to FIG. 4, a response is illustrated where no delay compensation is utilized (i.e. prior art system). As can be seen, a lightly damped response with overshoot and ringing is observed. This is caused by the delay which is not being compensated in the control.

[0033] Similarly, as seen in FIG. 5, the fixed delay compensation given in equation 1 is applied. This results in a drastic improvement in the transient response. However, overshoot in the q-axis current is visible, and there is still cross coupling into the d-axis.

[0034] Finally, as seen in FIG. 6, the compensation technique according to the present invention as set forth in equation 5 is employed. The transient response is almost ideal in this case. The q-axis regulator has no overshoot, and there is no visible cross coupling into the d-axis. This experiment demonstrates the effectiveness of the present invention.

[0035] The present invention provides a number of advantages over the prior art. By way of non-limiting example, the present invention provides a method of maintaining control stability of high speed motors. Additionally, by facilitating RPWM operation at high speed, EMI emissions are reduced, thereby requiring smaller filtering requirements. Smaller filtering requirement consequently lead to reduced overall size, reduced cost, and lower weight. Still further, the present invention leads to reduced acoustic noise. This is particularly important when lower switching frequency is used in that it results in lower switching losses in the inverter when operating at low speeds.

[0036] Those skilled in the art can now appreciate from the foregoing description that the broad teachings of the present invention can be implemented in a variety of forms. Therefore, while this invention has been described in connection with particular examples thereof, the true scope of the invention should not be so limited since other modifications will become apparent to the skilled practitioner upon a study of the drawings, the specification and the following claims.