selecting parameters for ATO

[garimella]

I was referring to the article AN1942, which gives comprehensive information about ATO with results. But I was unable to correlate how these coefficients relate to dynamic specifications such as tracking rate, acceleration constant , small signal bandwidth and resolution. I would like to know the method to fix wn which meets the customized dynamic specifications listed above. Please explain the procedure to do so

[xiangjun_rong]

Hi, Vishnu,

For the ATO, the AN1942 is the only application note, we have not the other application note to address the subject, I think the parameters wn and ζ are defined based on customer application requirement. we have the angle tracking observer library, I attach the user guide of the library.

Hope it can help you

BR

Xiangjun Rong

[garimella]

Hi xiang

I was interested to understand how ATO algorithm converges to zero with resolver signals as per the article. This is because in reality input theta can never equal angle phi. What was the work around applied to ATO to address this problem?

[xiangjun_rong]

Hi, Vishnu,

Regarding the question how ATO algorithm converges to zero with resolver signals, it is dependent on the transfer function, because the ATO system transfer function is EQ 3-7 based on 1942, if the pole point are all located at the left part of S field, the system is stable, which means that system can converge to zero from any error initial value, in other words, assume the G(s)=W**2/[(S+S1)(S+S2)], if the real part of S1 and S2 are positive, the system can converge to zero.

Hope it can help you

BR

XiangJun rong

[garimella]

Hi xiang,

Let me explain the problem in detail. ATO error converges to zero for ideal noise free resolver signals, whose amplitude and phase are balance. This I could simulate it matlab and get the results (based on AN1942). Now I created non idealities such as harmonic distortion, amplitude imbalance and quadrature phase shifts, which brings about lot of inaccuracies in measurement. AN1942 does not address mitigation of this very problem. I was interested to know a) Solution to overcome this problem and b) any hysteresis is provided in error amplifier to prevent output oscillations. Hope I am clear in my question

[MarMi]

Hi Vishnu,

AN1942 presents numerical algorithm and provides basic guidance on how user can tune it to get required dynamic performance as well as it shows some experimental results.

In order to get the best performance out of this algorithm, you need to supply algorithm with sine and cosine resolver waveforms that free of amplitude and offset variations. The basic pre-processing could be detecting max and min values of both sine and cosine waveforms and computing gain and offset factors for each of the waveform. It can be done on the fly or just as the initial calibration for given resolver type - up to user to decide.

I don't have any immediate suggestions on how to compensate for quadrature phase shift and / or harmonic distortion. 

Kind regards,

Martin M.

[garimella]

Hi Martin

Basically, I am looking for the information that correlates the tracking rate(RPS) vs the Rotor reference frequency vs coefficient settings.  Example if ref frequency is 1 KHz , what would be the max RPS possible and what are corresponding values of K1 and K2 ?.

[MarMi]

Hi Vishnu,

actually limitation of tracking speed for given sampling rate comes from fractional representation; refer to equation: EQ 4-19 and Table 4-2. There is an older version of the application note with additional details archived here: DSP56F80x Resolver Driver and Hardware Interface - PDF.

Imagine that rotor ramps up to rotate at constant speed. Because rotor speed is observed through an error accumulation then such observed speed should reach a steady state (causing input error equal to zero) while observer constants (~integration gain) impacting the time when steady state is reached but not bringing any limitations with regard to the observable speed value.

The maximum and minimum speeds are only limited by fractional representation on the contrary to observer constants defining dynamic response of the system. 

Kind regards,

Martin M.

[garimella]

Hi

Martin

I did go through the link provided by you and in the latest version of AN1942. These are my observations

1. ATO is a second order LPF with -20dB/decade. The cut off frequency is fixed based on noise filtering requirements. In case where damping ratio is 0.707 natural frequency wn= cut off frequency wc. The question is how to fix wc? ( basis for fixing 500rad/s or 1200 rad/sec as mentioned in AN1942 is not very clear)

2. Any tracking system is characterized by accleration constant Ka , tracking rate and resolution . This factor does not appear in the equation, but gives extensive implementation from software point of view. Suppose a customer requirement is recieved to meet Ka of 10000rad/s-^2, frequency response of 100Hz and Tracking rate of 50rps ( 12 bit resolution), how do we configure the driver software to meet this new specfication?

3. You have mentioned that there are no limitations with respect to tracking rate, but ATO being a second order filter should have a cut of rate( owing to group delay) beyond which it looses tracking. This point is not addressed.

regards

Vishnu

[MarMi]

Hi Vishnu,

Responses for 500 & 1200 rad/s were chosen to demonstrate dynamic behavior of the slower and faster tracking to the reader.

Your question was "What would be the max RPS possible and what are corresponding values of K1 and K2". Max RPS are limited indeed by fractional range and sampling rate (EQ 4-19). You are right, with regard to loosing tracking for given speed ramp to be dependent on tracking observer settings. 

In our app note, we don't go beyond natural frequency and damping factor computing meaning that we don't deal on how to compute in analytical / numerical way these parameters. I don't have any simple analytical solution to this problem that I could share with you.   

Kind regards,

Martin M.

[garimella]

Hi Martin

Thank you for the response. Analytically I found that tracking rate is limited to the frequency response of a second order filter to a ramp input. Since ramp has atleast 10 times the fundamental, filter cut off should be so designed to accomodate 10*f to ensure distorsion free signal at the output. For example 100RPS tracking requirements (100Hz ramp) contains upto 1KHz component and 2nd order 3-dB point should lie beyond this value.

Finally is the full source code for the resolver driver sharable?

regards

Vishnu

[MarMi]

Hi Vishnu,

thanks for sharing your findings.

The app note describes first library released +15 years ago. The most up to date code base was included in motor control libraries for DSC that are available from Real Time Control Embedded Software Motor Control and Power Conversion Libraries|NXP .

Kind regards,

Martin M.