Deciding the algorithm for tracking

[gary36]

I am currently trying to understand the concept of resolver to digital conversion from the web. After going through datasheets and appnotes,i concluded that companies use two algorithms for resolver to digital conversion, Viz.. Lead compensator on double integrator plant or Angle tracking converter.

The lead compensator based system has open loop TF = (k/s^2)* (s+a)/(s+b) and Angle Tracking observer has open loop TF = (k1+k2/s)*k3/s

How does one choose the control algorithms? I can see the both the implementations in place. Please explain the merits and demerits for each one

 

[D.A.(Tony)Stewart]

My quick overview of this paper

Angle Tracking Observer with Improved Accuracy for Resolver-to-Digital Conversion​

which you may have read is as follows;

1. ATO has higher complexity but greatly reduces position error for disturbances with acceleration, jerk and higher orders and may be called a type IV compensator.
2. The 2nd tradeoff is ATO has a slower response and longer settling time than Type II compensators but reduced noise and tuning sensitivity. .

So it depends on your application requirements for position error vs disturbances and noise on acceleration and what fits your time & budget. ATO has more benefits but more cost. and skill required.

 

[gary36]

Angle tracking converter is simple. It is a second order system. Lead compensator produces 3rd order system which May be complicated

 

[D.A.(Tony)Stewart]

Angle tracking converter is simple. It is a second order system. Lead compensator produces 3rd order system which May be complicated

I have the opposite understanding, the ATC has more complex processes.

A 3rd order lead comp, is just a simple RC lead-lag compensator to increase phase margin near 0dB by partial differentiation.

Review the conclusions.

Angle Tracking Observer with Improved Accuracy for Resolver-to-Digital Conversion

A resolver is an absolute shaft sensor which outputs pair signals with ortho-symmetric amplitudes. Ideally, they are sinusoidal and cosinusoidal functions of the shaft angle. In order to demodulate angular position and velocity from resolver signals, resolver-to-digital conversion (RDC) is...

www.mdpi.com

 

[aliarifat794]

An angle tracking observer might be more suitable if your application requires high accuracy at low speeds or precise tracking without phase lag.

 

[D.A.(Tony)Stewart]

The main benefit of ATC's is low position error at high acceleration and higher orders (jerk etc)
The bandwidth limitation is relative to the implementation speed limits of an embedded uC for servo control. Since the ATC has a 2nd order derivative, the sampling rate must be much higher to null the position error of acceleration.

 

[gary36]

Then why do classical resolver to digital converter from analog devices such as AD2S83 and other variants implement lead compensator ?

 

[KlausST]

Hi,

Then why do classical resolver to digital converter from analog devices such as AD2S83 and other variants implement lead compensator ?

I´m no expert in this.
But isn´t the phase lead to compensate for the processing time?

My idea:
There is one point of time where the position is captured.
... then there is a delay for the data to be processed (within the sensor or even in your application)
during this processing time the real position still advances.
So wihtout the compensation you get the position at the "time of capture" ..
But with compensation you get the (estimated) position at the "actual time"

Klaus

 

[D.A.(Tony)Stewart]

I had built a phase resolver using quadrature PLL's in the late 70's.
All PLLs and SMPS voltage servos may choose to implement phase Lead compensation ( partial derivative to boost phase or gain margin in the loop.

Classic resolvers use analog VCO's and phase detectors. ATC is all digital.

The AD2S83 is an analog servo with a VCO driving counter, and is reset or synchronized with an index pulse ( or North signal) using the ripple carry out counter pulse. The VCO tracks the motor velocity with 0 error using the index or North pulse and sin/cos to lock phase of each counter step but has position error with acceleration. ( classical control theory rules) .

The Angle Track Converter is a modern version using digital "Hall" matrix transforms that are far more complex and might be done with a high-end uC and DSP.

 

[garimella]

I just simulated the transfer function for the two algorithms. I observed that the lead compensator had a better attenuation for odd harmonics (if the reference is 50Hz), whereas Angle Tracking observer had less attenuation. With a Lead compensator , the closed loop transfer function becomes 3rd order and tuning for specifications such as required bandwidth and zeta becomes tedious. An angle tracking converter's characteristic equation matches with 2nd order system and hence it is easy to tune( App note AN1942). But it is very poor with respect to harmonic distorsion of the reference signal.