Real- -time Self Compensating AC/DC time Self Compensating AC/DC - - PowerPoint PPT Presentation

Fusion Digital Fusion Digital Fusion Digital Fusion Digital

Real Real-

• time Self Compensating AC/DC

time Self Compensating AC/DC Digitally Controlled Power Supply Digitally Controlled Power Supply

Dave Freeman, Mark Hagen Texas Instruments Digital Power Group

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Fusion Digital Fusion Digital Fusion Digital Fusion Digital

12Sep06

Digital Control Digital Control

• Problem: Determining optimal loop

compensation given uncertainties of:

• line, load and temperature variation
• component tolerance, parasitics
• step response
• Solution: Utilize the processing power of a

digital controller digital controller to measure the transfer function

• f the loop and from this measurement make

adjustments to the digital compensation coefficients.

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Transfer Function Measurement Transfer Function Measurement

• To perform Transfer Function Analysis (TFA) we

need to:

– Generate a sinewave excitation signal – Inject that signal at a summing junction – Capture the response of the system to the excitation

• From this response, calculate the open loop gain

– From the open loop gain determine key performance metrics of bandwidth, gain margin and phase margin.

• For a digitally controlled system the logical

location to make the measurement is just before

• r just after the digital compensator.

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Measurement Locations Measurement Locations

• Inject a sinewave at

d1 or d2

• Measure response at

node e, x, c or u

• Solve for GH

G(s) power stage H(z) digital compensator

• e

y' u'

digital controller ADC PWM

u y d2 d1 x r

y r e d e x Hx c d c u Gu y − = + = = + = =

1 2 2 1 2 1 2 1 2 1 2 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 d GH G d GH GH r GH e d GH G d GH r GH x d GH GH d GH H r GH H c d GH GH d GH H r GH H u d GH G d GH GH r GH GH y + − + − + = + − + + + = + − + + + = + + + + + = + + + + + =

Given the following basic system equations: The closed loop response for each node is

c

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Gain Gain calc's calc's for various nodes for various nodes

• Note that the formula for calculating open loop gain contains

the compensator gain H(f) if the system is excited before the compensator and measured after, or vice-a-versa.

• This is not a big problem since a digital compensator is

completely deterministic and its frequency response can be calculated as:

GH GH + 1 GH H + 1 GH H + 1 GH + 1 1 GH GH + − 1 GH G + 1 GH + 1 1 GH GH + − 1 GH G + − 1 GH G + − 1

d2 d1 e x c u y measure at inject at d2 d1 e x c u y measure at inject at

Y D Y −

1

1

1

− u Hd 1

1

− c Hd 1

1 −

x d e d e + −

1

Hy d Hy −

2

1

2 −

u d c d c + −

2

Hx d Hx + −

2

He d He + −

2

Transfer gains at each node: Calculation of open loop gain G(f)H(f) from measurements at each node:

( ) ( ) ( ) ( )

2 1 2 2 1 2

sin cos exp a z a z b z b z b f H T f j T f T f j z

meas s meas s meas s meas

+ + + + = + = = 2π 2π 2π

(for a 2nd order compensator)

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Sinewave Generation Sinewave Generation

• Use table look-up technique

– TI digital controllers, including the UCD9501, have a build-in sinewave table in ROM. – For each sample step through the table with a step size defined as – When the end of the table is reached, wrap to the beginning of the table by subtracting the table length from the index. – By maintaining the fractional part of the table index and rounding to determine the table entry, very high frequency resolution can be obtained.

step tableIndex tableIndex F N step

table

+ = = then

rate sample meas

F

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Response Measurement Response Measurement

• The definition of a Discrete Fourier Transform (DFT) is:
• This says that we can calculate the real and imaginary

magnitude of the kth harmonic of a signal by multiplying that signal by a sine and cosine sequence and summing.

• Since we've already generated a sinewave to inject into

the loop as the excitation signal, the response measurement is simply:

uCosSum += u*bcos; // Accumulate cosine // sum for measurement node u uSinSum -= u*bsin; // Accumulate sine // sum for measurement node u

(Note that the cosine sequence is easily generated by adding an offset to the sine table index of 1/4 the table length.)

( )

∑ ∑

− = − = −

              −       ⋅ = ≡

1 1 /

2 sin 2 cos

N n n N n N nk j n k

n N k j n N k v e v K π π

2π

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Example Calculation of Example Calculation of G( G(f f)H( )H(f f) )

G(s) power stage H(z) digital compensator

• e

y' u'

digital controller ADC PWM

u y dcos r

Inject at d2, measure at c Return cosSum and sinSum for each injected excitation frequency. Calculate open loop gain as follows:

c

z-1 z-1

dsin cosSum sinSum G(s) power stage H(z) digital compensator

• e

y' u'

digital controller ADC PWM

u y dcos r

( ) ( )

( )

2 2 2 2 2 cos 2

2 2 /

i r r r r i r i r r r

C C C D D C jD C C c D sinSum j cosSum D N sinSum j cosSum c d c GH + + + − + + − = ⋅ + + ⋅ + − = + − =

Inject at d1, measure at e

x

z-1 z-1

dsin cosSum sinSum

Then plot magnitude and phase of G(f)H(f) to determine phase margin and bandwidth

( ) ( )

( )

2 2 2 2 2 cos 2

2 2 /

i r r r r i r i r r r

E E E D D E jD E E E D sinSum j cosSum D N sinSum j cosSum e d e GH + + + − + + − = ⋅ + + ⋅ + − = + − =

Where Dcos is the base to peak amplitude

• f the excitation and N is the # samples.

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Practical TFA measurements Practical TFA measurements

• Windowing

– The definition for the DFT produces the response just at harmonic frequencies. These frequencies produce an integer number of cycles in the measurement interval. At other frequencies you need to do something to reduce "leakage".

• 1. Window the measurement data. A raised cosine or triangle

window are popular options.

• 2. Modify the measurement interval so that an integer number
• f cycles are measured. (What we implemented.)
• Settling

– We want just the forced response, so the controller needs to wait some number of samples for the natural response to decay.

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TFA Physical Implementation TFA Physical Implementation

Fully Digitally controlled Telecom Rectifier

• 48V-1000W output, 85V-260V 50/60 Hz input
• Interleaved Boost PFC stage
• Phase shifted full-bridge DC/DC stage

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Rectifier Schematic Rectifier Schematic

Digital Controller

• Implements 3 loops (PFC current, PFC voltage and DC/DC

voltage), plus current sharing between PFC phases.

• Sequencing, Soft start/stop and OC/OV/UV.
• Manages serial interface and performs TFA.

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Self Self-

• Measured Bode Plots

Measured Bode Plots

• PC program issues serial bus commands to

measure response at a given frequency.

– command defines

– frequency – amplitude – number of samples to delay – number of samples to measure

– controller returns

– cosine and sine coefficients for that frequency

• Repeated from start to stop frequencies to

produce Bode plot for each loop

• Calculate plant transfer function and use this to

explore effect of changes in compensation.

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TFA (Bode) Design Tool TFA (Bode) Design Tool

Status Digital coefficients Update coefficients based on PID gains Update coefficients based on analog poles & zeros magnitude plot Select control loop Select which part of the loop to display Transfer Function Analysis (measure Bode) BW gain margin phase margin phase plot

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Self Self-

• Compensation

Compensation

• Inject excitation signal at desired system BW frequency.
• Use adaptError = (Dcos + Cr•4/N) to locate the zero dB cross-over.
• Adjust compensator gain (numerator coefficients)

to zero adaptError.

• Calculate phase margin to check system stability.

Recall from sheet 8 that

2 2 2 2 2 2 2 2 2

2 2

i r r r r i r i r r r r i r r r

C C C D D C D j C C C D D C C C D c d c GH + + + − + + + + + − = + − =

( ) ( )

2 2 2 2 2 2 2 2

2 atan

i r r r r i r i r r r i r

C C C D D C C C D C GH mag C C C D C D GH phase + + + + = + − =         + + =

then Rearranging the equation for magnitude, at the zero dB cross-over frequency

( )

1 2

2 2 2 2 2

= +         − = +

i r r r r

C C mag mag C D D

10

3

10

4

10

5

• 3
• 2
• 1

1 2 3 freq normalized magnitude

• penloop gain

adaptError cosSum/N sinSum/N

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Summary Summary

• Digital Power enables sophisticated

characterization of each controlled power stage in situ (in place)

• Thus enabling (in order of complexity)

– No-test-equipment-required measurement during product development – Simplified manufacturing test – Auto tuning/customization during manufacturing – Auto tuning and customization in the end-equipment application

• Account for aging, changes to the end use system.
• Digital control enables multiple compensation settings:

standby, low-power, full load, etc. Each optimized in situ.