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PAGE 1 High Performance Digital Control IEEE APEC 2016 Long Beach March, 2016 Hamish Laird ELMG Digital Power
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PAGE 1
High Performance Digital Control
IEEE APEC 2016
Long Beach
March, 2016
Hamish Laird
ELMG Digital Power
PAGE 2
Outline for today
●Introduction ● Component Parts of Power Converter Control ● Power Converter Control Blocks
PAGE 3
Digital Control System ● Introduction
● Power Converter Control Blocks
● Modulators ● Digital VPO performance ● Precision in VPOs – Extending, improving and correcting resolution ● Digital PWM performance ● Correcting in PWM ● Extending PWM precision.
● Compensators ● Unit Circle and Pole Zero Plots ● Useful pole zero combinations ● Pole zero placement – where to put them. ● Implementing these pole zero combinations ● A good filter structure.
● More compensators ● IIR Biquads – number of bits ● Filter coefficients from pole zero placements ● Digital Integrators
● Do I have precision and resolution problems? ● How to determine this?
● How to fix this resolution problem?
● Analogue to digital converters ● Single sample noise
● Anti aliasing filters ● Cutoff frequencies and orders
● Summary
PAGE 4
About Hamish Laird
●CTO at ELMG Digital Power
●Power Electronics Career ● Induction Motor Drives ● Induction Motor Starters ● DC drives (analogue) ● HVDC and SVC ● Medical Devices – motor drives ● Household appliances ● Active Filters ● Medium voltage ● UPS ● Brushless DC drives
●All digital control ● Except analogue ● Microprocessors ● DSP ● FPGA
PAGE 5
Modulators
●Modulator
●PWM
●VPO
●Any modulator is a Harmonic Generator
●Both PWM and VPO are nonlinear
PAGE 6
Compensator
●Filter that ensures that connecting the system output to the system is useful and stable
●Usually low pass
●Useful means error is small
PAGE 7
Analogue to Digital Converter
●Samples analogue.
●Multiplies two signals ● Train of impulses ● Feedback
●A2D is a modulator
●Aliasing can happen – spectrum out is not the same as the spectrum in
PAGE 8
Anti Aliasing Filter
●Low pass filter
●Prevents Aliasing
●Makes A2D linear
PAGE 9
●Typically has a low pass filter characteristic
●Prevents aliasing
Power Converter
PAGE 10
Modulators
●Two kinds covered today
●Variable Period Oscillation ● For resonant power supplies
●Pulse Width Modulator ● Pulse modulator
PAGE 11
●Quantization in modulators
Modulators – Quantization
PAGE 12
VPO
PAGE 13
Oscillators (VPO)
●Example ● 10 MHz clock ● 250kHz out ● Count is 40
●For count of 41
●Out is 243,902 Hz
●For count of 39
●Out is 256,410 Hz
PAGE 14
VPO- characteristics
PAGE 15
VPO- characteristics
PAGE 16
VPO – characteristics
●For 100MHz clock
●715 counts is 9.48 bits
Count Frequency out Hz
285 350,877
1000 100,000
PAGE 17
VPO – Characteristics
●For 1000MHz clock
●7143 counts is 12.8 bits
Count Frequency out Hz
2857 350,017
10000 100,000
PAGE 18
VPO – Characteristics
●Effect of VPO error in feedback control
●Dead-band non linearity
●Slip strike behavior ● Typically requires more bandwidth in compensator
PAGE 19
PWM – Characteristics
PAGE 20
PWM – Characteristics
●Clock Frequency 10MHz
●PWM carrier frequency 25kHz
●Counter maximum = 10MHz/25kHz = 400
●Number of bits is 8.64
On Time Counts Duty On time
400 100% 40us
274 68.5% 27.4us
1 0.25% 0.1us
PAGE 21
PWM – Characteristics
●Clock Frequency 100MHz
●PWM carrier frequency 25kHz
●Counter maximum = 100MHz/25kHz = 4000
●Number of bits 11.96
On Time Counts Duty On time
4000 100% 40us
2740 68.5% 27.4us
1 0.25% 0.01us
PAGE 22
PWM – Characteristics
●Clock Frequency 1000MHz
●PWM carrier frequency 25kHz
●Counter maximum = 100MHz/25kHz = 40000
●Number of bits 15.28 bits
On Time Counts Duty On time
40000 100% 40us
27400 68.5% 27.4us
1 0.025% 0.001us
PAGE 23
PWM Characteristics
●Clock Frequency 1MHz
●PWM carrier frequency 25kHz
●Counter maximum = 1MHz/25kHz = 40
●Number of bits is 5.32
On Time Counts Duty On time
40 100% 40us
27 67.5% 27us
1 2.5% 1us
PAGE 24
Modulators Characteristics
●Spectra of PWM or VPO with quantization
PAGE 25
PWM – Characteristics
●Effect of quantization resolution error in feedback system
●Step non linearity
●Creates slip strike behavior
PAGE 26
Modulators error correction
●Resolution correction gives precision extension
●Resolution in VPO and PWM from timer precision.
●We know the quantization of the modulator
●So we know the error of each switching instant
●We can correct for the error on the next switching cycle
●In the long term we can apply the correct volt seconds.
●How to implement.
PAGE 27
How to correct errors
PAGE 28
Modulators error correction
●How it works
●1 sample at 14 and 1 sample at 15 for average of 14.5
Input Input + previous difference
Output Difference
14.5 14.5 14 0.5
14.5 15 15 -0.5
14.5 14.5 14 0.5
14.5 15 15 -0.5
14.5 14.5 14 0.5
14.5 15 15 -0.5
PAGE 29
Modulators error correction
●For a different value
●Three at 14 and one at 15 for an average of 14.25
Input Input + previous difference
Output Difference
14.25 14.25 14 0.25
14.25 14.5 14 0.25
14.25 14.75 14 0.25
14.25 15 15 -0.75
14.25 14.25 14 0.25
14.25 14.5 14 0.25
14.25 14.75 14 0.25
14.25 15 15 -0.75
14.25 14.25 15 0.25
PAGE 30
Modulators error correction
●Error correction or precision increase is spectral control
PAGE 31
Modulators error correction
●Error correction or precision increase is spectral control
PAGE 32
Modulators spectral effects
●Frequency components with error correction
●Without error correction
Input 0Hz Fs/2 Fs/4
14.5 14.5 0.636 0
14.25 14.25 0.318 0.448
Input 0Hz Fs/2 Fs/4
14.5 14 0 0
14.25 14 0 0
PAGE 33
Modulators –spectral control
PAGE 34
Modulators spectral control
●Simplest
PAGE 35
Modulators error correction
●How to code it
●difference[n]= input[n] – output[n]
●output[n] = input[n] + difference[n-1]
PAGE 36
●Increase filter order for less noise in the control band
Modulators - spectral control
PAGE 37
Modulators – spectral control
●H(z) = (1-z-1)N
●Often plotted on linear frequency scale
PAGE 38
Modulators – spectral control
●H(z) = (1-z-1)N
●Attenuates noise in the converter pass band
●Typically converter bandwidth target is 1/10th to 1/5th of the switching frequency
PAGE 39
Modulators – spectral control
●H(z) = (1-z-1)N
●Log Scale plot gives better insight
PAGE 40
Modulators error correction
●How many more bits?
●Frequency dependent ● At 0Hz get pre-quantization number of bits. ● At Fs/2 get no accuracy.
PAGE 41
Modulators – Summary
●Quantization in PWM and VPO modulators leads to white noise generation in control band.
●Fix this with a simple accumulate and correct.
●Use first order system with 1 delay. ● Typically need no more.
●Second or higher order if you really need to. ● Be careful – watch for its effect on the transient response.
●2nd order in our PWM IP Core block
●Because power converter, compensator and anti aliasing filter are all low pass ● High frequency noise is attenuated by the rest of the loop.
PAGE 42
Modulators error correction
●“This really works.” - Tomek Kotula
●Resolution corrected modulation: the practical realisation of ideal PWM waveforms. Boys and Handley - Electric Power Applications, IEE Proceedings B (Volume:139 , Issue: 4 ) 1992 (IET)
PAGE 43
Summary
●Modulators have low number of bits
●Increase the number of bits with precision extension
●Accumulate the error to correct the next switching
●Works with ● VPO for variable frequency converters ● PWM for pulse modulated converters
PAGE 44
Second Half Introduction
●Digital Control Design ● No analogue translation
●Unit circle
●Digital control blocks – a library
●Compensator form ● IIR Biquad ● Second order
●Design example ● Loop shaping ● Filter coefficients
●Things to watch out for
●Single sample noise
●Anti aliasing filters
PAGE 45
Digital controller design
●A way to design compensator frequency response directly in the digital domain.
●No analogue translation.
PAGE 46
Unit Circle – Poles and Zeros
●z Domain
●The unit circle
●Poles and Zeros in the digital domain
●Stability in z domain poles inside unit circle
●Zeros can be outside unit circle ● Avoid zeros outside unit circle.
●Laplace transforms uniqueness does not apply to the z domain
PAGE 47
Pole Zero combinations
●In analogue control design we use known frequency responses to create compensator
●Integrators
●Lead Lags
●Low Pass filters
●High Pass filters
●Let’s just do the same in the z domain
PAGE 48
Digital control blocks
●Useful digital blocks ● Integrator ● Differentiator ● Low pass filter ● High pass filter ● Lead ● Lag
●Some Others perhaps not so useful ● Complex poles and zeros
PAGE 49
Integrator
●Fs =
●Filter response continues above Fs/2
PAGE 50
Integrator
PAGE 51
Differentiator
PAGE 52
Differentiator
PAGE 53
High Pass Filter
PAGE 54
High Pass Filter
PAGE 55
Low Pass Filter
PAGE 56
Low Pass Filter
PAGE 57
Low Pass Filter
PAGE 58
Low Pass Filter
PAGE 59
Low Pass Filter
PAGE 60
Low Pass Filter
PAGE 61
High Pass Filter
PAGE 62
High Pass Filter
PAGE 63
Lead Lag
PAGE 64
Lead Lag
PAGE 65
Lag
PAGE 66
Lag
PAGE 67
Complex Poles and Zeros
PAGE 68
Complex Poles and Zeros
PAGE 69
Complex Poles and Zeros
PAGE 70
Complex Poles and Zeros
PAGE 71
Complex
PAGE 72
Complex
PAGE 73
Compensator design
●Compensator design is now ● Loop frequency response shaping
●Use one, two or three of the cookbook blocks to implement ● Integrator ● Lead Lag ● Low pass
●Shape the loop
●Pole and zero positions give compensator coefficients
●Compensator form?
PAGE 74
Digital filter implementation
PAGE 75
Second order blocks
●Second order blocks ● Signal to noise is good for 16 bit mathematics. ● Easy to find precision, resolution or quantization
problems.
PAGE 76
Second order blocks
●Useful precision is retained
●Usually good enough for what power electronics control requires (with care)
●Set a0 to -1 normalizes the filter.
PAGE 77
No analogue design
●fs/2 = 10kHz
●Plant measurement
●Made using the digital controller
PAGE 78
Direct Digital Compensator
●Add the integrator
●Scale to close the loop with reasonable margin
●Need an integrator gain of 1/4
PAGE 79
Get the poles and zeros
●Total loop with the integrator added
PAGE 80
Get the poles and zeros
●Integrator form
●Scale the basic integrator form to move the crossover frequency
PAGE 81
Get the poles and zeros
●Lead Lag pole and zero
PAGE 82
Lead Lag
●Lead Lag also
PAGE 83
Complete response
●Frequency response of the complete system
PAGE 84
Coefficients
●Zeros at -1 and 0.975
●Poles at +1 and +0.97
●Multiply out z polynomial to second order
●Divide top and bottom through by z2 to get delayed operator z-1.
Coefficient Value
b0 0.25
b1 -0.725
b2 -0.24375
a1 -1.972
a2 0.97
PAGE 85
All done?
●Increase the precision of the modulator
●Measure the plant frequency response
●Use the block cookbook to design the loop compensator
●Integrator and Lead Lag
●Implement these in a second order IIR biquad.
• Once you have the coefficients your compensator filter design work is only about 1/8 done!
• Usually OK but there are some things to check.
PAGE 86
Things to watch
●There is no a0 choice.
●As many poles as zeros
●Or less zeros than poles
●Precision! Quantization!
●Make the code so that the coefficients can be changed. ● Software engineer creates code for IIR biquad! ● Control design engineer designs compensator coefficients! ● Put the coefficients into the biquad.
●Verify that the filter blocks do what you need. ● Use an automated test harness
●Never never never tweak coefficients. ● a and b do not match directly to pole or zero positions
PAGE 87
Numeric precision ●Timer precision
● Effect of low precision ● Extending precision ● Things to watch out for with precision extensions.
●Extending precision ● Sigma delta approach ● Bandwidth limits ● Intermodulation
PAGE 88
Precision in filters ●Narrow bandwidth filter
●Low pass filter example
PAGE 89
Low pass filter example
PAGE 90
Quantization
PAGE 91
Poles and Zeros
PAGE 92
Low pass filter example
●Consider the case where input range is 40.96 Amps full range with 12 bits. 10mA per bit.
●16 bit maths – round to 16 bits.
●Put the A2D 12 bits in the MSBs
●b0 and b1 =1247
●At what coefficient precision do you lose accuracy?
●What about loss of function?
PAGE 93
Low pass filter continued
●Your control design engineer now suggests these filters instead
●What do you say?
●b0 and b1 are 5
●b0 and b1 are 78
PAGE 94
Low pass filter example 2
Input Digital Equivalent
b0 product b1 product Product Output
10mA 8 40 40 80 0
20mA 16 80 80 160 0
60mA 48 240 240 480 0
100mA 80 400 400 800 0
200mA 160 800 800 1600 0
600mA 480 2400 2400 4800 0
1A 800 4000 4000 8000 0
2A 1600 8000 8000 16000 0
6A 4800 24000 24000 48000 1
10A 8000 40000 40000 80000 2
20A 16000 80000 80000 160000 4
40.96A 32768 163840 163840 327680 10
PAGE 95
Low pass filter example 2
Input Digital Equivalent
b0 product b1 product Sum of Products
Output
10mA 8 632 632 1264 0
20mA 16 1264 1264 2528 0
60mA 48 3792 3792 7584 0
100mA 80 6320 6320 12640 0
200mA 160 12640 12640 25280 0
600mA 480 37920 37920 75840 2
1A 800 63200 63200 126400 3
2A 1600 126400 126400 252800 7
6A 4800 379200 379200 758400 23
10A 8000 632000 632000 1264000 38
20A 16000 1264000 1264000 2528000 769
40.96A 32768 2588672 2588672 5177344 1580
PAGE 96
Poles and zeros
●Second order blocks can have any poles and zeros from transfer function
●Look out for poles and zeros very close together – could you remove them?
●Poles and zeros definitely on top of each other should be cancelled.
●If you have two biquads spread the poles and zeros to minimize the quantization and precision loss.
PAGE 97
Precision vs dynamic range
●Direct trade off between quantization and saturation
●How much precision is enough?
● Second order block precision rules of thumbs – it will mostly be OK but check.
●Noise effect of saturation is the same as precision loss ● Consider letting things saturate but be careful
PAGE 98
Numeric Precision summary
• Once you have the coefficients for your compensator your design is only about 1/8 done!
• Usually OK.
• But • Check narrow band filters • Poles close to unit circle • Frequency response • Use a ramp to find places where LPF have problems
• Always • Work with biggest signals and biggest coefficients if possible • Check filter’s performance • Always CHECK it.
PAGE 99
Digital Integrators
●Classic digital integrator from process control is an accumulator
PAGE 100
Possible Digital Integrators
●Frequency response
PAGE 101
Digital integrator choices
●Sum only integrator has pole zero map
PAGE 102
Digital Integrator
●Better integrator has pole zero map
●Integrator has one pole and one zero
●Implement in biquad.
●Have spare pole and zero for something else.
●Most compensators need only one biquad!!!
PAGE 103
Choosing the Best Integrator
●Better integrator
●Attenuation at Fs/2 – this is good
PAGE 104
Implementing the Digital Integrator
●Use the biquad
●Put the pole and zeros into the biquad.
PAGE 105
Resolution integrators
●Lower crossover frequency
●b0=0.001 b1 = 0.001, a0 = -1
PAGE 106
Integrator Example
Input Digital In b0 product b1 product Sum of Products
Output
10mA 8 256 256 512 0
20mA 16 512 512 1024 0
60mA 48 1536 1536 3072 0
100mA 80 2560 2560 5120 0
200mA 160 5120 5120 10240 0
600mA 480 15360 15360 30720 0
1A 800 25600 25600 51200 0
2A 1600 51200 51200 102400 0
6A 4800 153600 153600 307200 9
10A 8000 256000 256000 512000 15
20A 16000 512000 512000 1024000 31
40.96A 32768 1048576 1048576 2097152 64
PAGE 107
Fixing integrators
PAGE 108
Analogue to digital converters
●A2Ds are clocked systems
●Power electronic switching is noisy
●In a microprocessor system have multiple clocks
●Some are PLL’d to each other ●All clocks jitter all the time.
●Can get single sample noise from the A2Ds when all the clock edges line up.
PAGE 109
Single Sample Noise
●What does it look like?
●Impulse response of closed loop – part digital part analogue
●This response is almost completely unrecognizable behavior in the output
PAGE 110
Single Sample Noise
●A true digital impulse
●System has all available energy of the power converter to put into the output ● Single sample noise issues often cause converter destruction. ● It might be the cause of your blow up.
●Input to modulator must be low pass filtered!!!!
●If you have single sample noise ● hopefully get reasonable occurrence rate – not too high not too low
●Find problem by looking at the digital stream. ● Build this feature into your converter controller.
●Solve problem by ● Dealing with the correlation ● Electrostatic shielding ● Change the A2D – qualify the A2D before you begin.
PAGE 111
Anti Aliasing Filters
●Always use anti aliasing filters ● Always
•Always
●Always design the anti aliasing filter
●Some of the filtering from the power converter
●Get the rest by adding lowest order filter possible
PAGE 112
Anti aliasing cutoff frequency
●Best case design rule ● Make the sampled ripple at the A2D input the same size as 1 LSB
change.
●Realistic Design Rule ● Choose the phase shift of the anti aliasing filter for stability ● Power converter phase shift ● Anti aliasing filter phase shift
PAGE 113
Anti aliasing filter tips
●Transient response shorter than the sampling time if possible
●First order RC normally enough
●Even if you are oversampling and have digital anti-aliasing filters use an analogue anti-aliasing filter
●For higher orders - well damped is best.
PAGE 114
Summary
●System
PAGE 115
Summary
●Modulators ● Effective numeric precision ● Quantization ● Correcting the precision ● Frequency weighting
●Compensators ● Block set of useful pole zeros combinations ● Direct digital design ● No analogue translation ● Second order blocks IIR biquads ● Coefficients of IIR biquad filters from poles and zeros
●Anti Aliasing Filter ● How to Design
●Single Sample Noise ● How to find ● Effects ● How to diagnose
PAGE 116
