Digital Control of Power Electronics Course Manual Index

©ELMG Digital Power, Inc. 601 E Daily Drive, Ste 112, Camarillo CA 93010 www.elmgdigitalpower.com 805 764 2027

Introduction to Advanced Digital Control of Power Electronics

August 22

2016Course Manual for the ELMG Digital Power Digital Control of Power Electronics Course

For Course Attendees Only


Contents Contents ................................................................................................................................ 2

1. Table of Figures .......................................................................................................... 11

2. Introduction to this course .......................................................................................... 13

Steve Waugh and Control .................................................................................................................................... 13

3. The extremely short quick history of control ............................................................... 15

Steam Engines, James Watt and the Governor ............................................................................... 15

Lyapunov – Mathematics of Dynamical Systems ............................................................................ 15

Hendrik Bode, Harry Nyquist and a guy called Harold Black ........................................................... 15

Bode Plots .................................................................................................................................... 15

Nyquist Diagrams ......................................................................................................................... 16

Harold Black, the ferry and the most important invention of the twentieth century. ...................... 16

............................................................................................................................................................................. 16

“Trust me – connecting the output to the input will make things better” .......................................................... 16

Russian control engineers to fore from 1950 to 1980 ..................................................................... 16

Digital control of power electronics ............................................................................................... 17

1980s saw last major theoretical control progress. ........................................................................ 17

4. Control FAQs .............................................................................................................. 18

What it control? ........................................................................................................................... 18

What control is not? ..................................................................................................................... 18

What it cannot do? ....................................................................................................................... 18

What it can do? ............................................................................................................................ 18

What it will always do................................................................................................................... 19

5. Block diagrams – the language of control ¿hablas control? ......................................... 20

Why block diagrams – control transfers ......................................................................................... 20

Things to watch out for with block diagrams ................................................................................. 21

Some examples ............................................................................................................................ 22

Voltage divider in block diagram format ........................................................................................ 24

6. Frequency responses – the magic of seeing everything all at once ............................... 26


Some frequency responses ........................................................................................................... 27

7. Domains and you ....................................................................................................... 35

What is a domain? ........................................................................................................................ 35

The Australian Domain ................................................................................................................. 35

The time domain – keep the brick wall in mind .............................................................................. 35

The frequency domain - jω and seeing colours............................................................................... 36

The s-domain – the complete transient frequency domain ............................................................. 36

The z-domain – enter the computer .............................................................................................. 37

The modified z transform .............................................................................................................. 37

The delta transform - the δ domain ............................................................................................... 37

So a journey through the domains ................................................................................................ 37

8. Key control concepts and words ................................................................................. 39

Transfer or Transfer Function ........................................................................................................ 39

Gain ............................................................................................................................................. 39

Phase ........................................................................................................................................... 39

Plant ............................................................................................................................................ 39

Compensator or Controller ........................................................................................................... 39

Demand or Input .......................................................................................................................... 39

Output ......................................................................................................................................... 40

Forward Transfer .......................................................................................................................... 40

Open Loop .................................................................................................................................... 40

Closed loop .................................................................................................................................. 40

Feed forward ................................................................................................................................ 40

Feedback ...................................................................................................................................... 40

Error............................................................................................................................................. 40

Disturbance .................................................................................................................................. 41

Linear ........................................................................................................................................... 41

Non- Linear................................................................................................................................... 41

Operating point ............................................................................................................................ 41


Poles ............................................................................................................................................ 41

Zeros ............................................................................................................................................ 41

The complex plane for the s-domain ............................................................................................. 42

The right half plane (RHP) for the s-domain ................................................................................... 42

The complex plane for the z-domain ............................................................................................. 42

The Unit Circle .............................................................................................................................. 42

Why the Controller is called K?...................................................................................................... 43

Why the plant is called G? ............................................................................................................. 43

9. Some more key concepts ............................................................................................ 43

The control band .......................................................................................................................... 43

Crossover ..................................................................................................................................... 43

Above crossover ........................................................................................................................... 43

Gain Margin ................................................................................................................................. 43

Phase Margin ............................................................................................................................... 44

Minimum phase. .......................................................................................................................... 44

10. Controllers you will meet and their frequency responses. ............................................ 44

The PI ........................................................................................................................................... 44

The PID......................................................................................................................................... 45

The Zeigler Nichols control rules ................................................................................................... 46

The I ............................................................................................................................................. 46

The P ............................................................................................................................................ 47

The LP or proportional plus low pass. ............................................................................................ 48

The P + Resonant .......................................................................................................................... 49

The recursive-predictive-“learning filter” controller ....................................................................... 49

11. Loop Shaping Control Design ...................................................................................... 50

12. What are the cold dark, wake you up at night, feedback control truths? ..................... 53

The lower the loss, the lower the stability, the more the power converter behavior will vary and so

the harder the control problem. .................................................................................................... 53

In feedback without the error there is no control .......................................................................... 53


The model you have of your power converter is not ever accurate enough. ................................... 54

Why you need plant bandwidth, why you never have enough and what to do about it................... 54

Why you need gain, why you never have enough and what to do about it. .................................... 54

What to do about it – remember the one equation to rule them all. .............................................. 54

www.ElmgDigitalPower.com ............................................................................................... 58

13. Enter the power converter .......................................................................................... 59

Why Power Converter Control Transfer Modeling wastes your time? And what to do about it? ...... 60

The solution to modeling inaccuracy is measurement. ................................................................... 63

14. How to make Manual Measurements ......................................................................... 63

How your MCU/DSP can make its own measurements. .................................................................. 66

Using an analyzer to make some measurements ........................................................................... 67

Trust, but verify ............................................................................................................................ 68

Do I need to make the measurement closed loop or open loop? .................................................... 68

Is it minimum phase? .................................................................................................................... 69

15. Measuring FAQs ......................................................................................................... 69

My converter is unstable in the open loop what shall I do? ............................................................ 69

Which operating points shall I start with?...................................................................................... 69

Do I need to do all operating points? ............................................................................................. 70

Why is no load and low load so different? ..................................................................................... 70

My synchronous rectifiers turn on and off during the measurement at one operating point. Is this

OK? .............................................................................................................................................. 70

Do I turn my synchronous rectifiers on or off? ............................................................................... 70

Do my synchronous rectifiers change gain and bandwidth? ........................................................... 71

How do I measure phase when the gain is 1/100? ......................................................................... 71

When should I do a manual measurement? ................................................................................... 71

How do I do a manual measurement? ........................................................................................... 71

What gear do I need to do a transfer measurement? ..................................................................... 72

I think there is a phase shift in my code that does the measurement. How do I check if there is? ... 72

16. Why you should design the Power Converter with control in mind. ............................. 73


Control checklist at design time .................................................................................................... 73

Sufficient Bandwidth ........................................................................................................................................... 73

Sufficient Linearity ............................................................................................................................................... 73

Minimal Crossover frequency variation............................................................................................................... 73

What happens if the converter has too little bandwidth, is too non-linear and has too much

crossover variation? ..................................................................................................................... 74

17. Why power converters non-linearity is really no problem? .......................................... 75

Operating points and gain changes ................................................................................................ 75

Operating point changes and bandwidth changes .......................................................................... 84

Operating point and mode changes ............................................................................................... 84

Low loss rectifiers. ........................................................................................................................ 84

Feed forward for disturbance rejection ......................................................................................... 84

Dead time compensation .............................................................................................................. 84

18. Linearizer FAQs .......................................................................................................... 84

Is linearizing simply gain scheduling? .................................................................................................................. 84

Will the linearizer work with the production variation of the converters? ......................................................... 85

How can a periodic signal do lineariastion? ........................................................................................................ 85

Why is the linearized variable different to the operating point variables? That is we linearize duty cycle but

write the operating point in terms of Vout over Vin? ......................................................................................... 85

I am going to linearize and do feedforward disturbance cancellation. Are there any issues with this. ............. 85

Can I do control without a linearizer? ................................................................................................................. 85

What should the variation be after the linearizer is in the system? ................................................................... 85

How smooth should my linearizer be? ................................................................................................................ 85

I am going to implement my linearizer as a lookup table in software. Are there any other ways? ................... 85

My linearizer is a bit innacuate. Does this matter? ............................................................................................ 86

I have curve fitted a polynomial linearizer but have two areas where it is not so accurate. Will this matter and

if so how do I fix it? .............................................................................................................................................. 86

My feedforward lineriser gain depends on the output of my power converter. How do I analyse the stability

of this? ................................................................................................................................................................. 86

19. Digital Controller ........................................................................................................ 87

How to choose the number of bits for the ADC .............................................................................. 87

How to choose the dynamic range for the ADC .............................................................................. 87

How to choose the ADC ................................................................................................................ 88

How to choose the signal conditioning .......................................................................................... 88

Choosing the Op-amp in the signal conditioning ............................................................................ 88


What if I cannot have an Op-amp .................................................................................................. 88

Choosing the processor – how much power? How many MIPS? ..................................................... 89

Timer Precision – why it does not matter too much ....................................................................... 89

The Unit Circle and Pole Zero Plots ................................................................................................ 90

Useful pole zero combinations and frequency responses ............................................................... 91

Integrator ............................................................................................................................................................. 91

Differentiator ....................................................................................................................................................... 92

High pass filter ..................................................................................................................................................... 93

Low pass filter ...................................................................................................................................................... 95

Lead ................................................................................................................................................................... 100

Lag ...................................................................................................................................................................... 101

Complex poles and zeros ................................................................................................................................... 102

20. Implementing these responses on your MCU/DSP ..................................................... 106

21. Where digital control is different .............................................................................. 108

Anti Aliasing filters ..................................................................................................................... 108

Bandwidth limited ...................................................................................................................... 108

Delay .......................................................................................................................................... 108

Impulse noise ADC noise ............................................................................................................. 110

Precision limitations ................................................................................................................... 110

Just because you can doesn’t mean you should. Rate limits ......................................................... 110

Flexibility.................................................................................................................................... 111

Configurability ............................................................................................................................ 111

Testability .................................................................................................................................. 112

Verification ................................................................................................................................ 112

Where digital control is the same ................................................................................................ 112

22. How to design a digital controller for your converter ................................................ 113

Follow the steps ................................................................................................................... 113

Choose number of ADC bits .................................................................................................. 113

Choose ADC ......................................................................................................................... 113

Choose processor based on target bandwidth and processing to get processing delay below 10

degrees. ..................................................................................................................................... 113

Assume 3 second order blocks for DC to DC. ......................................................................... 113


Assume 3 second order blocks and one repetitive filter or 8 second order blocks for AC to DC.

113

Increase the precision of the VPO/PWM with the accumulate value auto dither. ................... 113

Measure the plant transfer. ................................................................................................. 113

Measure this for the eight initial test operating points. ......................................................... 113

Review and analyse these measurements. Linearize if necessary. ......................................... 115

Complete the measurements for the complete operating point map. .................................... 115

Review and analyse these measurements. Linearize again if necessary. ................................ 115

Design the loop controller by loop shaping using pole zero placement in z plane and bode plots

115

Partition the controller function into second order blocks ..................................................... 115

Implement the control blocks in code ................................................................................... 115

Verify the control block transfers implement the frequency transfers required by measuring

them. ......................................................................................................................................... 115

Check the stability and output ripple at all operating conditions. .......................................... 115

23. Additional Resources ................................................................................................ 116

The ELMG Way ........................................................................................................................... 116

Sign Up for Our Newsletter ......................................................................................................... 116

Membership at the Digital Control group on LinkedIn .................................................................. 116

How to guides for sale ................................................................................................................ 116

The How to Measure Power Converter Transfers Guide ................................................................................... 116

How to Linearize your Power Converter Guide ................................................................................................. 116

Onsite Training Courses and Online and Homestudy Training courses .......................................... 117

Introduction to Digital Control of Power Electronics Training Course .............................................................. 117

Power Electronics and Control Mentoring ........................................................................................................ 117

www.ElmGDigitalPower.com ............................................................................................ 119

24. MIMO systems and where they occur in power electronics........................................ 122

1.1 Current sharing in DC to DC converters .............................................................................. 122

1.2 AC connected inverters with real and reactive power control ............................................ 122

25. Representing MIMO systems .................................................................................... 123

26. An example MIMO system to think about ................................................................. 124


1.3 The household shower with two taps ................................................................................ 125

1.4 Control objectives ............................................................................................................. 125

1.5 Control approaches .......................................................................................................... 125

1.6 Connecting showers in parallel .......................................................................................... 125

27. Possible approaches to dealing with MIMO using SISO techniques ............................ 126

Approach 1 ................................................................................................................................. 126

Approach 2 Diagonalise .............................................................................................................. 126

Simply Closing SISO loops – The servo control approach .............................................................. 126

28. MIMO Summary ....................................................................................................... 126

29. Back to Block Diagrams and Bode plots – sensitivity functions and robustness .......... 127

The internal model controller ..................................................................................................... 127

Model reference control ............................................................................................................. 131

Model predictive control MPC ..................................................................................................... 131

Sensitivity functions ................................................................................................................... 132

Using sensitivity functions .......................................................................................................... 132

Why use them- sensitivity functions give Fundamental limits of control ....................................... 133

Robustness analysis .................................................................................................................... 133

30. The Physical basis of stability ................................................................................... 135

Gain margin ................................................................................................................................ 136

Phase margin .............................................................................................................................. 136

How stable is stable enough? ...................................................................................................... 137

What low losses means to stability ................................................................................................................... 137

31. Stability FAQs ........................................................................................................... 137

The forward transfer has more than one place where the phase crosses -180 degrees. What does this mean

and what do I do about it? ................................................................................................................................ 137

What gain margin is enough? ............................................................................................................................ 138

What phase margin is enough? ......................................................................................................................... 138

Can I measure and ensure stability at automated test? .................................................................................... 138

32. Additional Resources ................................................................................................ 139

The ELMG Way ........................................................................................................................... 139

Sign Up for Our Newsletter ......................................................................................................... 139


Membership at the Digital Control group on LinkedIn .................................................................. 139

33. How to guides for sale .............................................................................................. 139

The How to Measure Power Converter Transfers Guide ................................................................................... 139

How to Linearise your Power Converter Guide ................................................................................................. 139

34. Onsite Training Courses and Online and Homestudy Training courses ....................... 140

Introduction to Digital Control of Power Electronics Training Course .............................................................. 140

Power Electronics and Control Mentoring ........................................................................................................ 140

www.ElmGDigitalPower.com ............................................................................................ 142


1. Table of Figures Figure 1 Harold Black invented feedback stabilized amplifiers on a boat travelling across the Hudson River. .......... 16

Figure 2 Regulator control block diagram. G is the Plant, K is the controller and Gd the disturbance transfer, input

is r and the output is y. ................................................................................................................................................ 20

Figure 3 Control transfer blocks for an impedance and an admittance. ..................................................................... 21

Figure 4 Transfers with dimensions prevent order of blocks being changed .............................................................. 22

Figure 5 Feedback block diagram ................................................................................................................................ 23

Figure 6 The regulator arrangement of a feedback system. ....................................................................................... 23

Figure 7 Feedback control block diagram – regulator form. ....................................................................................... 24

Figure 8 Typical controller structure for power electronics ........................................................................................ 24

Figure 9 Voltage divider circuit .................................................................................................................................... 25

Figure 10 Feedback equivalent of a voltage divider .................................................................................................... 25

Figure 11 Frequency response showing gain and phase for a power converter. The top curve is the gain and the

bottom curve is the phase. The figures 120V78A describe the voltage and the current and indicate the operating

point. ........................................................................................................................................................................... 27


bottom curve is the phase. Note that the curves are different from the figure above. This is due to the different

operating point. ........................................................................................................................................................... 28


bottom curve is the phase. Once again the operating point is different so the curves are different. ....................... 29

Figure 14 Frequency response of power converter and controller using AP instruments analyzer. "The Ray Ridley

Box." ............................................................................................................................................................................ 30

Figure 15 Transfer of power converter. Self measurement using DFT in the DSP controller. ..................................... 30

Figure 16 Frequency response of power converter, unit delay, PI controller. Produced with Sci Lab ....................... 31

Figure 17 Low pass filter response .............................................................................................................................. 31

Figure 18 Impedance of EMC filter. ............................................................................................................................. 32

Figure 19 Impedance of EMC filter with increased system impedances ..................................................................... 33

Figure 20 Frequency response of power converter inner current loop. ..................................................................... 34

Figure 21 In the time domain all the information comes at once. This makes the brick wall difficult to deal with. .. 36

Figure 22 PI Controller frequency response ................................................................................................................ 45

Figure 23 PI Frequency response (I gain is 1/10 of the above) .................................................................................... 45

Figure 24 PID Controller .............................................................................................................................................. 46

Figure 25 Integral Controller ....................................................................................................................................... 47

Figure 26 Proportional P Controller ............................................................................................................................. 47

Figure 27 Low pass filter controller ............................................................................................................................. 48

Figure 28 Proportional +Resonant Controller .............................................................................................................. 49

Figure 1 Problems with power converter model with bad estimate of capacitor ESR ................................................ 61

Figure 2 Model problem fixed after measurement ..................................................................................................... 62

Figure 3 Typical power converter model inaccuracy ................................................................................................... 62

Figure 4 Requirements for a network analyser are a signal source with variable signal frequency and magnitude

and the ability to measure the input and output. ....................................................................................................... 63

Figure 5 Simple control transfer measurement tools. (The human brain provides the interface to the computer.) 64

Figure 6 Connection of analyser. DC bias adjust sets operating point. ...................................................................... 65


Figure 7 Typical analogue controller with connection point shown............................................................................ 65

Figure 8 Eight initial operating points for measurements ........................................................................................... 70

Figure 9 Schematic of Digital Control - The power converter is the DAC .................................................................... 87

Figure 10 Precision Extension for PWM and NCOs and VPOs ..................................................................................... 90

Figure 11 Extended precision PWM or VPO. By accumulating the lost bits the total precision is retained. .............. 90

Figure 12 Integrator frequency response .................................................................................................................... 91

Figure 13 Integrator Poles and zeros ........................................................................................................................... 91

Figure 14 Digital filter implementation and difference equation .............................................................................. 106

Figure 15 Second order block implementation. ........................................................................................................ 107

Figure 16 Suggested operating points for first measurements ................................................................................. 114

Figure 1 Classic Transfer form of MIMO system ........................................................................................................ 123

Figure 2 Alternate V Form of MIMO representation. (G values in this diagram are not the same as those in the

transfer form) ............................................................................................................................................................ 124

Figure 3 Classic controller view of control problem with controller K and reference shaping P. ............................. 128

Figure 4 By replacing the controller K with a feedback controller with a model of the plant in the feedback, the

sensitivity to the plant variation can be determined. ............................................................................................... 128

Figure 5 Internal model controller that allows sensitivity of plant variation from nominal to be quantified. .......... 129

Figure 6 When the demand shaping P is removed the internal model controller shows the effect of plant variation.

................................................................................................................................................................................... 130

Figure 7 Weighted sensitivity function allows robustness to be quantified.............................................................. 134

Figure 8 Gain Margin and Phase Margin ................................................................................................................... 136


2. Introduction to this course So for me it all started with a guy named Professor Harsha Siresina. He was my under graduate control systems

lecturer at the University of Canterbury in Christchurch, New Zealand. He is a brilliant man and he knew, and

knows, lots about control. I choose to do my final year project in Non Linear Control Theory with him as my

supervisor. At the same time I was playing my guitar in a band and enjoying life. Control for me was an interesting

distraction full of philosophical questions and very few answers. For my project I got to work with Optimal Control

for Non-Linear Systems, even worked on Lyapunov functions and quickly realized why phase margin and gain

margins were so important.

“What are these Lyapunov things, how do I even pronounce that, and how are these margins relevant to my

unstable power converter?” You say.

You then say “What am I going to say to my impatient manager and his, even more impatient, manager?”

Well this course will show you just what you need to do to get your converter stable and doing what it should and

can. You will also get some polite things to say to your impatient manager.

Steve Waugh and Control

So if there was one thing to say about control it would be best said by quoting Steve Waugh, the famously

successful Australian cricket captain? Steve is a man of few words. He chooses his words and his moments for

those words well. Such is the legend of the man and his few words, that he is often credited with saying things

that he denies. One such denied quote is the legendary “Mate, You just dropped the World Cup” to Hershel Gibbs.

Steve has repeatedly denied saying this. Some say he did say it.

However Steve Waugh did comment after winning the World Cup. He said that South Africa lost and Australia won

because toward the end of the game South Africa stopped trying to play well and started trying to win.

If Steve Waugh was a control engineer of some experience, having closed many control loops, stabilized many

converters and reduced output ripple below the specified value many times he would say

“Mate, you just dropped the World Cup”

Or maybe

“…but test cricket is generally all about good line and length. There are no magic formulas to winning.”

Date post:	16-Apr-2017
Category:	Engineering
Upload:	hamish-laird
View:	109 times
Download:	1 times

Digital Control of Power Electronics Course Manual Index

Engineering