Comparison of Digital Control Loops Analytical Models, …€¦ · Comparison of Digital Control Loops Analytical Models, Laboratory Measurements, and Simulation Results Phil Cooke

Comparison of Digital Control Loops Analytical Models, Laboratory

Measurements, and Simulation Results

Phil CookeRohan SamsiTom Wilson20 October 2009

Page 2 20 October 2009 IBM Power and Cooling Technology Symposium 2009

Outline

Application Circuit & IC Block Diagram

Control Loop Model, Design, and Analysis

PID Design – Analytical Design Procedure

Simulation & Experimental Circuit Schematics

Time-Domain Simulation Model vs. Experimental Results

Frequency Domain Comparison

Summary


Application Circuit

MOSFETGate DriverPX3511 or PX3515

Optional I2C/PMBusCompatible Connection

MinimalExternal PassiveComponents

Voltage and CurrentSensing Networks

ProgrammableFaults

Input Voltage Decoupling

Set Frequency and Output Voltage

SlaveAddress


IC Block Diagram

Internal“Brain”

“Controller”PIDPost FilterDPWM

PWMCommandtoMOSFETDriver

Internal“Memory”

VoltageFeedbackPath

CurrentFeedbackPath

Input & Output OVP, UVPPeak, Average, Current LimitInternal/Ext. Temp. Alert/Shutdown

TrimmedRef. & Oscillator

Mux. toFeed inVoltage,Current,& Temp.

To SyncConverters

EnableOutputs


Control Loop Model: Mostly Small-Signal

Transfer functionsin Continuous “s” orDiscrete “z” frequencydomains

Lumped Total DelayCan include delayfrom DPWM block

FeedbackGain1, 1/2, 1/3

OutputImpedanceTransferFunction

Line-to-OutputTransferFunction

Control-to-OutputPowerConverterAveragedModel


Control Loop Design – What Do We Want To Do

Loop Gain

Control-to-Output

Controller

Phase Boost

-180º

CrossoverFrequency


Control Loop Design – What Do We Want To Do

Control-to-Output

Controller

Phase Boost

-180º

CrossoverFrequency

and Gain Adjust

Loop Gain


Analysis: Small-Signal Equations

GC z =A az 2+bz+cz2−1+K FD z+K FD

=A [K I⋅1

1−z−1K P+K D⋅1−z

−1 ⋅ 11−K FD z

−1 ]

GZ1 z =n1 z+n0

z2+d 1 z+d 0H

Total Discrete Plantand FeedbackThese values(n

1, n

0, d

1, d

1, H)

are known

Discrete Controller

20log ∣GC zC GZ1 zC ∣=0 or ∣GC zC GZ1 zC ∣=1Solution:Solve at Crossover

∣T z ∣=∣GC z GZ1 z ∣Loop Gain



1. Select desired analog crossover frequency fC, this is the loop bandwidth,

and calculate system resonance fO

from the power converter reactive

components

2. Set the “analog” post filter pole, fPA2

, to 3·fC, and find K

FD

A reasonable starting range is from fPA2

= fC/2 to 3·f

C

KFD

is one of the following {0.125, 0.25, 0.375, 0.50, 0.625, 0.75, 0.875, 1.00} for the PX7510D

3. Start with fX = 0.85·f

O and Q

X = 0.7 for the controller zeroes and find the

required loop-gain (i.e., find α) to have T(z) crossover at fC

fX should be equal to or less (for design margin) than f

O, but not too low

4. Find α from: GZ1 z =n1 z+n0

z2+d 1 z+d 0H α=

∣n1 zC+n0∣

∣zC2 +d 1 zC+d0∣

HUsing



Where GZ1

is the total discrete plant and feedback gain

5. From the discrete controller transfer function, find β

6. Using pole-zero mapping (z=esT), along with the discrete crossover zC,

find γ

7. Solve for r using fX and Q

X in:

GC z =Aaz 2+bz+c

z2−1+K FD z+K FDβ=∣zC

2−1+K FD zC+K FD∣

z=es⋅T S zC=e

− jwC⋅T S wC=2πf C

1+s /Q X w X s /wX 2

z−zZN1 z−z ZN2

analog digital Find γ

Find β

r=e−π⋅f X⋅T S

/QX

maps toγ=∣zC−z ZN1∣.∣zC−z ZN2∣



8. Finally the a, b, and c controller terms are:

9. Alternatively, the KP, K

I, and K

D terms are:

a=β

α⋅γ⋅A

b=−2⋅a⋅r⋅cos [2⋅π⋅f X⋅T S⋅1−1/ 2⋅QX 2]

c=a⋅r2

K D=c

K I=a+b+K D

1−K FD

K P=a−K I−K D


Time-Domain Simulation Model

PX7510D IC Controller Model

SIMPLIS Simulation Circuit & IC Model

PX3511D Gate Driver

PowerConverter


Experiment Circuit Schematic

Integrated Driver and MOSFETs (PX4660)

Latest PX7510D Controller


Time-Domain Simulation vs. Experimental Results

5 A to 10 A Load Step

Imported Scope Data

SIMPLIS Simulation Model




Imported Scope Data





Imported Scope Data





Imported Scope Data



Experiment Results: Time-Domain

5 A to 10 A Load Step 10 A to 5 A Load Step

Actual Scope PlotsAll data was extracted to .csv file for comparison


Frequency-Domain Comparison: Original Design

fsw is theSwitchingFrequency

The MatLab modelshown here usesa more accuratedigital loop model


Frequency-Domain Comparison: Original Design

The MatLab modelshown here usesa simplifieddigital loop model

Both the gainand phase areless accurate atthe higherfrequencies


Frequency-Domain Comparison: Design Procedure

This is a moreaggressive design

More phase boostthroughout, highercrossover achievable

The MatLab modelshown here usesa more accuratedigital loop model


Summary

Understanding Digital Control systems requires control loop models - The behavior can be better appreciated by analytical analysis aided with computer simulation tools in the time and frequency domain to gain further insight


Summary


Models for a typical digital PID voltage mode controller was provided


Summary



A digital design procedure starting from analog frequency domain specifications was given using these models to calculate the controller PID coefficients


Summary




Comparison of the time and frequency data was made between the models and simulation results to the real experimental data, simulation tools can further the accuracy of the validation before designs are released to production


Summary




Comparison of the time and frequency data was made between the models and simulation results to the real experimental data, simulation tools can further the accuracy of the validation before designs are released to production

This represents a digital design example where all of the results are compared – this provides confidence that these systems are understood and designs can be robust using these approaches

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Comparison of Digital Control Loops Analytical Models, …€¦ · Comparison of Digital Control Loops Analytical Models, Laboratory Measurements, and Simulation Results Phil Cooke