predictive control - a simple and powerful method to ... · technische universität münchen...

Technische Universität München

Predictive Control - A Simple and Powerful Method

to Control Power Converters and DrivesRalph M. Kennel, Technische Universitaet Muenchen,Germany

Marian Kazmierkowski, Technical University of Warsaw, Poland

José Rodríguez, Universidad Técnica Federico Santa María, Chile


Outline

Introduction

Predictive Control Methods

Predictive Control versus Cascaded Control

Conclusions/Discussion


State of the Art : Field Oriented Control

model

PWM

mainsstator coordinatesfield coordinates

currentcontrollers

fluxcontroller

speedcontroller

encoder

M3~

r

r

is

is

us

ej

e-j

us

6


Problems of Linear Algorithms

Linear control characteristics Drive systems characteristics

• Control unit and controlled unit

are assumed to be linear

• Drive systems are non-linear

• Control unit

are assumed to be time constant• Drive systems are time-variant

• Linear circuits

show identical reactions

in each operation range

under the same

reference commands

• The behavior of a drive system

is depending

on the operation range


Problems of Linear AlgorithmsFeedforward Control Feedback Control

Advantages• high dynamic behaviour

• no impact by sensor characteristics

• high accuracy

• high reliability

• high longterm stability

• simple optimization/adjustment procedure

• controlled quantities can be monitored

Disadvantages• models are not absolutely accurate

• high accuracy requires

knowledge of all quantuities

• temperature and drift behaviour

often cannot be described/modeled

• (re)action only,

when there is a control difference already

• sensors cause measuring errors



• any controller optimization is a compromise

making the inverter unnecessarily slow

in many operation points

• controllers with parameter adaptation and/or structure adaptation

are very complex

they often have bad effects during the adaptation process itself

• converters cause harmonics

leading to offset effects

in combination with fast control loops

• the elimination of harmonics by filtering

causes a time delay in the feedback

and therefore leads to a less dynamic control


Typical Cascaded Structure of Drive Control

inertia gear etc.

I

current controller

speed controller

positioncontroller

– – –

motorwindings

powerelectronics



• using cascaded PI(D) control

most problems (= differences between theory and practical results)

occur with the (inner) current control

• a linear controller tries to control an extremely non-linear inverter

whose behaviour is depending on the modultaion method

• most developments of converter control

deal with current control or flux control

because these elements are closest to the inverter itself

• the behaviour of any improved current control

is expected to be more linear than the inverter itself

speed and position controllers

can be designed as PI(D) controllers as before


in cascaded control structures

speed control must be much faster than position control

and current control must be much faster than speed control

current control must be very fast

to achieve position control with reasonable cycle times

in the controlled system (drive, converter, …)

however, there is no time constant justifying cycle times

of 100 µs or less



Outline

Introduction





General Structure of a Predictive Controller

inertia gear etc.

switchingstate

actual

machine state

I

prediction andcalculation

machine andpower electronics

model

motorwindings

powerelectronics

reminds slightly to state control

state control, however, is basically a linear control

predictive control is not !!!


Usual Structure of Drive Control

DC link

PI controller


Usual Structure of Drive Control

DC link

PI controller

why PWM ?

• linearization of the inverter

consequences ?

• very high switching frequency


Structure of a Direct Control

DC link

direct controller


Principle of Predictive Control

inverter

definite number of

switching elements

definite number of

switching states

definite number of

equivalent circuits

without switching

elements

precalculation of the

behaviour for each of

the switching states

next switching state

or switching time

can be fixed

comparison between

precalculation and

reference commands

reference

commands


direct controlof IM currents(Mayer/Pfaff)

direct digital predictivecurrent controller(Holmes/Martin)

digitalcurrent controller

(Betz/Cook/Henriksen)

current control(Choi/Sul)

direct torque control (DTC)(Takahashi/Nogushi)

(Tiitinen/Lalu)

multilevelhysteresis DTC

(Purcell/Acarnley)

direct torquecontrol (DTC)

(Chapuis, et.al.)

DTC with ORS(Moucary et.al.)

DTC-PPWC(Nillesen et.al.)

direct mean torquecontrol (DMTC)(Flach, et.al.)

new directtorque control

(Kang/Sul)

torque pulsationreduced DTC(Vas, et.al.)

DTC + dithering(Noguchi, et.al.)

DTC with reductionof torque ripple(La/Shin/Hyun)

DTDTC(Maes/Melkebeek)

DTC-SVM(Lascu et.al.)

DTC-DSVM(Casadei et.al)

adaptive switchingpattern (ASP)

(Nagy)

direct currentcontrol

(Pfaff/Wick)

current controlmethod

(Salama et.al)

adaptive andoptimized regulator

(Ackva, et.al.)

“space vector”control

(Wuest/Jenni)

“space vector”control

(Kazmierkowski, et.al.)

direct selfcontrol (DSC)(Depenbrock)

direct speedcontrol (DSPC)

(Mutschler)

integralspace-vector PWM

(Trzynadlowski, et.al.)

direct selfcontrol (DSC)

(Bonanno, et.al.)

predictive control(Kennel/Schröder)

fast-responsecurrent control(Holtz, et.al)

improvedpredictive control(Warmer et.al.)

new predictivecurrent control

(Hecht)

Family tree of predictive control algorithms

optimal on-line-tuningcurrent regulator

(du Toit Mouton/Enslin)

predictive current controlfor resonant link inverter

(Oh/Jung/Youn)

vectorial torque control(Attaianese, et.al.)

trajectorytracking control(Holtz/Beyer)

sliding mode control(Emeljanov)

trajectory based strategies

predictivecurrent control

(Holtz/Stadtfeld)

hysteresis control(bang bang)

PROMCvoltage control

(Hintze)

PROMCcurrent control

(Kohlmeier et.al.)

hysteresis based strategies


Family tree of predictive control algorithms

Part 2 MPC

Continuous-Set-Model based strategies Finite-Set-Model based strategies

DMC

(Cutler/Ramaker)

GPC

(Clarke)

Modular multilevel converter

(Perez/Rodriguez)

Direct matrix converter

(Vargas/Rodriguez)

Indirect matrix converter

(Correa/Rodriguez/Espinoza)

Fast online optimization

Fast gradient method for converter

control

(Richter/Morari)

LP solution for quadratic cost

(Stumper/Kennel)

Explicit MPC

(Bemporad)

MPC with MPT

(Kvasnica)

MPC for PMSM

(Kuehl/Bolognani/Kennel)

Dead beat control

(Lee)

dc-dc converter

(Geyer/Morari)

MPTC

(Rodriguez)

Predictive current control

(Rodriguez)

Predictive speed control

(Fuentes/Rodriguez/Kennel)

Heuristic direct MPC

(Stolze/Kennel)

Sensorless MPC

(Wojciechowski/Strzelecki)

Saliency based encoderless

PTC

(Landsmann/Kennel)

Observer-based sensorless

PTC

(Davari/Wang/Kennel)

Weighting factors design

(Cortes/Rodriguez)

Weighting factor optimization

(Davari/Kennel)

2-steps MPC of 3 phase UPS

inverter

(Cortes/Rodriguez)

FPGA-based PCC

(Naouar/Monmasson)

ac-ac converter

CRHPC

(Clarke/Scattolini)

GPC--PID

(Nakano)

GPC for motor control

(Linder/Kennel) dc-ac converter

2L-VSI

(Cortes/Rodriguez)

3L-NPC

(Geyer/Rodriguez)

CHB

(Perez/Rodriguez/Cortes)

Flying capacitor converter

(Lezana/Aguilera/Quevedo)

Current source rectifier

(Correa/Rodriguez)

ac-dc converter


Outline

Introduction

Predictive Control Methods (Kennel)

Trajectory Based Predictive Control

Hysteresis Based Predictive Control

Long-Range Predictive Control

Predictive Control with Heuristic Preselection


Example : Trajectory Based Predictive Control

Predictive Current Control acc. to Kennel

DC drive supplied by a line commutated thyristor inverter

+ + +

grid

U0≈

- - -

=



Predictive Current Control acc. to Kennel


Trajectory Based Predictive Control Strategies

system states are forced to follow

(pre-)defined natural reference trajectories

difference to sliding mode control

there the trajectories are not natural



Direct Speed Control acc. to Mutschler

model andprediction

3~M

*

ud

uk

isus

=~

e

e = – ref

a =

e ak k/

e ak+3 k+3/

e ak+1 k+1/

e ak+2 k+2/

+Hy–Hy

Sk

Sk+1

Sk+2


Characteristicsof Trajectory Based Predictive Control

• system states are forced to follow (pre-)defined reference trajectories

• switching takes place at intersections

between different system-trajectories or at (pre-)defined instants

• switching frequency of the inverter can be fixed to a constant value

• control behaviour comparable to feedforward control

• exact knowledge of system parameters is required

• appropriate for realisation by digital circuits or controllers


Example : Trajectory Based Predictive ControlDirect Self Control (DSC) acc. to Depenbrock


Example : Hysteresis Based Predictive ControlDirect Self Control acc. to Takahashi


Outline

Introduction







Hysteresis Based Predictive Control Strategies

switching of inverter takes place

at the (multi-dimensional) border(s)

of a hysteresis area


Example : Hysteresis Based Predictive ControlPredictive Current Control acc. to Holtz


Re

jIm

0

s

is

is*

din

dt

3~M

=predictis

model

uduk

usk

is

is

disk

is

*

dt us

~



Characteristicsof Hysteresis Based Predictive Control

• switching takes place at borders of a hysteresis area

• a maximum error can be (pre-)defined

• switching frequency of the inverter is not constant

• control behaviour comparable to feedback control

• exact knowledge of system parameters is not required

• appropriate for realisation by analog circuits


Comparison

of different

predictive control

schemes


Flux Trajectories10 Hz fundamental frequency

500 Hz switching frequency

standard PWM

DSC (Depenbrock)

bang-bang control

DSC (Takahashi)

7 % hysteresis

predictive control

(Holtz)DSC (Takahashi)

2 % hysteresis

source Andreas Haun, Vergleich von Steuerverfahren …, VDI-Fortschrittsbereichte, Reihe 21, Nr. 113, 1992:


Flux Trajectories40 Hz fundamental frequency


standard PWM

DSC (Depenbrock)

bang-bang control

DSC (Takahashi)

7 % hysteresis

predictive control


2 % hysteresis



standard PWM

DSC (Depenbrock)

bang-bang control

DSC (Takahashi)

7 % hysteresis

predictive control


2 % hysteresis

Stator Current Trajectories40 Hz fundamental frequency





Frequency Spectrum of Torque

a) 40 Hz fundamental frequency


b) 45 Hz fundamental frequency


1. standard PWM

2. bang-bang control

3. predictive control (Holtz)

4. DSC (Depenbrock)

5. DSC (Takahashi) with 7 % hysteresis



Additional Losses

under Inverter Supply

a) variable fundamental frequency


b) 40 Hz fundamental frequency

variable switching frequency

1. standard PWM

2. bang-bang control

3. predictive control (Holtz)

4. DSC (Depenbrock)




Outline

Introduction







switching control

SVM(space vector modulation)

directly

steps of

prediction

(prediction

horizon)

1

>1

• DTC

• DSC

• DSPC

• direct control of

IM currents

• DFC

• DMC

• GPC

• DMPC

predictive control categoriesanother way of distinction


• the player calculates

in advance

all possible moves

until a „prediction horizon“

• the player chooses

the move with the best

expectations of success

• after each opponent‘s move

pre-calculation and

optimization is repeatedDMPC is like playing chess

The „Human Behaviour“ of DMPC


Model Predictive Control

History Future


Model Predictive Control

Overview


Direct Model Predictive ControlSystem Model / Cost Function


Direct Model Predictive Control

System Model / Cost Function


Characteristicsof Model Based Predictive Control

• basic ideas are derived from state-space control

• the past is explicitely considered (mostly by the system state)

• future control values are pre-calculated and optimized

until a (pre-)defined „horizon“

• the first of the precalculated control values only

is transmitted to the controlled system

• model parameters can be estimated on-line

• extension to MIMO-control is possible with little additional effort

• use of non-linear model is possible for non-linear control systems

• a lot of calculation power is required


strategy Np max. calculation timecases

complete enumeration 2 35 µs64

online-optimization is not applicable for drive control

Calculation TimesDMPC - control, implicite solution

complete enumeration 3 > 500 µs512

branch and bound 2 27 µs 64

branch and bound 3 186 µs 512

processor:

900 MHz AMD Duron, 128 MB RAM

Linux 2.2.14 with RTAI 1.3


Model Based Predictive Current Control

there are

7 (or 8) possiblities

for “the following

switching state”

the respective

system behaviour (current)

can be calculated

in advance

complete enumeration extensive processing power needed

a chess player, however, does not really consider each possibility



there are

7 (or 8) possiblities

for “the following

switching state”

the respective

system behaviour (current)

can be calculated

in advance

complete enumeration extensive processing power needed

… so why should we do that in predictive control ???


further prediction, however,

is only considered for

the candidate sequences

staying within

the permitted limits


… so why should we do that in predictive control ???


… determine those switching possibilities only

that are either feasible or point in the proper direction

these are candidate sequences

feasible pointing in the proper direction



not feasible not pointing in the proper direction


… determine those switching possibilities only

that are either feasible or point in the proper direction

these are candidate sequences



… for the candidate sequences, further prediction (e. g. by a reduced system model) is performed

example : the number of steps after which the first of the two variables the isa and iisb

leaves the feasible regionis the number h


h1 = 4

h1 = 4






h1 = 4 h2 = 10






Different Way of Thinkingin Model Based Predictive Control

1. model of the controlled system

this is no difference to conventional control

the better the model, the better the prediction

2. cost function

the engineer has to learn to describe

what he wants the controlled system really to do !!!

3. stability

… that‘s a really good question … next question ?


Experimental Results (DMPC)current control

comparison : PI control model predictive control



Low switching frequency high switching frequency

dynamic of step response is identical !



a change of the cost function (nothing else !!!)

results in different behaviour !


Features of (Longe Range) Predictive Control

Advantages

• possibility to use foreknowledge about drive system (system model)

• inverter limitations and dynamic behaviours are taken into account

• improved representation of non-linear systems

• no need for time challenging cascade structure

• improved dynamic behaviour

Disadvantages

• high processing capability required

• for industrial use change in teaching engineers necessary

• stationary accuracy and dynamic behaviour

depend on accurracy of model parameters


Actual Situation




current control must be extremely fast


at the time most requirements in industrial applications are satisfied sufficiently

there is no strong need for improvement in industry

however – at a certain time there will be a demand for improvement

with respect to a future increase of requirements

more investigations should be done


Discussion

• predictive control strategies

offer the possibility to use foreknowledge about the drive system

• physical limitations and dynamic behaviour of power electronics

are taken into account

• non-linear systems are represented better (by non-linear models)

• no need for time challenging cascaded structures

• the way of thinking is different

model of the controlled system cost function


more investigations should be done


Outline

Introduction







Control task

Current control of a three-phase resistive-inductive-active load


Heuristic method

• Calculation effort rises exponentially with the prediction horizon

• Three or four prediction steps impossible in real-time

(online as well as offline)

• Cost function to describe the performance to be obtained

• Basic idea of Heuristic Method :

• Optimum integer solution of a linear program

is close to the continuous-valued solution of the integer problem

=> Important: Optimum integer solution is not necessarily

the integer solution which is closest to the continuous-valued optimum

=> Not all integer points have to be examined,

only the ones closest to the continuous-valued optimum

Peter Stolze


Heuristic method• Continuous-valued “switching states“ in the range [0; 1]

• Determination of the sector in which the

continuous-valued optimum lies (I to VI)

• For the first two prediction steps the three

closest integer solutions are used for

an exhaustive search

(corners of the triangle)

• For the 3rd and 4th prediction step only the

2 closest integer solutions are used

• 3 prediction steps: 18 possible combinations

4 prediction steps: 36 possible combinations

• In more than 95% of the cases the “real“ optimum is still found


Simulation Results

Sinusoidal references Back EMF voltages

R = 10Ω, L = 10mH, Vdc = 540V, T = 100μs


Peter Stolze

Finite-Set Model Predictive Control of a

Flying Capacitor Converter with Heuristic

Voltage Vector Preselection


Control task• Current control of a three-phase resistive-inductive-active load

• Hysteresis controller for voltage balancing

C1

i1

S11

S12

S13

S14

C2

i2

S21

S22

S23

S24

C3

i3

S31

S32

S33

S34

0.5Vdc

0.5Vdc

R

L

R

L

R

L

E1

E2

E3


General remarks

• Heuristic voltage vector

selection algorithm basically

the same as for two-level

inverters but now the

continuous-valued “switching

states“ can be

in the range [-1; 1]

• 24 possible sectors

Re

Im

++-

+0-

+--

+-0

+-+0-+--+

-0+

-++

-+0

-+- 0+-

0+0

-0-

++0

00-

+00

0--

+0+

0-0

00+

--0

0++

-00

+++

000

---

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24


Simulation Results

Sinusoidal references Flying capacitor voltages

R = 10Ω, L = 10mH, Vdc = 540V, T = 100μs, C = 480μF


• system states are

forced to follow

(pre-)defined reference

trajectories

• examples

– Direct Self Control

– Direct Speed Control

Predictive Control Strategies

trajectory basedhysteresis based model based

• switching of inverter

takes place at the

(multi-dimensional)

border(s) of a

hysteresis area

• examples

– hysteresis control

(bang-bang control)

– Direct

Torque Control (DTC)

• future control values

are pre-calculated

and optimized until a

(pre-)defined „horizon“

• examples

– Dynamic

Matrix Control

– Generalized

Predictive Control

– Predictive Control with

Heuristic Pre-Selection


Outline

Introduction





State of the Art : Field Oriented Control

model

PWM

mainsstator coordinatesfield coordinates

currentcontrollers

fluxcontroller

speedcontroller

encoder

M3~

r

r

is

is

us

ej

e-j

us

6


Typical Cascaded Structure of Drive Control

inertia gear etc.

I

current controller

speed controller

positioncontroller

– – –

motorwindings

powerelectronics





current control must be very fast


in the controlled system (drive, converter, …)

however, there is no time constant justifying cycle times

of 100 µs or less



General Structure of a Predictive Controller

inertia gear etc.

switchingstate

actual

machine state

I

prediction andcalculation

machine andpower electronics

model

motorwindings

powerelectronics


• control behaviour

comparable to

feedforward control

• exact knowledge of

system parameters is

required

• appropriate for

realisation by digital

circuits or controllers

Predictive Control Strategies

trajectory basedhysteresis based model based

• control behaviour

comparable to

feedback control

• exact knowledge of

system parameters is

not required

• a maximum error can

be (pre-)defined

• the past is explicitely

considered

• future control values are

pre-calculated and

optimized

until a (pre-)defined

„horizon“

• model parameters can be

estimated on-line

• use of non-linear model is

possible for non-linear

control systems


Outline

Introduction





Actual Situation




current control must be extremely fast


at the time most requirements in industrial applications are satisfied sufficiently

there is no strong need for improvement in industry

however – at a certain time there will be a demand for improvement


investigations should be done



• predictive control strategies

offer the possibility to use foreknowledge about the drive system

• physical limitations and dynamic behaviour of power electronics

are taken into account

• non-linear systems are represented better (by non-linear models)

• no need for time challenging cascaded structures

• the way of thinking is different

model of the controlled system cost function


investigations should be done


Thank you !

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