Demonstrator of advanced controllers

Demonstrator ofadvanced controllers

Hans Dirne

Supervisorsprof.dr.ir. J. van Amerongen

dr.ir. J.F. Broeninkdr.ir. T.J.A. de Vriesir. P.B.T. Weustink

May 25th, 2005

Master of Science assignment

May 25th, 2005 Demonstrator of advanced controllers 2

Why this assignment?

The Major ‘Mechatronics’ provides several courses in control theory, in which the theory is often supported by simulations.

A physical setup might, in addition to simulations,be an enrichment for demonstrating control theory.

Such a demonstration setup will be able to makethe theory more insightful and will show real limitations in practical setups.


Objectives

1. To design, build and test a mechatronic demonstration setup, with which several control algorithms can be shown in practice

2. To be able to demonstrate performance differences of control algorithms in practice


Overview

1. Demonstration setup options2. Control systems3. Design of the new demonstrator4. Experiments5. Demonstration6. Conclusions & recommendations


Demonstration setup optionsDemonstration setup options


1. Mechatronic system2. Portable and easy to set up3. Robust, safe and failsafe design4. High level of observability5. Representable by linear 4th order model6. Clear link with well known device

Criteria


Three options

1. ‘Linix’ laboratory setup

2. Setup of ‘Controllab Products B.V.’

3. New build


Option 1: ‘Linix’ Laboratory Setup


‘Linix’ Laboratory Setup

motor

encoders

inertia 2

inertia 1transmission



Major disadvantage:

slip between belt and inertias


Option 2: CLP setup


CLP setup


Sensor positions


Option 3: New Build

Advantage• Pure design freedom

Disadvantage• Requires very much time and

effort to design

New build Linix CLP-setupMechatronic system √ √ √

Linear 4th order model √ limited linear to bedetermined

Portable, easy to set up √ √ not in currentform

Robust, safe, failsafe √ √ feasible

Observability √ yes, 2 positionSensors

yes, 4 positionsensors

Link with practical device √ transmission printer

Shows controller differences √ no, due tononlinearities

To bedetermined

Remarks Time constraint

Overview demonstrators


Control SystemsControl Systems


Mathematical model – 6th order

NMotorCurrent

m

Load

P

LoadSensorWorld

F

Motor

m

Frame

FrameFlex

m

MotorInertia

BeltFlex

P

MotorSensor

P

LoadSensorFrame

K

MotorGain

Damper

ViscousPLUScoulomb friction


Focus

1. Linear Quadratic Gaussian (LQG)2. Proportional, Integral, Differential (PID)


LQG explanation

u y

statesLQG

Reference PLANT Output

LQE

LQR

A LQG control algorithm is a combination of1. Lin. Quad. Regulator (state feedback)2. Lin. Quad. Estimator (state estimation)

4th order linear model required!


4th order linear model

Nremoved at order downsizing

m

Load

P

LoadSensorWorld

F

Motor

m

Frame

FrameFlex

m

MotorInertia

BeltFlex

P

MotorSensor

P

LoadSensorFrame

K

MotorGain

Damper

Required steps:1. Downsize system order2. Linearize system: discard coulomb friction

Result: linear 4th order model (e.g. State Space)


V A

Xref

LQR

PLANT

LQE

Estimated States

.

L

Cx(k|k)=x(k|k-1) +Le(k|k-1)

+_

m

Load

P

LoadSensorWorld

F

motor

m

FrameFrameFlex

P

LoadSensorFrame Damper

K

Motor

K

Amplifier

m

motortraagheid

motorflex

P

motorsensor

K counter

AD

DA1

ENC encoder

K

A2V

M

K

_

ENCencoder2

Kcounter2

Z-1

LQG controlled system


PID

Plant

anti-windup reset

PID-controller

m

Load

P

LoadSensorWorld

F

motor

m

FrameFrameFlex

Damper

reference

K

Motor

K

Amplifier

m

motortraagheid

motorflex

K

counter

AD

DA1

ENC

encoder

K

A2V

K

Kp

-1zddt

-1z

K

Kd

K

Ki


Tuning (1)

For proper comparison of the PID with the LQG controlled system, tuning with the same criteria is required.

1. Avoid actuator saturation2. Minimization of criterion:

dtuuJ TT RQ ee

position error controller output


Tuning (2)

Tuning procedure:1. Set Q and R2. Minimize criterion J by optimizing

controller gains (KLQG and KP,KI,KD)

Xref

PID

ref

u

x

K

Kp

d/dt

K

Ki

K

Kd

Process

Criterion


Tuning (3)

Xref

PID

LQR

K

Kp

-1zddt

K

Ki

-1z

K

Kd

Plant1

M

K

_ Plant2

Optimization results

KP = 15.7

KI = 42

KD = 1.6

KLQG= [3.7, 74, 8.2, 70]T


model

0 0.5 1 1.5 2 2.5 3 3.5 4time {s}

0

0.1

0.2

0.3

0.4PowerPIDPowerLQG

model

0 0.5 1 1.5 2 2.5 3 3.5 4time {s}

-0.001

-0.0005

0

0.0005

0.001

FramePIDFrameLQG

PID vs LQG (1)

• The PID controlled system consumes twice the power of the LQG system

• The maximum frame movement in the PIDcontrolled system is twice compared to LQG


PID vs LQG (2)

model

0 0.5 1 1.5 2 2.5 3 3.5 4time {s}

0

0.05

0.1

0.15 xPositionPID {m}PositionLQG {m}

The LQG control algorithm leads to an unacceptable position error with the nonlinear process


LQG+

Xref

LQR

LQE

FRAMEWORLDPlant

Estimated States

.

L

Cx(k|k)=x(k|k-1) +Le(k|k-1)

+_

Z-1

AO526

analog_output

ENC526

Encoder1

KCounter1

ENC526

Encoder2

K Counter2

K

A2V

K Kcomp

-1z

M

K

_


LQG+ vs LQG

System Results

-0.05

0

0.05

0.1Reference

-0.05

0

0.05

0.1Output {m}

0 0.5 1 1.5 2 2.5 3 3.5time {s}

-0.05

0

0.05

0.1Error

Effect of integrator:Static error is minimized!

Interesting to seethe performance ofLQG+ in practice…


Design of the new demonstratorDesign of the new demonstrator


Goal: to test a control algorithm on a physical setup

Procedure

How?

ModelingCode

GenerationLoad Codeat Target

Testing

PC PlantPC(realtime server)(client)


System overview (1)

PC PlantPC(realtime server)(client)

Client:• Runs MS Windows• Generating models• Model control (start/stop/upload/delete)• Setting parameters of controlled system real-time• View parameters of controlled system real-timeServer:• Runs Linux, with real-time kernel• Runs control system• Performs I/O


System overview (2)

CPU

I/O interface

RouterStorageDevice

Demonstrator Actuator & Sensors

MotorAmplifier

Encoders MotorCurrent

Cable to PC


Realization

Mechatronics

Embedded PC+ I/O

Power (CPU)

Power (motor)

Motor amplifier


ExperimentsExperiments


Experiments

• Comparison of PID/LQG/LQG+ performanceon the new demonstration setup

• Same controller parameters used as insimulation (after tuning)

• Performance comparison on:1. Static error2. Frame vibration3. Power usage


0 2 40

0.05

Time

Pos

. [m

]

LQG without I-term

0 2 40

0.05

Time

[m]

LQG with I-term

0 2 40

0.05

Time

[m]

PID

0 2 4-0.04

-0.02

0

0.020.04

Time

Err

. [m

]

0 2 4-0.04

-0.02

0

0.020.04

Time

[m]

0 2 4-0.04

-0.02

0

0.020.04

Time

[m]

0 2 4

-0.2

0

0.2

Time

Fra

me

[mm

]

0 2 4

-0.2

0

0.2

Time

[mm

]

0 2 4

-0.2

0

0.2

Time

[mm

]

0 2 4-1

0

1

Time

Cur

r. [

A]

0 2 4-1

0

1

Time

[A]

0 2 4-1

0

1

Time

[A]

0 2 40

500

1000

Time

Pow

er [

A2]

0 2 40

500

1000

Time

[A2]

0 2 40

500

1000

Time

[A2]


Results

The LQG+ controlled system outperforms the PID controlled system:

• Maximum frame movement differs factor 3• Total power consumption differs a factor 2• Both control algorithms minimize the static error, but the

LQG controlled system is faster

More performance increase is expected with a better model

Differences in performance between 2nd order PID and 4th order LQG have now been

demonstrated in practice


DemonstrationDemonstration


Demonstration

What will be shown:1. ‘Homing’ of the demonstrator

1. Determining absolute position2. PID controller in practice with various controller gains

Furthermore:1. Online adjustment of parameters2. Real-time variable monitoring3. Real-time animation of demonstration setup


Conclusions Conclusions &&

RecommendationsRecommendations


Conclusions

1. The new mechatronic demonstration setup is a compact, integrated machine that forms a versatile developmentenvironment for testing various control algorithms in practice

2. The new demonstrator allows for easy comparison of differentcontrol algorithms

3. Non-linear friction elements in the process will lead to lowerperformance in position control of a 4th order LQG-controlled system compared to a 2nd order PID control algorithm

4. Addition of an integrating term leads to an ‘LQG+’ control algorithm that can compensate for differences betweenprocess and reference model.


Recommendations

Hardware• Expand safety system• Reduce weight of the demonstrator (next version)• Add parallel processing (e.g. distributed control)

Software / control• Experiment with more control systems (MRAS, (L)FF, ILC etc)• Perform system identification

General1. Set up lab work assignments for student


Questions…?Questions…?


THANK YOU FOR THANK YOU FOR YOUR ATTENTIONYOUR ATTENTION

you are all invited for you are all invited for DRINKSDRINKS

at ‘De Tombe’, floor 0at ‘De Tombe’, floor 0

Demonstrator of advanced controllers

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