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PACIFIC Conference 2011. 8 th December 2011 Amiens, France Dr. Simon Walters (University of Brighton, UK) Professor A. Rachid –Project Leader – Universite de Picardie Jules Verne Professor A. Mpanda (ESIEE-Amiens). The ‘PACIFIC’ Project. Pantograph- Catenary (PAC) Models

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pacific conference 2011

PACIFICConference 2011

8th December 2011

Amiens, France

Dr. Simon Walters (University of Brighton, UK)

Professor A. Rachid –Project Leader – Universite de Picardie Jules Verne

Professor A. Mpanda (ESIEE-Amiens)

Dr.S.D.Walters Prof.A.Rachid Prof.A.Mpanda

the pacific project
The ‘PACIFIC’ Project
  • Pantograph-Catenary (PAC) Models
  • Open-loop Test Results
    • Sixth order PAC model
  • PAC System Controller (LMI)
    • LMI – Linear Matrix Inequalities
  • PAC System Controller (PID/PD+I)
    • PID – Proportional Integral Derivative
    • FPD+I - Fuzzy Proportional Derivative + Integral
  • PAC Scale-model Test-rig
  • Physical Phenomena and SIMPAC (To be presented by Professor Mpanda)
    • Electric Arc Modelling
    • Thermal Modelling
    • SIMPAC

Dr.S.D.Walters Prof.A.Rachid Prof.A.Mpanda

1 pantograph catenary pac models
1. Pantograph-Catenary (PAC) Models
  • Finite-element catenary model
  • Fourth order PAC system
    • Including time-varying catenary stiffness function
  • Sixth order PAC system
    • Including time-varying catenary stiffness, damping and mass function

Dr.S.D.Walters Prof.A.Rachid Prof.A.Mpanda

2 open loop test results

fvcat(t)

kcat(t)

xcat

Mcat(t)

Fcp

Fpc

ks

xh

Mh

fvh

kh

xf

Mf

Fup

fvf

kf

2. Open-loop Test Results

Sixth order

PAC model

Dr.S.D.Walters Prof.A.Rachid Prof.A.Mpanda

model parameters
Model Parameters

Dr.S.D.Walters Prof.A.Rachid Prof.A.Mpanda

system equations
System Equations

This system may be described by a system of differential equations:

These equations may be rearranged as follows:

Dr.S.D.Walters Prof.A.Rachid Prof.A.Mpanda

slide7

The system may be solved in state-space form, assuming in this case that:

Where:

Dr.S.D.Walters Prof.A.Rachid Prof.A.Mpanda

catenary model
Catenary Model

Time-varying Functions of Mass, Stiffness and Damping for the Catenary Model

Model source: [Pisano &Usai, 2008];parameters from [ESIEE, 2010]:

Dr.S.D.Walters Prof.A.Rachid Prof.A.Mpanda

open loop test 1
Open-loop Test 1

Dr.S.D.Walters Prof.A.Rachid Prof.A.Mpanda

open loop test 2
Open-loop Test 2

Dr.S.D.Walters Prof.A.Rachid Prof.A.Mpanda

open loop results 1
Open-loop Results 1

Dr.S.D.Walters Prof.A.Rachid Prof.A.Mpanda

open loop results 2
Open-loop Results 2

Dr.S.D.Walters Prof.A.Rachid Prof.A.Mpanda

open loop results 3
Open-loop Results 3

Dr.S.D.Walters Prof.A.Rachid Prof.A.Mpanda

open loop results 4
Open-loop Results 4

Dr.S.D.Walters Prof.A.Rachid Prof.A.Mpanda

3 pac system controller lmi
3. PAC System Controller (LMI)

PAC Modelling

Dr.S.D.Walters Prof.A.Rachid Prof.A.Mpanda

slide16

Multiple Model

Dr.S.D.Walters Prof.A.Rachid Prof.A.Mpanda

4 pac system controller pid pd i
4. PAC System Controller (PID/PD+I)

Reference Force In

Reference

voltage

Upward force Fup

Catenary Dynamics

Pant.-Cat. Interface

Input Sensor

Controller

Actuator

Pantograph Dynamics

+

-

Output Sensor

Measured

voltage

Contact Force Fpc

Dr.S.D.Walters Prof.A.Rachid Prof.A.Mpanda

fuzzy logic control design process
Fuzzy Logic Control Design Process
  • Design a PID controller that works
  • Design a linear Fuzzy PID controller that works
  • Add non-linearity, if required, and test well

After: [Jantzen, 2007]

Dr.S.D.Walters Prof.A.Rachid Prof.A.Mpanda

pid calculation
PID Calculation

Error Integral of Error Derivative of Error

Dr.S.D.Walters Prof.A.Rachid Prof.A.Mpanda

generalised fuzzy system

Crisp inputs: x1 x2 x3 ... xn

Fuzzification

Rule 1

Rule 2

Rule 3

Rule n

Aggregation

Defuzzification

Crisp output: y

Generalised Fuzzy System
  • Inference

Dr.S.D.Walters Prof.A.Rachid Prof.A.Mpanda

fpd controller 4 rules
FPD Controller (4 rules)

Input Membership Functions

Error ‘e’

neg

pos

100

0

neg

pos

100

0

Output Membership Function

Control Output ‘U’

Rules

If e = neg & ce = neg THEN U = low

If e = neg & ce = pos THEN U = 0

If e = pos & ce = neg THEN U = 0

If e = pos & ce = pos THEN U = high

100

0

low 0 high

Derivative of Error ‘ce’

Dr.S.D.Walters Prof.A.Rachid Prof.A.Mpanda

fpd i controller

e

E

PD Rules

GE

ce

e

CE

D

Estimate

U

GCE

u

GU

Σ

ie

I

Estimate

IE

GIE

FPD+I Controller

Dr.S.D.Walters Prof.A.Rachid Prof.A.Mpanda

simulated acceleration
Simulated Acceleration

Dr.S.D.Walters Prof.A.Rachid Prof.A.Mpanda

simulation results pid
Simulation Results - PID

Dr.S.D.Walters Prof.A.Rachid Prof.A.Mpanda

simulation results fpd i
Simulation Results – FPD+I

Dr.S.D.Walters Prof.A.Rachid Prof.A.Mpanda

phase plane analysis
Phase-plane Analysis

Dr.S.D.Walters Prof.A.Rachid Prof.A.Mpanda

next stage go non linear and test well
Next Stage – Go Non-linear (and Test Well)!
  • Different Surfaces:
  • Linear
  • Saturation
  • Dead-zone
  • Quantizer

Figures adapted from [Jantzen, 2007]

Dr.S.D.Walters Prof.A.Rachid Prof.A.Mpanda

references pid pd i comparison section
References (PID/PD+I Comparison Section)
  • [Atherton, 2009], ‘Control Engineering’, D. Atherton, Ventus Publishing ApS, BoonBooks, 2009.
  • [Hedayati et al., 2010], ‘Pantograph–Catenary Interaction: A literature Review’, Reference: RTT_PACIFIC.2010.2.SHK-FB, S. HedayatiKia, F. Bartolini,
  • A. Mpanda, ESIEE-Amiens, 2010.
  • [Jantzen, 2007], ‘Foundations of Fuzzy Control’, Jan Jantzen, Technical University of Denmark, John Wiley and Sons Ltd., 2007.

[Lee et al., 2007], ‘Fuzzy Logic and Neuro-fuzzy Modelling of Diesel Spray Penetration: A Comparative Study’, S. H. Lee, R. J. Howlett, C. Crua, S. D. Walters,

Journal of Intelligent and Fuzzy Systems, ISSN: 1064-1246 vol 18, no 1, pp 43-56, 2007.

[Pisano& Usai., 2008] ‘Contact Force Regulation in Wire-actuated Pantographs’, A. Pisano, E. Usai, Modern Sliding Mode Control Theory, Vol. 375, pp. 447-463, 2008.

Dr.S.D.Walters Prof.A.Rachid Prof.A.Mpanda

5 pac scale model test rig
5. PAC Scale-model Test-rig

Dr.S.D.Walters Prof.A.Rachid Prof.A.Mpanda

the test rig electromechanical part
The Test-rig – Electromechanical Part

Dr.S.D.Walters Prof.A.Rachid Prof.A.Mpanda

conclusions so far
Conclusions So Far...

‘PACIFIC’: several approaches to PAC modelling and control:

  • Various mechanical models of PAC systems considered
  • Open-loop tests undertaken
  • Multiple model with LMI control technique - new control combination
  • Crisp and fuzzy controllers under comparison
  • A new convenient scale-model of a PAC system
  • Physical Phenomena and SIMPAC: will be presented by Professor Mpanda – next!

Dr.S.D.Walters Prof.A.Rachid Prof.A.Mpanda

acknowledgements
Acknowledgements
  • The Presenter should like to acknowledge the international contributions of the other PACIFIC project partners:
  • Professor Ahmed Rachid (Universite de Picardie Jules-Verne)
  • Professor Augustin Mpanda (ESIEE-Amiens)

Dr.S.D.Walters Prof.A.Rachid Prof.A.Mpanda

acknowledgements1
Acknowledgements

This project was selected under the European Cross-border Cooperation Programme

INTERREG IVA France (Channel) – England, co-funded by the ERDF.

Co-funded by the European Regional Development Fund.

European Union. Investing in your future.

Dr.S.D.Walters Prof.A.Rachid Prof.A.Mpanda

slide38

Any Questions?

Dr.S.D.Walters Prof.A.Rachid Prof.A.Mpanda