Computational Intelligence for Control System Design

Computational Intelligence for CSDA

Computational Intelligence for Control System Design Automation F. O. RAMOS

1

1 Space Systems Division (ASE) Instituto de Aeronáutica e Espaço (DCTA/IAE, Brazil)

EuroGNC 2015

Fausto RAMOS (DCTA/IAE)

3rd CEAS EUROGNC CONFERENCE

13-15/Apr/15, Toulouse

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Contents 1

Introduction Some comments on CSD

2

Control System Design Automation Implementation Proposing a mechanism

3

CSDA 1: Satellite Design Set & Design Automation Results

4

CSDA 2: Benchmark Design Set & Design Automation Results - w/ and w/o an initial elite Results - with the original metric

5

Remarks Fausto RAMOS (DCTA/IAE)



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Introduction

Contents 1


2


3


4


5




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Introduction

Introduction • Some comments on CSD Design Set

Design Set Given a design set D = {A, S, T , K} composed of: a given control system architecture (including the plant), A; system specifications to be achieved, S; a controller technique to be chosen, T ; a controller to be designed, K. would be consistency (S fulfilment) enough?




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Introduction

Introduction • Some comments on CSD Design Set

Design Set Given a design set D = {A, S, T , K} composed of: a given control system architecture (including the plant), A; system specifications to be achieved, S; a controller technique to be chosen, T ; a controller to be designed, K. would be consistency (S fulfilment) enough?




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Introduction

Introduction • Some comments on CSD Consistency × Internal Flexibility




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Introduction


Internal Flexibility Internal Flexibility A characteristic of a design set D related to the allowed margins for interactions between its internal elements while still keeping its consistency. { GM , PM, · · · } (IF) → { GM+ , PM+, · · · } (IF+) How far one can advance D’s IF during the design process?




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Introduction






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Introduction






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Control System Design Automation

Contents 1


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3


4


5




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CSDA • Implementation

Implementation of CSDA A collection of objective functions, constraints and evaluation criteria sets up a multi-objective problem. A CSDA mechanism is built with Computational Intelligence. The solution space is searched by means of the CSDA mechanism. The automated search is not purely random (such as Monte Carlo runs), but drifts towards




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Implementation of CSDA A collection of objective functions, constraints and evaluation criteria sets up a multi-objective problem. A CSDA mechanism is built with Computational Intelligence. The solution space is searched by means of the CSDA mechanism. The automated search is not purely random (such as Monte Carlo runs), but drifts towards the best compliance with the constraints and objectives.




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CSDA • Proposing a mechanism Genetic Algorithms CI-based design mechanism Genetic Algorithm

ratings

GA parameters

Requirements

individuals Cont. System Design Design model and technique

K

Fuzzy System

Review data and restart

Human evaluation and decision

indexes

controllers

Cont. System Analysis

K

Detailed model

Cont. System Validation Digital & HWIL models

Genetic Algorithms Initially proposed as models of adaptive processes [FA00]. GAs emulate the Darwinian theory of the life evolution, where individuals are created, combined and mutated. Descendants of the best-fitted ones are propagated.




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ratings

GA parameters

Requirements


K

Fuzzy System

controllers



indexes Cont. System Analysis

K

Detailed model






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ratings

GA parameters

Requirements


K

Fuzzy System

controllers




K

Detailed model






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ratings

GA parameters

Requirements


K

Fuzzy System

controllers




K

Detailed model






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CSDA • Proposing a mechanism Fuzzy Systems CI-based design mechanism Genetic Algorithm

ratings

GA parameters

Requirements


K

Fuzzy System

controllers




K

Detailed model


Fuzzy Systems FSs are “a class of objects with a continuum of grades of membership” [Zad65]: “small ts ” instead of ts ≤ 1s. FSs are non-linear functions, used here to map design indexes (stability, performance, and so on) ... ... into ratings (or fitness scores). Fausto RAMOS (DCTA/IAE)



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ratings

GA parameters

Requirements


K

Fuzzy System

controllers




K

Detailed model





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ratings

GA parameters

Requirements


K

Fuzzy System

controllers




K

Detailed model





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CSDA • Proposing a mechanism Fuzzy Systems

−3

x 10

4

Rating

3

2

1

0 0 5

10 10

8 15

6 20

4 25

2 30 0

SettlingTime


GainMargin



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CSDA 1: Satellite

Contents 1


2


3


4


5




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CSDA 1: Satellite

CSDA 1: Satellite • Design Set & Automation Design Set

Design Set [AJ05] A / model: see the full paper. A / actuator: 0.065Nm reaction wheel. S: ts ≤ 20 minutes, β ≤ 0.025 Nm. T : pole placement. K: 

 −76.1644 0 0.4071 −0.3805 0 0   0 −5.0908 0 0 −0.0142 0 0.4071 0 −72.772 0 0 −0.2721




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CSDA 1: Satellite



 −76.1644 0 0.4071 −0.3805 0 0   0 −5.0908 0 0 −0.0142 0 0.4071 0 −72.772 0 0 −0.2721




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CSDA 1: Satellite



 −76.1644 0 0.4071 −0.3805 0 0   0 −5.0908 0 0 −0.0142 0 0.4071 0 −72.772 0 0 −0.2721




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CSDA 1: Satellite



 −76.1644 0 0.4071 −0.3805 0 0   0 −5.0908 0 0 −0.0142 0 0.4071 0 −72.772 0 0 −0.2721




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CSDA 1: Satellite



 −76.1644 0 0.4071 −0.3805 0 0   0 −5.0908 0 0 −0.0142 0 0.4071 0 −72.772 0 0 −0.2721




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CSDA 1: Satellite

CSDA 1: Satellite • Design Set & Automation Design Automation

Genetic Algorithm 1 chromosome = 8 pairs of genes {gk,1 , gk,2 } (non-zero gains of K), where each gene is a binary 8-bit number and: gk,1 ∗ , gk,2 +1 : MSB(g ) = 0 MSB←0 = gk,2 , sig (g ) = −1 : MSB(g ) = 1 Ki,j = sig (gk,2 )

∗ with: gk,2

Original controller K is the initial elite.




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CSDA 1: Satellite


Genetic Algorithm 1 chromosome = 8 pairs of genes {gk,1 , gk,2 } (non-zero gains of K), where each gene is a binary 8-bit number and: gk,1 ∗ , gk,2 +1 : MSB(g ) = 0 MSB←0 = gk,2 , sig (g ) = −1 : MSB(g ) = 1 Ki,j = sig (gk,2 )

∗ with: gk,2

Original controller K is the initial elite.




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CSDA 1: Satellite


Fuzzy System R1 : If (“Actuation R2 : If (“Actuation then (“Rating R3 : If (“Actuation then (“Rating


is is is is is

Large”) then (“Rating is Bad”) not Large”) and (“Settling Time is Satisfactory”) Regular”) Satisfactory”) and (“Settling Time is Satisfactory”) Good”)



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CSDA 1: Satellite

CSDA 1: Satellite • Results Results Search space = 28×2×8 possible combinations. IntFlex: 68 % reduction of β, 17 % reduction of ts . −3

20

x 10

Actuation (Nm)

u1,PP 15

u

10

u3,PP

5

u2,CI

2,PP

u

1,CI

u

3,CI

0 −5

0


500

1000 Time (s)


1500

2000


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CSDA 2: Benchmark

Contents 1


2


3


4


5




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CSDA 2: Benchmark

CSDA 2: Benchmark • Design Set & Automation Design Set

Design Set [Tho95] A / mass-spring-mass + disturbances. S: PM, GM, ts , umax , kmin , kmax , pm . T , K: various. The design with the worst rank (12th ) was chosen for CSDA: T = “Maximum Entropy”, K = 6th order controller.




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CSDA 2: Benchmark






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CSDA 2: Benchmark






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CSDA 2: Benchmark






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CSDA 2: Benchmark

CSDA 2: Benchmark • Design Set & Automation Design Automation

Genetic Algorithm 1 chromosome = 12 pairs of genes (5 zeros, 6 poles and a gain factor of the 6th order controller). Worst rank controller K is the initial elite.




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CSDA 2: Benchmark


Genetic Algorithm 1 chromosome = 12 pairs of genes (5 zeros, 6 poles and a gain factor of the 6th order controller). Worst rank controller K is the initial elite.




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CSDA 2: Benchmark


Fuzzy System R1 : If (“Settling Time is Large”) or (“Actuation is Large”) or (“Gain Margin is Unsatisfactory”) or (“Phase Margin is Unsatisfactory”) or (“kmin is Unsatisfactory”) or (“kmax is Unsatisfactory”) or (“pm is not Satisfactory”) then (“Rating is Bad”) R2 : If (“Settling Time is not Large”) and (“Actuation is not Large”) and (“Gain Margin is not Unsatisfactory”) and (“Phase Margin is not Unsatisfactory”) and (“kmin is not Unsatisfactory”) and (“kmax is not Unsatisfactory”) and (“pm is Satisfactory”) then (“Rating is Regular”) R3 : If (“Settling Time is Satisfactory”) and (“Actuation is Satisfactory”) and (“Gain Margin is not Unsatisfactory”) and (“Phase Margin is not Unsatisfactory”) and (“kmin is not Unsatisfactory”) and (“kmax is not Unsatisfactory”) and (“pm is Satisfactory”) then (“Rating is Good”)




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CSDA 2: Benchmark


Fuzzy System




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CSDA 2: Benchmark

CSDA 2: Benchmark • Results With and and without an initial elite

With an initial elite ts

umax

kmin → kmax

pm

GM (dB)

PM (deg)

Scorea

CSDA?

4.80 13.42

665.78 6.16

0.10 → 1.90 0.24 → 3.17

0.47 0.80

5.67 14.08

30.88 37.87

12th 3rd

No Yesb

a

The final score value was computed with the original metric [Tho95]. b The CI exploration was based on the FS metric.

The design left the last position and achieved the 3rd place of the rank. IntFlex: 99 % reduction of umax , 180 % increase of ts (S still complied).




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CSDA 2: Benchmark



umax

kmin → kmax

pm

GM (dB)

PM (deg)

Scorea

CSDA?

4.80 13.42

665.78 6.16

0.10 → 1.90 0.24 → 3.17

0.47 0.80

5.67 14.08

30.88 37.87

12th 3rd

No Yesb

a






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CSDA 2: Benchmark



umax

kmin → kmax

pm

GM (dB)

PM (deg)

Scorea

CSDA?

4.80 13.42

665.78 6.16

0.10 → 1.90 0.24 → 3.17

0.47 0.80

5.67 14.08

30.88 37.87

12th 3rd

No Yesb

a






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CSDA 2: Benchmark


Without an initial elite ts

umax

kmin → kmax

pm

GM (dB)

PM (deg)

Scorea

CSDA?

4.80 13.42 13.03

665.78 6.16 7.98

0.10 → 1.90 0.24 → 3.17 0.48 → 3.37

0.47 0.80 0.85

5.67 14.08 16.80

30.88 37.87 37.87

12th 3rd 3rd

No Yesb Yesc

a c

The final score value was computed with the original metric [Tho95]. b The CI exploration was based on the FS metric. The CI exploration was based on the FS metric without an initial elite.

The design kept the 3rd place of the rank.




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CSDA 2: Benchmark

CSDA 2: Benchmark • Results With the original metric

With the original metric ts

umax

kmin → kmax

pm

GM (dB)

PM (deg)

Scorea

CSDA?

4.80 13.42 13.03 >100

665.78 6.16 7.98 0.32

0.10 0.24 0.48 0.31

0.47 0.80 0.85 0.88

5.67 14.08 16.80 18.59

30.88 37.87 37.87 42.18

12th 3rd 3rd 1st

No Yesb Yesc Yesd

a c

→ → → →

1.90 3.17 3.37 3.55

The final score value was computed with the original metric [Tho95]. b The CI exploration was based on the FS metric. The CI exploration was based on the FS metric without an initial elite. d The CI exploration was based on the original metric [Tho95].

The design achieved the 1st place of the rank with a huge ts .




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Remarks

Contents 1


2


3


4


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Remarks

Remarks • Concluding remarks Motivation and benefits of CSD automation

Motivation and benefits of CSD automation CSDA reveals the internal flexibility of D. CSDA produces high quality structures, interesting for the designer: ◮ to compare with your own pre-existent CSD design; ◮ to start with, as a baseline design.

Design flaws are “amplified” in a CSDA environment.




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Remarks







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Remarks

Remarks • Additional remarks Snapshot of the Evolutionary Simulation

Snapshot of the Evolutionary Simulation

Leave the office at 5pm and, while the simulation is running, have a happy hour, meet the family, sleep... then get the design in the next morning.




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Remarks

Remarks • Additional remarks Snapshot of the Evolutionary Simulation

Snapshot of the Evolutionary Simulation

Leave the office at 5pm and, while the simulation is running, have a happy hour, meet the family, sleep... then get the design in the next morning.




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Remarks

Remarks • Additional remarks Book publishing

Book publishing A book about CSDA is being edited and will be published this year. The book will detail the CI-based mechanism used in this EuroGNC paper to develop the evolutionary simulations. A small set of case studies will also be presented. A 2nd book is expected to be published next year. It will be a collection of new case studies, coming from the scientific community. Feel free to contact the author for collaborative research by e-mail: [email protected] or [email protected].




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Remarks

References E. Abdulhamitbilal and E. M. Jafarov. Linear attitude stabilization of a geosynchronous communication satellite with small inner torquers. In Proceedings of the 2nd International Conference on the Recent Advances in Space Technologies, 2005. D. B. Fogel and R. W. Anderson. Revisiting bremermann’s genetic algorithm. i. simultaneous mutation of all parameters. In Proceedings..., pages 1204–1209, San Diego, 2000. IEEE Congress on Evolutionary Computation. P. M. Thompson. Classical/H2 solution for a robust control design benchmark problem. Journal of Guidance, Control and Dynamics, 18(1):160–169, 1995. L. A. Zadeh. Fuzzy sets. Information and Control, 8(3):338–353, 1965.




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