Controller Tuning for DC Motor Speed Control Using Genetic ...Saurabh Jain Dan Simon September 21,...
Transcript of Controller Tuning for DC Motor Speed Control Using Genetic ...Saurabh Jain Dan Simon September 21,...
Aerospace Power & Electronics Simulation Workshop 2004
Controller Tuning for DC Motor Speed Control Using
Genetic Algorithms
Saurabh Jain Dan Simon
September 21, 2004
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Presentation Overview
Purpose of researchSolution strategyIntroduction to Genetic Algorithms (GA’s)
Concept of GAsBasic AlgorithmRepresentation
Simplorer and Matlab implementationConclusions and future work
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Purpose of research
To investigate a new method (Diploid GA) of motor controlTo use Simplorer to evaluate design performanceTo consider a broad optimization function for parameter evaluation
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Problem Statement
Speed Control of DC MotorsController tuning (finding Kp & Ki)
Aerospace ApplicationsFlywheel energy storageFlight control trim surfacesHydraulicsFansThrust vector controlFuel pumps
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Presentation Overview
Purpose of researchSolution strategyIntroduction to Genetic Algorithms (GA’s)
Concept of GAsBasic AlgorithmRepresentation
Simplorer and Matlab implementationConclusions and future work
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Solution Strategy
Spe
edS
peed
Motion Profile
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Optimization function I
Minimize Overshoots
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Optimization function II
1 1 2 3 41 2max ( ) ( )s t a m m m ms tc s tc
F w i t k O k O k O k O= + + + +
( ( ), ( ))s mF i t O tφ=
min ormax 1/s sF F
is the maximum overshoot
is the rotor current
are the weighting factorsik
mO
ai
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Presentation Overview
Purpose of researchSolution strategyIntroduction to Genetic Algorithms (GA’s)
Concept of GAsBasic AlgorithmRepresentation
Simplorer and Matlab implementationConclusions and future work
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Introduction to GAs
Genetic algorithms (GA’s) are a technique to solve problems which need optimizationGA’s are a subclass of Evolutionary Computing
GA’s are based on Darwin’stheory of evolution
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Concept of GAs IMost often one is looking for the best solution in a specific subset of solutionsThis subset is called the search space (or state space)Every point in the search space is a possible solutionTherefore every point has a fitness value, depending on the problem definitionGA’s are used to search thesearch space for the bestsolution, e.g. a minimum
Difficulties are the local minima and the startingpoint of the search
0 100 200 300 400 500 600 700 800 900 10000
0.5
1
1.5
2
2.5
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Concept of GAs II
Starting with a subset of n randomly chosen solutions from the search space (i.e. chromosomes). This is the population
This population is used to produce a next generation of individuals by reproduction
Individuals with higher fitness have more chance to reproduce (i.e. natural selection)
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The Basic Algorithm0 START : Create random population of n
chromosomes1 FITNESS : Evaluate fitness f(x) of each
chromosome in the population2 NEW POPULATION
0 SELECTION : Based on f(x)1 RECOMBINATION : Cross-over chromosomes2 MUTATION : Mutate chromosomes3 ACCEPTATION : Reject or accept new one
3 REPLACE : Replace old with new population: the new generation
4 TEST : Test problem criterium5 LOOP : Continue step 1 – 4 until criterium is
satisfied
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Representation IGenetic information is stored in the chromosomesEach chromosome is build of DNAThe chromosome is divided in parts: genesGenes code for propertiesThe posibilities of the genes for one property is called: alleleEvery gene has an unique position on the chromosome: locus
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Types of GAs
Haploid GAsEasy to useLess Computation
Diploid GAsGood for Dynamic EnvironmentsMore Diversity
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Representation IIThe entire combination of genes is called genotypeA genotype develops to a phenotypeAlleles can be either dominant or recessiveDominant alleles will always express from the genotype to the phenotypeRecessive alleles can survive in the population for many generations, without being expressed
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Cell Division
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Genetic Operators
Meiosis
Selection
Next Population
Mutation
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Haploid Reproduction
3.7
3.9
4.3
Haploid adults
fusion
meiosis
“crossover” P’
diploid“zygote”
haploidchild
HA
PLO
ID
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Diploid Reproduction
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Presentation Overview
Purpose of researchSolution strategyIntroduction to Genetic Algorithms (GA’s)
Concept of GAsBasic AlgorithmRepresentation
Simplorer and Matlab implementationConclusions and future work
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Simplorer and Matlab implementation: Matlab Processing
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Simplorer and Matlab implementation: Simplorer Processing
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Simplorer Model
xn
POW
CONSTDivisorMUL
CONSTSet_Point_Speed_rpm
NEG GAIN
P_Control
I
I_Control Controller
LIMIT
NEG
Control_Out
GAIN
Measured_Iamps
GAINMeasured_Hz
M
MOS1
MOS2
MOS3
MOS4
D1
D2
D3
D4
E
DCMOTOR
D5
NEG
SiM2SiMSIMPLORER Link InterfaceSiM2SiM
SIM2SIM1
P := P
I := I
OVERSHOOT
INTEGRAL
OVERSHOOT
INTEGRAL
Count1_Reset
Count1_Enable
PI_SET_STATETRANS2
EQUBL
LOAD_TORQUE
TRANS3
TRANS4
TRANS5 TRANS6
EQUBL
TRIGGER
TRANS1TERMINATION_STATE
MEASURE
CONDITION
CONST
CONST1
EQUBLTRIGGER1
EVENT
Igain
Pgain
Igain
Pgain
CONDITION.VAL := CONDITION.VALTRIGGER.VAL[0] := TRIGGER.VAL[0]
IA
LOAD
GAIN
GAIN1
D
DIFF
CALC
e:=m c²
PROBE21
CONST
CONST2
CONST
CONST3
CALC
e:=m c²
PROBE22EVENT1
CONST
IMAX
CONST
RIMAX
CONST
CONST4
IAE
TF := TF
OVERSHOOT
OVERSHOOT1
OVERSHOOT OVERSHOOT2
OVERSHOOT
OVERSHOOT3
EQUBL
O_SUM
CLR
Q2
Q3
Q1
Q0
Binary
CLK
CLK
AND2
Q=>BS
CLR
Q2
Q3
Q1
Q0
Binary
CLK
DAC
VAL[3:0]INPUT
RESET_CLK
DAC1
CONST
AND2B1
DAC
VAL[3:0]INPUT
DAC2
Q=>BS
Q=>BS
GA
IN
GA
IN
Count3_Reset
Count3_Enable
Count4_Reset
Count4_Ebable Simulink_Trigger
Load_Torque
TRANS9
Load_Torque
TRANS10
CLR
Q2
Q3
Q1
Q0
Binary
DAC
VAL[3:0]INPUT
DAC3
CLR
Q2
Q3
Q1
Q0
Binary
DAC
VAL[3:0]INPUT
DAC4
GAIN
GAIN Q=>BS
Q=>BS
AND2
AND2
CLK
Q=>BS
CLK
Q=>BS
GAIN
GAIN
EQU
TIMERST := ST
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Functional Blocks
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State Flow
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Simulink Model
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Simulation Results
Plot of Population Average Fitness and Maximum fitness in each generation vs Number of Generations
Parameters
Population Size 200Max Generations 150
Mea
n fit
ness
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Simulation ResultsR
espo
nse
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Simulations Results
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Simulation Results
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Conclusions and Future work
Considering the optimization criteria we have achieved satisfactory results. Longer GA runs are expected to perform even betterThis can be expanded to encompass more parameters from the systemReal time implementation (on-line tuning)Comparison with other tuning methods / haploid GA’s