Chapter 4 Decoupled Optimization of PowerElectronics Circuits Using Genetic AlgorithmsJ. Zhang, Henry S. H. Chung†, W. L. Lo, S. Y. R. Hui, and A. Wu
Department of Electronic Engineering
City University of Hong Kong
Tat Chee Avenue
Hong Kong
Abstract
This chapter presents an implementation of a decoupled optimization techniquefor design of switching regulators using genetic algorithms (GA). Theoptimization process entails selection of the component values in the regulator tomeet the static and dynamic requirements. Although the proposed approachinherits characteristics of evolutionary computations that involve randomness,recombination, and survival of the fittest, it does not perform a whole-circuitoptimization. Consequently, intensive computations that are usually found instochastic optimization techniques can be avoided. In the proposed optimizationscheme, a regulator is decoupled into two components, namely the powerconversion stage (PCS) and the feedback network (FN). The PCS is optimizedwith the required static characteristics such as the input voltage and output loadrange, while the FN is optimized with the required static characteristics of thewhole system and the dynamic responses during the input and outputdisturbances. Systematic procedures for optimizing circuit components aredescribed. The proposed technique is illustrated with the design of a buckregulator with overcurrent protection. The predicted results are compared with thepublished results available in the literature and are verified with experimentalmeasurements.
4.1 IntroductionIt is now widely recognized that computer-aided-design (CAD) tools can reducethe time and cost of production for electrical circuit design. Although muchresearch work is focused on the analysis of periodically switching circuits [1]-[3],techniques developed so far are not fully applicable for power electronics circuits(PEC). As the operation of the switches in PEC is dictated by various constraint
equations, the topology duration and sequence of operation are dependent on theintrinsic circuit waveforms [1], [3].
In the last two decades, small-signal models have been widely applied in thedesign of feedback circuit for switching regulators. Among various approaches,the state-space averaging and its variant [4]-[7] are the most common ones. Byrecognizing that a converter has an output filter with corner frequency, which ismuch lower than the switching frequency, a linear time-invariant model can bederived to approximate the time-variant PEC. Based on the generic feature ofslow-varying output, a concept of injected and absorbed current has beenproposed [5]. This concept extracts the output capacitor from the circuit, yieldingan order reduction in the system differential equations [6]. By performing a Bodeplot of the converter characteristics and applying the classical control theories,circuit components in the feedback compensation network can be designed.Although the procedures are simple and elegant, they are usually applied tospecific circuits and control schemes [8]-[9], which require comprehensiveknowledge on the circuit operation. In addition, as the circuit has been convertedinto a mathematical model and its state variables have been averaged, no detailedinformation about the exact waveforms and the response profiles can be obtained.Circuit designers would sometimes find it difficult to predict precisely the circuitresponses under large-signal conditions [7].
As power electronics technology continues to develop, there is a continuous needfor automated synthesis that starts with a high-level statement of the desiredbehavior and optimizes the circuit component values for satisfying some requireddesign objectives. About two decades ago, techniques for analog circuit designautomation began to emerge. These methods incorporated heuristics [10],knowledge bases [11], simulated annealing [12], and other algorithms, in whichcircuit optimization techniques are a powerful adjunct in the design stage.Classical optimization techniques such as the gradient methods and hill-climbingtechniques have been applied [13]-[14]. However, some methods might be subjectto becoming trapped into local minima, leading to sub-optimal parameter values,and thus, having a limitation of operating in large, multimodal, and noisy spaces.
Over the last few years, modern stochastic optimization techniques involvingevolutionary computation such as genetic algorithms (GA) [15] have been shownto be an effective way to find solutions close to the global optimum and are lessdependent upon the initial starting point of the search [16]. A set of guidedstochastic search procedures that are based loosely on the principles of genetics isformulated. The procedures are flexible, allowing mixed type, bounded decisionvariables and complex multifaceted goals. Although GA are appropriate forsolving off-line engineering design problem, the stochastic search procedures arecomputationally intensive. The additional burden of performing an exhaustive or
probabilistic search of each proposed trial solution in order to establish itssensitivity is very tedious. This chapter presents an implementation of adecoupled optimization technique for design of switching regulators using GAs.Circuit components are depicted as vectors of parameters that are usually namedchromosomes. The constructed data structures are manipulated with the GA. Theoptimization process entails selection of the component values in the regulator tomeet the static and dynamic requirements. Although the proposed approachinherits characteristics of evolutionary computations that involve randomness,recombination, and survival of the fittest, it does not perform a whole-circuitoptimization so that intensive computations can be lessened. In the proposedoptimization scheme, a regulator is decoupled into two components including thepower conversion stage (PCS) and the feedback network (FN). The circuitcomponents in the PCS are optimized with the required static characteristics suchas the input voltage and output load range. The circuit components in the FN areoptimized with the required static behaviors of the whole regulator and thedynamic responses during the input voltage and output load disturbances. Sec. IIshows the decoupled regulator configuration. Section 4.3 describes thechromosome structures and the fitness functions for the PCS and FN in the GAoptimization. Section 4.4 describes the optimization procedures. In Section 4.5,the proposed approach is illustrated with the design of a buck regulator withovercurrent protection. A prototype using the GA-optimized component valueshas been built. Simulated results are compared with the waveforms obtained inavailable literature and experimental measurements.
4.2 Decoupled Regulator ConfigurationThe basic block diagram of a power electronics circuit including the PCS and FNis shown in Figure 4.1. The PCS is supplied from the source vin to the load RL. ThePCS consists of IP resistors (R), JP inductors (L), and KP capacitors (C). The FNconsists of IF resistors, JF inductors, and KF capacitors. The resistors in the PCSrepresent the parasitic resistors of the components such as the equivalent seriesresistance of inductors and capacitors since no explicit resistors are usually addedin power processing. The signal conditioner Ho converts the PCS output voltage vo
into a suitable form (i.e., vo′) for comparing with a reference voltage vref. Theirdifference vd is then sent to an error amplifier (EA). The EA output ve is combinedwith the feedback signals Wp, derived from the PCS parameters, such as theinductor current and input voltage, to give an output control voltage vcon afterperforming a mathematical function g(ve, Wp). vcon is then modulated with a pulse-width modulator to derive the required gate signals for driving the switches in thePCS. Mathematically, all passive components in the PCS and the FN can berepresented with the use of two vectors ΘPCS and ΘF N, respectively. They aredefined as follows.
Figure 4.1 Block diagram of power electronics circuits: chromosomestructures and the fitness functions
Apart from satisfying the operating requirements, including the static anddynamic responses, the components might also be required to optimize for otherfactors such as the physical size and the total cost of the components.Conventional techniques usually perform a whole-circuit optimization, in whichall components are optimized at the same time. Such approach will becomputationally intensive because it involves considerable searching dimensions.In this chapter, ΘPCS and ΘFN are optimized separately with the GA by decouplingthe PCS and FN. For example, if the searching dimension of the PCS is NPCS andthat of FN is NFN, the total training time is equal to the sum of the time taking to
train NPCS parameters in the PCS and NFN parameters in the FN. The required timewill be shorter than training (N PCS + NFN) parameters in the whole-circuitoptimization. This new approach greatly simplifies the optimization proceduresand reduces the computation time. The parameters in ΘPCS is optimized byconsidering the steady-state operating requirements in the PCS such as the inputand output load range, steady-state error, and output ripple voltage. With thedetermined ΘPCS, parameters in ΘFN are then optimized for the whole-systemsteady-state characteristics and dynamic behaviors such as the maximumovershoot and undershoot, and the settling time during the input and outputdisturbances.
4.2.1 Optimization Mechanism of GA
The parameters in ΘPCS and ΘFN are grouped in a chromosome-like structure. Agroup of these chromosomes constitutes a population. An index of merit (fitnessvalue) is assigned to each individual chromosome, according to a defined fitnessfunction. A new generation is evolved by a selection technique, in which there isa larger probability of the fittest individuals being chosen. Pairs of chosenchromosomes are used as the parents in the construction of the next generation. Anew generation is produced as a result of reproduction operators applied onparents. There are two main reproduction operators, namely mutation andcrossover. New generations are repeatedly produced until a predefinedconvergence level is reached.
4.2.2 Chromosome and Population Structures
The chromosome structure for optimization of ΘPCS and ΘFN is similar to Equation(1). The formats of the chromosome CP for the PCS and the chromosome CF forthe FN in a population are as follows;
]||[ 212121 PPP KJI CCCLLLRRRCP LLL= (2)
]||[ 212121 FFF KJI CCCLLLRRRCF LLL=
CP and CF are coded as vectors of floating point numbers, of the same length asthe solution vector. Each parameter in CP and CF is forced to be within thedesired range. The precision of such an approach depends on the underlyingmachine, but is generally much better than that of the binary representation inconventional GA-training [17]. Same chromosome structure is defined in Clanguage for CP and CF in their respective population,
typedef struct long double ∗RValue, ∗LValue, ∗CValue;
The values of the component are stored in arrays, which are pointed by RValue,LValue, and CValue, corresponding to each individual component type. Thefitness value of the chromosome is stored in FitnessValue, which is determinedby considering the static and dynamic responses, and its computation will bedescribed in the next section. The chromosomes in the population are also storedin the form of structures. That is,
The number of chromosomes in a population is stored in NumOfChromosome.The chromosomes in the respective population are stored in arrays, which arepointed by CF and CP, respectively. The numbers of R, L, and C in a chromosomeare stored in NumOfR, NumOfL, and NumOfC, respectively. The searchingspace of each component value is bounded within a predefined range. That is, thevalues of R, L , and C will lie between [Rmin, Rmax], [Lmin, Lmax], and[Cmin, Cmax] in the respective population.
4.2.3 Fitness Functions
An index (fitness value) is assigned to each chromosome in the populationaccording to a predefined fitness function. The fitness value shows the degree ofattainment of the chromosome on the optimization objectives. In this chapter, amulti-objective optimization is adopted. Better chromosome will have a higherfitness value. The optimization objectives of the PCS are based on the steady-state behaviors and the optimization objectives of the FN are based on the steady-state behaviors of the whole system and dynamic responses under the input andoutput disturbances. Their definitions are described as follows.
4.3 Fitness Function for PCSThe fitness function ΦP for evaluating each chromosome in PCS_Populationis based on the following considerations, including
1) The steady-state error of vo within the required input voltage range vi n ∈[Vin,min , Vin,max] and output load range RL ∈ [RL,min , RL,max ]
2) The operation constraints on circuit components, such as the maximumvoltage and current stresses, ripple voltage and ripple current
3) The steady-state ripple voltage on vo,
4) The intrinsic factors concerning with the components in the selectedchromosome, such as the total cost, physical size, etc.
Hence, ΦP measures the attainment of a generic chromosome CP for the abovefour objectives in the static operating conditions. Each objective is expressed byan objective function (OF). For the nth chromosome in the population, ΦP isexpressed in the form of
ΦP n L in n L in nv V v
V
R R R
R
l in n L in n
CP OF R v CP OF R v CP
OF R v CP OF R v CP
in in in
in
L L L
L
( ) [ ( , , ) ( , , )
, , ( , , )]
,min
,max
,min
,max
,,
= + +
( ) +
==∑∑ 1 2
4
δδ
(3)
where δRL and δvin are the steps in varying RL and vin, respectively, for evaluatingΦP. The definitions all OFs in Equation (3) are defined as follows.
4.3.1 OF1 for Objective (1)
The steady state vo is a crucial factor that considers the suitability of ΘPCS in thepopulation. The implied goal is to find whether there exists a value of vcon inFigure 4.1 such that the value of vo after the signal conditioning of Ho [i.e., vo′ ] issame as vref. An iterative Secant method [18] is applied to determine the steadystate waveforms. An integral square error function Ε2
(r) is defined in the rthiteration in order to estimate the closeness of vo” with vref in Ns simulated samples,where
∑=
−=ΕsN
mref
ro
r vmv1
2)()(2 ])(’[
(4)
vo′ is obtained by performing a time-domain simulation for a given value of vcon
and the initial state vector x(0) in the PCS with the FN excluded. If Ε2 is less thana tolerance ε, it is assumed that the system is in steady-state conditions.Otherwise, another guess of vcon
r xvx = .)1(~ +rx will be used in the next iteration until a steady-state solution is determined.
However, the iteration will also be terminated when r is larger than a presetnumber Nr.
Formulation of OF1 is based on Ε2. The major objective is that if no steady-statesolution can be found if OF1 should be small. Otherwise, OF1 should be large.OF1 is defined as follows,
)(/11
22 εΕ−= KeKOF (6)
where K1 is the maximum attainable value of OF1 and K2 adjusts the sensitivity ofOF1 with respect to Ε2. The relationships between OF1 and (Ε2 / K2 ε) are shownin Figure 4.2(a). It can be seen that OF1 decreases as Ε2 increases. It shows a 90%reduction when Ε2 is larger than 2.3 times K2 ε. Thus, if K2 is set smaller, highercreditable components will be selected for ΘPCS. However, the searching processwill become tight, causing longer computation time.
Under the steady-state condition, there are constraints that control the operatinglimits of some waveforms. For example, if λC is the limit of a considered quantityq, such as the maximum voltage stress across a switch, OF2 is defined as
∑=
−λ−+=
C
mmCm
N
mqK
m
e
KOF
1)(
,32
,,41(7)
where NC is the number of constraints, K3,m is the maximum value of the mthconstraint, and K4,m determines the sensitivity of considered quantity. If K4,m islarge, the variation of OF2 is more critical to the quantity variation. It will affectthe searching process in the optimization. The relationships between (qm′ = λC,m -qm) and OF2 are shown in Figure 4.2(b). If qm” is large, OF2 will also be large. Forexample, if λC represents the maximum voltage rating of a switch and q is theactual voltage stress, OF2 is large when q is much smaller than λC (i.e., qm′ >> 0).
The ripple voltage on vo has to lie within a limit of ±∆vo around the expectedoutput vo,exp. A measure of the attainment of the chromosome CPn in this objectiveis to count the area of vo outside vo,exp ± ∆vo in Ns simulated samples. Hence, OF3
is defined as61 /
53KAeKOF −= (8)
where K5 is the maximum attainable value for this objective, K6 is the decayconstant for OF3, and A1 is the ripple area outside the tolerance band, for example±2% of vo,exp. Its form is similar to OF1. Thus, OF3 decreases as A1 increases.
4.3.4 OF4 for Objective (4)
Apart from the electrical performance of the PCS, some intrinsic factors relatingto the components are considered in this objective function. Factors such as thecost, physical size, lifetime of the components can be included. In general, theyare in nonlinear relationships with the components. Thus, OF4 can be expressed as
∑∑∑===
φ+φ+φ=PPP K
k
kC
J
j
jL
I
i
iR CLROF111
4 )()()((9)
where φ R , φ L , and φC are the objective functions for measuring individualcomponent type. For example, if the cost of L increases with its inductance, φL
can be expressed
jjL
L
KL 7)( =φ
(10)
where K7 is a scaling factor. If Lj is large, φL will decrease accordingly.
4.4 Fitness function for FNSimilar to the PCS, the fitness function ΦF for evaluating each chromosome inFN_Population is based on several operating conditions, including
1) The steady-state error of vo within the required input voltage range vin ∈ [Vin,min
, Vin,max] and output load range RL ∈ [RL,min , RL,max ]
2) The maximum overshoot and undershoot, and the settling time of vo (or vd)during the startup
3) The steady-state ripple voltage on vo
4) The dynamic behaviors as in 2) during the input voltage and output loaddisturbances.
ΦF measures the attainment of CF for the above four objectives. Mathematically,for the hth chromosome in the population, ΦF is expressed as
ΦF h L in h L in hv V v
V
R R R
R
L in h h
CF OF R v CF OF R v CF
OF R v CF OF CFin in in
in
L L L
L
( ) [ ( , , ) ( , , )
( , , )] ( ),min
,max
,min
,max
,,
= +
+ +==∑∑ 5 6
7 8
δδ
(11)
The definitions of all OFs are described as follows.
4.4.1 OF5 for Objective (1)
With a defined set of component values in the PCS, the steady state condition ofthe whole system is determined by the dual loop iteration method in [18]. As thisobjective is similar to OF1, formulation of OF5 is also based on Ε2 in Equation (5)and is defined as
)(/85
92 εΕ−= KeKOF (12)
where K8 is the maximum attainable value of OF3 and K9 adjusts the sensitivitywith respect to Ε2.
4.4.2 OF6 and OF8 for Objective (2) and Objective (4)
During the start-up or external disturbances, a transient response appears at vd,where
’orefd vvv −= (13)
A typical response of vd is shown in Figure 4.3. OF6 and OF8 are used to measurethe transient response of vd, including (1) the maximum overshoot, (2) themaximum undershoot, and (3) the settling time of the response, during the startupand disturbances, respectively. The general form of OF6 and OF8 can beexpressed as
where NT is the number of the input and load disturbances in the performance test.
In the above expressions, O V, UV, and ST are the objective functions forminimizing the maximum overshoot, maximum undershoot, and settling time ofvd. They are defined as,
where K10 is the maximum attainable value of this objective function, Mp0 is thedesired maximum overshoot, Mp is the actual overshoot, and K11 is the passbandconstant.
130 /]/)[(
12
1 KvMM refvve
KUV −−+
=(16)
where K12 is the maximum attainable value of this objective function, Mv0 is thedesired maximum undershoot, Mv is the actual undershoot, and K 13 is thepassband constant.
150 /)(14
1 KTT SSeK
ST −−+=
(17)
where K14 is the maximum attainable value of the objective function, Ts0 is thedesired settling time, Ts is the actual settling time, and K15 is the passbandconstant. TS is defined as the settling time of vd that falls within a ±σ % band. Thatis,
The definition of OF8 is the same as the criteria in the PCS optimization, in whichthe number of samples that are outside the tolerance band of the steady stateoutput ±∆vo are measured. Hence OF8 is same as Equation (8). That is,
61 /538
KAeKOFOF −== (19)
The values of ΦP and ΦF are stored in the FitnessValue in the chromosomestructure for quantifying their attainments. Their usage is described in the nextsection.
4.5 Steps of OptimizationThe optimization procedures for the PCS and FN are similar. Their majordifferences are in the definitions of the fitness functions and population. Thus,with the aid of the flowchart in Figure 4.4, only the steps of optimizing the PCS inone generation are illustrated in the following.
Step 1: Initialization
The population size (Np), which is the NumOfChromosomes in Section 4.2, themaximum number of generations (Gmax), the probability of crossover operation(px), the probability of mutation operation (pm), and the generation counter (gen)are initialized at the start of the optimization. Moreover, all chromosomes areinitialized with random numbers, which lie within the practical design limits (i.e.,Rmin ≤ RI ≤ Rmax, Lmin ≤ Lj ≤ Lmax, Cmin ≤ Ck ≤ Cmax). By using (4)[or (12) for FN optimization], the fitness values of all chromosomes are thencalculated. The best chromosome in the initial generation CPB(0) having thehighest fitness value i.e., Φ[CPB(0)] = MaxΦ[CPn(0)], n = 1, … Np, is thenselected as reference for the next generation.
Step 2: Selection of Chromosomes
A selection process, which is based on applying the roulette wheel rule, isperformed. It starts with the calculation of the fitness value Φp[CPn(gen)], therelative fitness value Φp,r[CPn(gen)] and the cumulative fitness valueΦp,c[CPn(gen)] for the CPn(gen),
A random probability variable p ∈ [0,1] is generated and compared with thecumulative fitness values Φp,c[CPn(gen)] for n = 1 … Np. If Φp,c[CPz-1(gen)] < p <Φp,c[CPz(gen)], CPz is selected to be a member of the new population. Thisselection process is repeated until Np members have been selected for the newpopulation. In this selection process, the chromosomes with higher fitness valueswill have higher probability to survive. It is noted that same chromosome ofhaving high fitness value might appear repeatedly in the new population.
Step 3: Reproduction Operations
After the above selection process, a new chromosome is reproduced byperforming two operations including crossover and mutation operations. Thecrossover operation is illustrated in Figure 4.5(a), in which two chromosomes areselected from the population for the crossover operation. In order to determinewhether a chromosome will undergo a crossover operation, a random selectiontest (RST) is performed. The RST is based on generating a random number p ∈[0, 1] for the considered chromosome. If p < px , the chromosome will be selectedfor crossover. By performing a similar procedure, another chromosome will bechosen. [In Figure 4.5(a), CP1 and C P2 are illustrated.] A crossover point isselected randomly with equal probability from 1 to the total number ofcomponents in the chromosomes. The genes after the crossover point will beexchanged, thus, forming two new chromosomes (i.e., CP1′ and CP2′). The aboveoperations are repeated until all members in the population have been considered.
The mutation operation, which is illustrated in Figure 4.5(b), also starts with aRST for each chromosome. If the generated random number p ∈ [0, 1] for achromosome is larger than pm, the chromosome will undergo mutation. In Figure4.5(b), CP1 is illustrated. The mutation is slightly different from the method withchromosome using binary representation. A random number will be generated forthe respective type of component with the value lie within the limits of thecomponents. For example, if a capacitor is selected for mutation, a randomnumber will be generated in the range of [Cmin, Cmax] and will be substitutedinto the original component value (i.e., CP1′). The procedures will be repeateduntil all members have been considered.
After finishing the reproduction operation and the calculation of the fitness valueof each chromosome, the best member CPB(gen) that has the largest fitness valueand the worst member C Pw(gen) that has the smallest fitness value will beidentified. CPB(gen) will be compared with the best one in the last generation
[i.e., CPB(gen – 1)]. If the fitness value of CPB(gen) is smaller than the one ofCPB(gen – 1), the chromosome content of CPB(gen – 1) will replace the content ofCPB(gen). Afterwards, the chromosome content of CPB(gen – 1) will besubstituted into CPw(gen) and the next GA cycle will be started from step (2).
4.6 Design ExampleThe proposed optimization scheme is illustrated with the design of a buckregulator with overcurrent protection [1]. The schematic is shown in Figure 4.6.The regulator consists of a classical buck converter and a proportional-plus-integral (PI) controller. The required specifications are as follows.
Figure 4.6 Buck regulator with overcurrent protection
For the PCS, L and C are the design parameters and RL, rC , and rE are assumed tobe known parameters. For the FN, all components are the design parameters. Theparameters for the GA optimization are tabulated in Table 4.1. It takes 1 hour to
optimize the PCS and 2 hours to optimize the FN on a Pentium II 300 MHz PC.Based on the design criteria in Section 4.3.1, Table 4. 2(a) shows the initial valuesof L and C and the results after 500 generations. The optimized values of theinductor and capacitor in the buck converter were found to be 194 µH and 1054µF, respectively. These two values are close to the ones in [1]. The PI controlleris then optimized after the PCS optimization. Table 4.2(b) shows the initialcomponent values for the controller and the optimized results after 500generations. Figure 4.7 shows the fitness values of ΦP and ΦF versus the numberof generation. It can be observed that the fitness value has come to a satisfactorylevel after 500 generations. The predicted results are then verified withexperimental measurements.
Table 4.1 Parameters in GA optimization
Power Conversion Stage (PCS) Feedback Network (FN)
Table 4.2(a) Initial values of L and C and the results after 500 generations
Component Initial Value Optimized value after 500 generations
L 200 µH 194 µH
C 1000 µF 1054 µF
Table 4.2(b) Initial component values for the controller and the results after500 generations
Component Initial Value Optimal Value after 500 generations
RC3 4.7 kΩ 3.448 kΩC2 2 µF 5.863 µF
C3 3.3 µF 0.461 µF
R2 300 kΩ 766.56 kΩC4 1.8 µF 1.089 µF
R4 1 kΩ 6.535 kΩR1 0.6 kΩ 1.09356 kΩ
Firstly, two extreme operating conditions with input voltage equal 20 V and 60 Vare studied, respectively. The simulated startup transients when the input voltageis 20 V and the output load is 5 Ω are shown in Figure 4.8. Compared with theoriginal component values used in [1], the GA-optimized component values havebetter performance, giving smaller overshoot in the inductor current and fastersettling time. Moreover, the steady-state error is zero and the output ripple voltageis less than 1%. Figure 4.9 shows the experimental results, which are all in closeagreement with the predicted waveforms. When the input voltage is 60 V, thestartup transients are shown in Figure 4.10 and the experimental results are shownin Figure 4.11. The settling time is less than 20ms in both input voltages. They arestable in the two extreme operating conditions. This confirms that the regulatorwith the GA-optimized component values give satisfactory results for the start-uptransients.
A similar large-signal disturbance test as [1] is performed. When the input voltageis 20 V and the regulator is in steady state, the input voltage is suddenly changedinto 40 V. The transients are shown in Figure 4.12. The experimental results areshown in Figure 4.13. Compared with [1], when the voltage is changed into 40 V,the system will become unstable and is in sub-harmonic oscillation. With theoptimized component values, the system is still stable.
-2
0
2
4
6
8
10
12
14
0.0250.0150.005 0.030
vcon
vo
0.0200.0100
V
olta
ge(V
)
Time(Sec)
(a) vo and vcon.
0
1
2
3
4
0.0250.0150.005 0.0300.0200.0100
Cur
rent
(A)
Time(Sec)
(b) iL.
Figure 4.12 Simulated transient responses when vin is changed from 20 V to40 V
Similar tests on load disturbances are performed with the input voltage at 40 V.When the system is in the steady state, the output load is suddenly changed from5 Ω into 10 Ω . The simulated and experimental transients are shown in Figure4.14 and Figure 4.15, respectively. Afterwards, the output load is changed into 5Ω. The simulated and experimental transients are shown in Figures 4.16 and 4.17,respectively.
-1
0
1
2
3
4
5
6
7
0.005 0.0250.015
vcon
vo
0.0300.010 0.0200
V
olta
ge(V
)
Time(Sec)
(a) vo and vcon.
0
1
2
3
0.0250.005 0.015 0.020
0.02
0.0300.0100
Cur
rent
(A)
Time(Sec)
(b) iL
Figure 4.14 Simulated transient responses when RL is changed from 5 Ω to10 Ω and vin is 40 V
The experimental measurements agree well with the predicted results using theproposed off-line GA optimization technique. Both the static and the dynamicresponses are close to the designed specifications, confirming the validity of theproposed optimization approach. In addition, it can be seen from the above teststhat the proposed technique is independent of the operating mode of the PCS. Forexample, during the transient period at startup or large-signal disturbances, theconverter may operate between continuous and discontinuous mode. It is becausethe optimization is based on the actual time-domain performance, withoutassuming any predetermined operating mode.
4.7 ConclusionsThis chapter presents a systematic decoupled optimization technique for thedesign of switching regulators using genetic algorithms. The process entails theselection of the component values in the power conversion stage and the feedbacknetwork in the regulator to meet some defined static and dynamic requirements.No complicated mathematical analysis of the whole system is needed. Thealgorithm automatically determines the optimum values of the components tomeet the specifications, independent of the circuit structure and control schemes.The proposed technique is illustrated with an example of a buck regulator. Thepredicted results are compared to the performance of the one in the availableliterature and are verified with experimental measurements. Further research willbe dedicated to an automated synthesis of the circuit structure of the regulator.
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