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Applied Soft Computing 11 (2011) 49–55

Contents lists available at ScienceDirect

Applied Soft Computing

journa l homepage: www.e lsev ier .com/ locate /asoc

references in multi-objective evolutionary optimisation oflectric motor speed control with hardware in the loop

iotr Wozniak ∗

nstitute of Automatic Control, Technical University of Łódz, 18/22 Stefanowskiego St., 90-369 Łódz, Poland

r t i c l e i n f o

rticle history:eceived 20 December 2007eceived in revised form7 November 2008ccepted 17 October 2009vailable online 5 November 2009

eywords:ulti-objective optimisationecision maker preferences

a b s t r a c t

This paper presents the design of a robust Pareto-optimal controller with the designer preference articula-tion for a Permanent Magnet Synchronous Motor (PMSM). An evolutionary multi-objective optimisation(EMOO) algorithm is used to tune the proportional integral (PI) speed regulator in the Direct TorqueControl drive system.

Approximation of the Pareto front with hardware in the loop (HiL) is chosen as an alternative to thetime-consuming software simulation studies. Thanks to this approach problems of un-modelled plantdynamics are alleviated and additional manual tuning on-line is not required. The weak point of theHiL approach is caused by disruptive presence of noise which affects the performance of EMOO. Thisinfluence is strongly problem-dependent; therefore no generalized results have yet been presented in

ardware in the loop designlectrical drive system

the literature. In this paper the robustness features of the proposed design approach are verified usingthe state-of-the-art multi-objective evolutionary Non-dominated Sorting Genetic Algorithm (NSGA-II;Deb, 2001 [1]).

The on-line optimised motor drive speed controller is shown to be effective, possessing good dynamiccharacteristics, demonstrating applicability of the a priori preference articulation technique to the

al Pareto f

controller design. The finarticulation before the Pa

. Introduction

Real-world optimisation problems are characterised by the exis-ence of multiple, often conflicting, criteria. In the absence ofnformation about the relative importance of each objective, suchptimisation problems typically allow numerous solutions to exist,nown as Pareto-optimal solutions. These solutions are optimaln the wider sense, meaning that no other solutions in the searchpace are superior to them when all objectives are considered. Forach of the solutions no further improvement in one objective cane obtained without sacrificing performance in other objectives.earching through the Pareto front for a solution appropriate fromhe perspective of the designer is crucial for the effectiveness ofhe multi-objective design. The search through the decision space

ay be deteriorated by many factors. One of the most important isoise.

In control system design optimisation should be robust becauseuring its operation the control signal will be based on outputeasurements. As a result the evaluation of objectives cannot be

onsidered accurate unless the level of noise is sufficiently small.

∗ Tel.: +48 42631559.E-mail address: piotr.wozniak@p.lodz.pl.

568-4946/$ – see front matter © 2009 Elsevier B.V. All rights reserved.oi:10.1016/j.asoc.2009.10.015

reto-optimal solution is selected according to the designer’s preferenceront is approximated by EMOO.

© 2009 Elsevier B.V. All rights reserved.

For this reason the candidate algorithm should search for the robustsolution, i.e. the one for which the on-line quality of control willnot deteriorate under the presence of the noise. It should be notedthat the term “robustness” has other meanings in the context ofmulti-objective optimisation [2]. Among them there are:

(i) The ability of an algorithm to handle different classes of prob-lems.

(ii) Insensitivity of the results to certain parameter values usedwithin the algorithm (e.g. mutation rate in evolutionary com-putations).

In this paper control of the electric drive system is realised bya single control loop with a simple and well-known proportionalintegral (PI) controller. Its most important feature is the abilityto eliminate steady-state offsets through integral action. Althoughone may consider a more versatile proportional integral derivative(PID) controller which can “anticipate the future” through deriva-tive action, we consider it too vulnerable for the high frequency

changes in power supply introduced by the pulse width modulated(PWM) inverter in the drive system under consideration.

Even though the number of parameters to adjust in a PI con-troller is very small, there are over 1100 tuning rules can be foundin the literature (as summarised recently for PI and PID controllers

5 t Computing 11 (2011) 49–55

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n [3]). However, despite all research work, recent results cited in3] report that 80% of controllers are badly tuned.

In recent years genetic algorithms have been used for tuning PIontroller parameters [4–6] (to cite only a few). These applicationsave all been based on identification of the model of the controlledystem, whereas the multi-objective optimisation with hardwaren the loop approach without the model has to be investigatedhoughtfully.

Evolutionary algorithms have been applied to noisy optimi-ation problems for nearly two decades, but robustness analysesave been applied mostly to the single objective optimisation [7].esearch in the area of multi-objective problems is at an earlytage. Recently such methodology taking robustness into accountas been presented [2] and was applied to problems with severalptimal Pareto fronts with the aim to identify the most robust.owever, the problem at hand is not restricted to the approxima-

ion of a whole most-robust Pareto front, but may be formulated asearch of the most-robust regions of the Pareto front.

The results of the PI controller tuning presented in this paperre obtained by minimisation of two standard control performanceriteria evaluated over a finite time needed to reach the steady statef the PMSM rotor speed:

(i) Integral of Time multiplied by the Absolute value of Error (ITAE)criterion.

ii) The control effort in the form of integral of absolute value of thecurrent

∫|i(t)| dt.

The main contribution of this paper is the way the multi-bjective problem is solved. First, the noise influence on the controlystem performance is investigated with hardware in the loop.he analysis is based on the fitness landscape since no model ofhe PMSM drive system is assumed. Second, a set of candidate PIpeed controllers (approximation of the Pareto front) tuned on-ine by the EMOO algorithm is explored. To ease assessment byhe designer, the solutions are presented in the argument spaceather than the objective space. Third, the a priori technique ref-rence point method is integrated with one of the most efficientulti-objective evolutionary algorithms using elitist approach, theSGA-II algorithm [1], and applied to formulate the final, single

olution to the PMSM rotor speed control problem. A conferenceersion of this paper was presented in the IMCSIT Symposium ondvances in Artificial Intelligence and Applications [8].

The rest of this paper is organized as follows. Evolutionary multi-bjective algorithm NSGA-II and designer’s preferences issues arentroduced in Section 2. The design robustness problem is formu-ated in Section 3. Controller tuning design problem is describedn Section 4. Here, specification of the test rig, NSGA-II parametersnd performance measures for the PI controller are stated. Also,he on-line acquired criteria values are presented in form of thetness landscape for feasible arguments are examined. The tuningesults are presented in Section 5. Finally, the conclusions are givenn Section 6.

. Issues in evolutionary multi-objective optimisationlgorithms

Evolutionary algorithms are stochastic search and optimisationeuristics derived from the classic evolution theory, working on aopulation of potential solutions to a problem. The basic idea is that

f only those individuals reproduce, which meet a certain selectionriteria, the population will converge to solutions that best meet theelection criteria. If imperfect reproduction occurs, the populationan begin to explore the search space and will move to individu-ls (solutions) that have an increased selection probability. Genetic

Fig. 1. NSGA-II pseudo code.

algorithms exhibit the clearest mapping from the natural process ofevolution into a optimisation algorithms of single fitness function.In early nineties the approach was extended to the multi-objectiveproblems [1,2].

2.1. Structure of the EMOO

There are four primary goals of evolutionary multi-objectiveoptimisation algorithms:

Goal 1. Preserve the elite of the known Pareto front before intro-ducing the new candidate solutions.

Goal 2. Guide the known Pareto front towards true Pareto front(which is unknown).

Goal 3. Generate and maintain diversity of solutions of the knownPareto front (phenotype) and Pareto set (objectives’ argu-ments which are equivalent to the genotype).

Goal 4. Enable selection of one from the approximated Pareto frontsolution according to the designer’s preferences either in apriori or a posteriori procedure.

Every candidate solution is treated as an individual in the pop-ulation of prospective solutions to the optimisation problem. Thepopulation is evolved over a series of generations (i.e. iterations ofthe algorithm) to produce better off-springs. In the EMOO algo-rithms selection of the potential parent solutions is based onranking criteria, because vectors from the objective evaluationare not sufficient ranking criteria. Various ranking methods havebeen suggested in the literature [2]. They sort the population inthe space of objectives before selecting of the individual’s genes(i.e. solution) for propagation to the next generation (iteration).In this paper the state-of-the-art EMOO algorithm NSGA-II [1] isused for optimisation. Its pseudo code is presented in Fig. 1. Inthe NSGA-II algorithm the population is ranked on the basis ofnon-domination. All non-dominated individuals are classified into

penalised according to the population density of the correspond-ing region of the Pareto front. The procedure then performs nichingby adding a crowding distance to each individual. This keeps thepopulation diverse and helps the algorithm to explore the fitnesslandscape.

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.2. Preferences in the EMOO

Solutions in the Pareto-optimal set perform better in somebjectives and worse in other. Since no single solution optimises allbjectives, decision-making based on designer’s preference articu-ation is a natural element in solving final MOO problems. Relationetween search and decision-making is one of the main criteria inlassification of the MOO algorithms [2]. One may search for pre-erred solution basing on prior articulation or on a “search before

aking decision” approach (i.e. a posteriori articulation).

(i) A priori methods are such when the preferences are expressedprior to search. This group of techniques includes globalcriterion method [2] and approaches that assume certain pre-ordering of the objectives which can be performed by thedesigner.

ii) A posteriori methods are such when the approximation of thePareto-optimal front is available to the designer for selectionaccording to his preferences.

In this paper the a priori approach based on the reference pointethod [9] is considered. It has been chosen as the most suitable

or the problem under investigation, although some of its require-ents are higher than those for a posteriori methods. However, theain advantage over all a posteriori approaches is that there is no

eed to approximate the whole Pareto front.

.3. Designer’s preferences articulation

In the reference point method the aim is to reach a Pareto frontegion located near a specific pre-defined reference point or set ofoints. The main ideas underlying this method are the following:

(i) Solutions closer to reference point in the objective space arepreferred.

ii) Solutions within a ε-neighbourhood to a near-reference pointare preferred in order to maintain a diverse set of solutions.

To allow the identification of the solutions located near the ref-rence point the normalised Euclidian distance (dij) between eacholution of the best non-dominance level and the reference points calculated:

ij =

√√√√ k∑i=1

wi

(fi(X) − zi

f maxi

− f mini

)2

(1)

here f maxi

and f mini

are the maximum and the minimum values ofhe objective function for criterion i, respectively, and zi and wi arehe ith components of the reference point and weight vector.

The distance (1) simultaneously takes into account the relativemportance of the different criteria, quantified through the weightector, and the distance between the solution and the referenceoint. The solutions with shorter distance to the reference pointnd those with higher weight vector will be selected preferentially.

This procedure has been implemented through the modificationf the NSGA-II algorithm niching strategy [10]:

tep 1. For each reference point, the distance (1) of each solution

from the front is calculated and the solutions are sorted inascending order of distance. This way, the solution closestto the preference point is assigned a rank of one.

tep 2. After computations in Step 1 are performed for all referencepoints, the solutions with a smaller preference distance arepreferred in the tournament selection.

puting 11 (2011) 49–55 51

Step 3. To control the coverage of obtained solutions an ε-neighbourhood is used in the niching operator. First,a random solution is picked from the non-dominatedset. Thereafter, all solutions having a sum of normaliseddifference in objective values of ε or less from thechosen solution are assigned an artificially large pref-erence distance. This way, only one solution within anε-neighbourhood is emphasised. Then, another solutionfrom the non-dominated set is picked and the above proce-dure is repeated. The use of the ε-based selection strategyensures a spread of solutions near the preferred Pareto-optimal regions.

The main change in NSGA-II was made to the crowding operator,since in this case the aim is not to obtain a great diversity of solu-tions along the Pareto frontier but only a subset of these solutionsthat minimises the distance to the reference point.

3. Robustness of the control design using EMOO technique

The performance of a particular control design is fundamentallytied to the accuracy of the model upon which it is based. This is espe-cially true for iterative control design and optimisation procedures.The substitution of hardware in the loop (HiL) for the softwaremodel in the MOO opens up new possibilities for design based onreal-world performance indices. In real optimisation problems awide range of uncertainties have to be taken into account. Gen-erally, uncertainties in EMOO can be categorised into four classes.Each of them is presented with additional comments concerningthe HiL setup to be presented in Section 4.2:

(i) Noise in the HiL it comes from measurement errors from sen-sors.

(ii) Errors in approximations induced by mathematical modelling;the HiL approach eliminates this type of uncertainty.

iii) Time-varying parameters of fit; in the considered HiL-basedcontrol system design changes in environment may beneglected because in this study evaluations are available in lessthan 0.5 s, that is in time shorter than all time constants in theconsidered system [11].

(iv) Perturbations of parameters and environmental parametersafter the optimal solution has been determined; this type ofuncertainty is not considered in this paper, however it may beeasily included in the HiL by the appropriate design of experi-ment’s sampling approach.

4. Permanent Magnet Synchronous Motor speed controldesign using EMOO technique based on hardware in theloop approach

In the electric drive control system the PI controller to be opti-mised is positioned in the speed control loop of the PermanentMagnet Synchronous Motor (PMSM) with Pulse Width Modulated(PWM) inverter and Direct Torque Control (DTC) (Fig. 2).

The output of the proportional integral (PI) controller is appliedto the PMSM motor via the PWM channel of the microcontrollerand converter. The dynamic performance of the system is limited bycurrent and voltage restraints (not shown in the diagram) specifiedby the motor manufacturer.

Traditional objective evaluation by software-based simulation

has the disadvantage of being unable to exactly replicate real oper-ational conditions of the hybrid, discrete- and continuous-timesystems. One way to bridge the gap between optimisation and realconditions is to use the HiL approach, which puts hardware directlyinto the objective evaluation procedure. This provides access to the

52 P. Wozniak / Applied Soft Computing 11 (2011) 49–55

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duration of all experiments. Sample sequence of six, 0.8 s long testsis presented in Fig. 3.

The considered fitness landscape is obtained with HiL over aconstrained parameters’ space, as presented on Figs. 4 and 5. It isderived from 120 measurements (which form the mesh of 10 × 12

Fig. 2. Block diagram of robust multi-o

ardware features currently not available in software-only simu-ation models and, hence, reduces the risks of discovering an errorn the very last stage of the testing before running. The HiL on-line

easurements may also cut down the run-time when compared tohe software simulation models. Over the years, many such real-ime simulation (RTS) experiments have been proposed in [12,13],owever these systems are non real-time.

The application of RTS to power electronics system is, in par-icular, a very active field of research and may be considered aignificant challenge for the RTS approach.

Consider the continuous-time PI speed controller of the PMSMFig. 2) given by

(t) = kpe(t) + 1Ti

∫ t

0

e(�) d� (2)

here u(t) is the output of the controller at time t, e(t) is the erroretween the actual and the desired speed of the motor shaft andp, Ti are constants of the controller, and the decision parametersf the EMOO problem.

Because there is no analytical way of finding the optimal setf parameters (kp, Ti) various methods exist to calculate the gainsff-line. Depending on the choice of kp, and Ti the response of theontroller to a given error signal will vary significantly. The mainesign goal is to attain the prescribed transient response and ful-l the steady-state error criteria [14] of the closed-loop system.p-to-date search methods generally involve some form of iter-tive approach to achieve performance criteria such as rise-time,vershoot and settling-time, as well as integral-type criteria [3].

.1. Objective functions

The step response is considered as the basic transient for eval-ating the dynamic control systems [14]. The main performanceeasures of the speed control of the drive system (Fig. 2) are

ffective dumping of the speed deviation and the low power con-umption of the PWM inverter. The best representation of thesedeas in computations is two integral-type objective functions:

(i) Integral of Time multiplied by the Absolute value of Error (ITAE)criterion:∫

ITAE = |ep(t)|t dt (3)

ii) The control effort in the form of integral of absolute value of thecurrent. This objective (denoted hereafter as Int(i)) is related to

ve optimal speed control of the PMSM.

the power consumption of the system:

Int(i) =∫

|i(t)| dt (4)

In this way, it is required the search be performed based on twonon-commensurable objectives. In this research the fitness land-scape in the objective space is used to investigate the vital featuresof the control problem prior to the optimisation. Using the fitnesslandscape the effective optimisation of the deterministic dynam-ics, where every vector (kp, Ti) in the argument space has a certain“height” corresponding to its fitness value in the objective space,can be represented by a downward move in the landscape. Whenit has reached the point satisfying the Pareto-optimum conditions,the algorithm should consider it as a good approximation of thePareto front. Note that this is visualisation of the controller optimi-sation without the model of the dynamics of the PMSM.

Measurements of fitness functions were realised for each pair ofarguments (kp, Ti) for the step-response test [14]. Thanks to reversalmode of the test rig operation, it is possible to alter the sign of thesuccessive step-response tests from +ωr, to −ωr. This reduces the

Fig. 3. Sequence of six, 0.8 s long, speed step-response tests with altering sign forωr = 25 rad/s.

P. Wozniak / Applied Soft Computing 11 (2011) 49–55 53

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Fig. 4. Fitness landscape for objective functions (3) and (4).

venly distributed nodes) of the design arguments (kp, Ti) valuesatisfying constraints:

p ∈ [ 0.5 20 ],1Ti

= [ 2.5 250 ] (5)

hese values are based on the general rules of the PI controlleruning [3].

.2. Noise effect on the objective functions

To evaluate the influence of noise on the objective functions ofhe control problem the statistics of the measurement series haveeen calculated. The 120 measurements, necessary to plot fitness

andscape as shown in Fig. 3, were repeated 20 times. The meanalues were calculated and chosen to represent the elevation ofhe fitness landscape. Above the surface (or beneath, depending on

he relation its to the mean value) are plotted all measurements.he results are presented in Fig. 6 for the ITAE (3) and in Fig. 7or Int(i) (4) objectives, respectively. Note that the average noiseevel in the measurement series is smaller than ±5% of the meanalues. Furthermore, for the Int(i) (4) the average noise level in the

ig. 5. Rotated fitness landscape from Fig. 3 with normalisation to [0, 1] for bothbjectives.

Fig. 6. The ITAE mean value fitness landscape (10 × 12 mesh) with characteristicnoisy measurements.

measurement series presented in Fig. 6 significantly increases forkp > 8.

4.3. The experimental rig of the PMSM drive

The software-implemented PI controller (5) performs trackingof a speed set value ωr for the PMSM manufactured by Kollmor-gen in the single-input–single-output closed-loop control systempresented in Fig. 2. This is achieved through the standard torquehysteresis controller. The DTC switching table connector generatesthe current demand for the PWM power module. This control actionis realised by the dSpace control module from standard laboratoryPC computer, as presented in Fig. 8. The PMSM magnetic flux isstabilised by the independent inner loop, where the shaft speed(signal from the speed sensor), and the constant value of the load(motor type DynamAx DS manufactured by Control Technologies

Dynamics Ltd.) measured by the manometer are fed back as, shownin Fig. 7.

During the PI controller tuning by the EMOO algorithm, allcalculations are performed in the Matlab Real-Time Workshop

Fig. 7. The Int(i) mean value fitness landscape (10 × 12 mesh) with all measure-ments.

54 P. Wozniak / Applied Soft Computing 11 (2011) 49–55

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mated front lies close to the true front [2]. The Pareto front for theconsidered speed control of the PMSM proved to concentrate in arelatively small part of the argument space as shown in Fig. 10.

Fig. 8. The experimental rig of the PMSM P

nvironment [15] with the MLIB library. All measurements are per-ormed through the dSpace control module DSP 1103.

The structure of the test rig used in the presented research isresented in Fig. 8.

.4. The EMOO setup

The parameters of the optimisation algorithm implementeduring evolutionary multi-objective optimisation of the problemefined by (2)–(4) under the following constraints:

(i) in the parameters space defined by inequalities 0.25 < kp < 20;25 < 1/Ti < 200;

ii) in the HiL installation (not presented; for details see [11]).

A Simulated Binary Crossover (SBX) with the crossover proba-ility of 0.9 ensures a good mixing of genetic material, while theolynomial mutation is used in mutation probability of 0.33 guar-ntees that on average one parameter of each individual will beutated (Table 1). The detailed investigation in [11] proved there

s no significant influence of small changes of these parameters onhe robustness of resulting Pareto solutions (as discussed in Section.1).

. Results

The optimal tuning of the PMSM speed regulator using evolu-ionary multi-objective algorithm was performed successfully onhe basis of noisy measurements without the need to model anyf the elements of the system presented in Section 4. The short

Table 1Basic parameters of the NSGA-II algorithm.

Algorithm parameter Value

Population, N 60Generations, G 50Pool size, N/2 30Tour size 2Crossover probability 0.9Mutation probability 0.33

d controller evolutionary multi-objective.

cycle time needed for data collection during stabilisation of theshaft speed enabled resampling, which is the simplest approach todeal with noise.

Taking advantage of the low dimensionality of the argumentspace, the results of the speed control design may be presented inform of three-dimensional plots, as shown in Sections 4.1 and 4.2.Full cycle multi-objective optimisation results in the approxima-tion of the Pareto set and the Pareto front as presented in Fig. 9. Eachvector of arguments (kp, Ti) (point on the base plane) is mappedto the objective space. Elevation of the resulting two points is veryclose to the mean value fitness landscape presented in Figs. 6 and 7.Examination assuming different (i) population size and (ii) numberof generations, revealed good approximation of the Pareto frontusing as low as 20 solutions.

The increased number of generations (iterations of the algo-rithm) does not improve the quality of approximation. This effecthas been reported in the literature and is observed when the esti-

Fig. 9. The Pareto front approximation by 20 solutions, plotted on the fitness land-scape.

P. Wozniak / Applied Soft Com

Fig. 10. Single solution selected from the Pareto front approximation (stars) at the50th iteration, along with all elite solutions from 100 iterations.

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ig. 11. Step response of speed control for the selected single Pareto-optimal solu-ion (bold line) and four argument vectors (as defined by boundary values at (5)).

The impact of measurement noise on the EMOO of speed controlesign is presented in Fig. 10. All elite solutions obtained during 50

terations of evolutionary non-dominated sorting are plotted here.hey are contained in a trapezoid shape along the line approximat-ng the Pareto front. The final 50th generation is presented as a setf stars. Closer examination of results confirms these solutions areon-dominated, which proves the effectiveness of the EMOO withardware in the loop.

A small population size still leaves the designer some degreef freedom for final selection of the preferred solution. Apply-ng the reference point method the solution marked by the red

ot has been selected. In the argument space this solution givesp = 2.01, and 1/Ti = 29.3 1/s. The quality of the chosen is confirmedy the step response in Fig. 11. The solution is compared with theour extreme argument vectors defined by the boundaries of theonstraints (5).

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puting 11 (2011) 49–55 55

Please note that there is no simple way to compare this resultwith classical tuning of the PI controller because no model of thedrive system has been developed.

6. Conclusions

This paper investigates the design of an optimal dynamic con-troller with conflicting criteria for the electric drive system directlyonto hardware. The hardware in the loop approach alleviate therequirement of modelling of any of the considered control systemwhich contains both continuous-time and discrete ones with manyconstraints on signals. Standard approach to the problem is bysoftware-based simulation of such model which is hard numericalproblem and introduces numerical induced errors.

An extensive investigation using the fitness landscape showedbounded influence of the measurement noise on the proposedobjective functions. The conflicting requirements of the design arefulfilled using the multi-objective optimisation by the evolutionaryalgorithm NSGA-II. The research showed that measurement noisepresent during each objective evaluation at run-time does notsignificantly deteriorate the quality of the Pareto front approx-imation. This confirms the robustness of the proposed EMOOapproach. The additional modification to the NSGA-II algorithm isintroduced to assist the designer in selecting the one solution outof the Pareto front. The reference point method enabled a priorieffective articulation of the designer’s preferences in the hardwarein the loop test rig.

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