Latency Effect in a Variable Speed Control onTorsional Response of Elastic Drive Systems

M. Rossi, Member, IEEE, M. Mauri, Member, IEEE, M.S. Carmeli, Member, IEEE,and F. Castelli-Dezza, Member, IEEE

Abstract—Torsional vibration issues in elastic drive systemsare a well-known topic also in the industrial field. The torquepulsations produced by the drive are the main causes of thesetorsional resonance excitations. However, it will be analysedin this paper how some side-effects in the control strategy,like the latencies, are critical as the torque ripple. Indeed, thesuppression of this vibrations phenomenon cannot be achievedcorrectly without analysing and quantifying the time-delaysthat affect the system. This paper aims to provide both acomprehensive analysis on such latencies and introduces amethod to proof the relationship between the damping capabilityof the process and the time-delays. It will be defined a processdamping coefficient in order to explain the relations betweenthe electrical damping, related to the control architecture, thelatencies and the mechanical damping.

Index Terms—VSD applications, TNFs excitation, pulsatingtorque, latency, stability analisys, process damping

I. INTRODUCTION

Every plant like turbo-machinery systems, liquefied nat-ural gas plants (LNG), rolling mills, etc. are equipped witha mechanical transmission that present an elastic behavior.The complexity of these systems and the electromechanicalinteractions between the Voltage Source Drives (VSDs), usedas power units in these systems, and the shaft-line define anew challenge for the shaft torsional behavior description,Fig. 1. Typical problems of uncontrolled torsional vibrationssuch as coupling failures, broken shafts, etc., are reportedin [1]. Some papers analyzes the overall system describingthe interactions between electrical and mechanical parts ina drive-line in terms of harmonics contents considering anideal control of the drive [2], [3], [4]. This is a key point inorder to avoid the excitation sources of the Torsional NaturalFrequencies (TNFs) designing properly the entire shaft-lineand managing the drive control strategies in order to minimizethese excitations. However, the pulsating torque ripple inVSD applications due to the electro-mechanical interactionbetween electrical drive and the mechanical load is not theonly root cause of the torsional vibrations. In this paper it willbe highlighted a complete approach that explain in-depth the

M. Rossi is with the Department of Mechanical Engineering, Politecnicodi Milano, 20156 Italy, (e-mail: mattia1.rossi@mail.polimi.it)

M. Mauri is with the Department of Mechanical Engineering, Politecnicodi Milano, 20156 Italy, (e-mail: marco.mauri@polimi.it)

M.S. Carmeli is with the Department of Mechanical Engineering, Politec-nico di Milano, 20156 Italy, (e-mail: stefania.carmeli@polimi.it)

F. Castelli-Dezza is with the Department of Mechanical Engineering, Po-litecnico di Milano, 20156 Italy, (e-mail: francesco.castellidezza@polimi.it)

side-effects produced by the implementation of a closed-loopcontrol strategy to suppress these vibrations. This problemmight be related to the discretization and processing of thecontrol variable, especially for the presence of some latencies.These effects are not evidenced in the classical torsional anal-ysis because it is only performed considering an open-looparchitecture. From a theoretical point of view, an appropriatedesign of the VSD control will damp the oscillations but it isalso necessary to take in account of some unavoidable time-delays coming from the digital implementations that mightamplifying the torsional vibrations. Without analysing theseeffects, both the additional active or passive control dampingor even an optimal control strategy can be underperformedand not useful. In this paper it will be presented an intuitiveapproach to define an overall damping coefficient of theprocess and the relations between this coefficient and thecomplete control architecture. If this damping coefficient isvery low the mechanical vibrations can reach dangerouslyhigh levels of magnitude, especially in turbomachinery andoil&gas applications [3], [5]. The paper is organized in thisway: Sections II analyse the effects of torsional resonanceexcitations due to the interactions between the drive and themechanical system modelling a Medium Voltage (MV) 6MWinduction motor drive, Section III introduces the latencieseffect on the process damping coefficient related to suchresonances, Section IV explains the latencies root cause andthe effects on the control stability, Section V defines theprocess damping coefficient and it describes how latencyeffects can change this coefficient considering the applicationof Section II.

II. ELASTIC DRIVE SYSTEM MODELING

There are different sources of torsional vibrations: me-chanical imbalance, shaft/coupling misalignment, weak bear-ings, etc. All these sources lead to vibrations due to me-chanical aspects [6] however, the mechanical parts are driven(directly or with gearbox) by an electrical motor. Thus, inaddition to the previous issues, the torque pulsations producedby a VSD can present a harmonic content that match themechanical TNFs. To analyse these issues, it is necessaryto define an accurate drive system model.

A. Dual-Inertia Elastic ModelA dual inertia model is an effective representation of the

mechanical part of Medium Voltage Drives in most cases.

Fig. 1. Control scheme of a dual-inertia elastic system

The main reason is due to, in the common speed operatingregion of these systems, only the 1st and maybe 2ndTNF

can be excited by the harmonic content of the drive itself.Obviously, in special operating conditions could be necessaryto extend the model complexity in order to consider higherTNFs as for example the 3rd, 4th. From Fig. 2 can be built adual-inertia elastic representation in terms of MIMO transferfunctions with spring and damping elements between driveand the load stage. The mechanical equations of this modelare indicated in (1) and starting from them, it is possible tobuilt an augmented state-space representation [x] = [A][x] +[B][u] and [y] = [C][u] where it is also defined the couplingtorque relation.8>>>>>><

>>>>>>:

m

mot

�m

coupling

= J

mot

⌦

mot

m

coupling

�m

load

= J

load

⌦

load

m

coupling

= K

el

(✓mot

� ✓

load

) + C

el

(⌦mot

�⌦

load

)

⌦

mot

= ✓

mot

⌦

load

= ✓

load

(1)based on the following matrix

[A] =

2

664

0 0 1 00 0 0 1�↵ ↵ �� �

� �� � ��

3

775↵ = K

el

J

mot

� = C

el

J

mot

� = K

el

J

load

� = C

el

J

load

[C] =

[I]4⇥4

K

el

�K

el

C

el

� C

el

�[B] =

2

4[0]2⇥21

J

mot

00 1

J

load

3

5

(2)where [x] = [✓

mot

✓

load

⌦

mot

⌦

load

]t, [u] = [mmot

m

load

]t,and [y] = [✓

mot

✓

load

⌦

mot

⌦

load

m

coupling

]t. The angularpositions of the motor and the load are ✓

mot

and ✓

load

, and⌦

mot

and ⌦

load

are the angular speeds of the motor and theload respectively. The electromechanical torque is m

mot

, theload torque is m

load

and the coupling torque is m

coupling

.The moments of inertia of the motor and the load are J

mot

and J

load

and the torsional stiffness and the damping of theshaft are K

el

and C

el

.

[Gm

(s)] = [C] (s[I]� [A])�1 [B] =

2

66664

G11 G12

G21 G22

G31 G32

G41 G42

G51 G52

3

77775(3)

Fig. 2. Electrical conversion topology on motor side

Based on (3), the transfer function relationship for themotor speed is ⌦

mot

= G31(s)mmot

+ G32(s)mload

wherethe transfer function from ⌦

mot

to m

mot

is given in (4).

G31(s) =⌦

mot

m

mot

=1

(Jmot

+ J

load

)s

1 + 2 ⇠

ant

!

ant

s+ 1!

2ant

s

2

1 + 2 ⇠

res

!

res

s+ 1!

2res

s

2

(4)The four main mechanical parameters that characterize theelasticity of the shaft ⇠

res

, !

res

, ⇠

ant

, !

ant

can be computedas indicated in (5), where !

res

is associated to the polesof denominator and ⇠

res

is the damping coefficient; !ant

isassociated to the zero of numerator and ⇠

ant

is the dampingcoefficient.

!

res

=q

J

mot

+J

load

J

mot

J

load

K

el

⇠

res

= 12Cel

qJ

mot

+J

load

J

mot

J

load

1K

el

!

ant

=q

K

el

J

load

⇠

ant

= 12Cel

q1

J

load

K

el

(5)These two eigenvalues define two points: the anti-resonancefrequency at lower frequency (parallel resonance frequency)and the peak represent the 1stTNF at higher frequency(serial resonance frequency) as shown in Fig. 3.

B. Electrical Sources of ResonancesAlthough it is well known that an electrical drive system

with a power electronics converter generates torque fluctua-tions, it is not simple to correlate the generated harmonicswith the TNFs because the torque ripple is not necessarilythe primary root cause of an excessive vibration of the

Fig. 3. G31(s) bode diagram with !res

and !ant

system, but the control structure itself can influence thefinal behaviour too. Assuming a correct mechanical designand assembly, most cases where there are vibration problemsare related to an improper integration of the VSD into thesystem in terms of closed loop strategy. In order to mitigateVSDs vibration risk, it is important to analyse:

• the electrical conversion topology• the control structure and how are measured/estimated

the system variablesConsidering the conversion chain reported in Fig. 2, it isnecessary to distinguish between integer harmonics, directlyrelated to the rectifier unit and inverter unit, and non-integerharmonics, also called interharmonics, related to the DC-link voltage fluctuations. A detailed analysis of the integerharmonics and interharmonics production is reported in [1]and [3]. It is possible to generalize the computational formulaconsidering the combined effects of rectifier and inverter unitsas in (6) computing f

excit (1,�,1), fexcit (1,+,2), ...

f

excit (m,±,k) =

������n

rec

p

rec| {z }m

f

line

± n

inv

p

inv| {z }k

f

mot

������(6)

where the pulsating torque content is f

excit (m,±,k).; thenumber of pulses in the rectifier and in the inverter arep

rec

, p

inv

respectively; the supply frequency is f

line

whilethe output inverter frequency is f

mot

and n

rec

, n

inv

areinteger multiplier. The f

excit (m,±,k) are computed as functionof f

mot

. Considering (6), we have the following cases:• m = 0 and k 6= 0 ! integer multiples of f

mot

• m 6= 0 and k = 0 ! integer multiples of fline

• m 6= 0 and k 6= 0 ! non-integer harmonicsThe converter topology plays a big role on the systeminfluence of the harmonics defined by the previous generalformula: if it is considered a Voltage-Source-Inverter theinterharmonic components are less relevant compared to theharmonic components as reported in [1], [3], [5], hence in aVSI the highest excitations come from the integer harmonicdefined by the 6th, 12th, 18th harmonics. Fig. 4 reports someexperimental results on a 6 MW motor, so in the next sectionwe are going to use this assumption.

III. VSD SYSTEM ANALYSIS

A. Critical speeds and Campbell DiagramConsidering the modelling results of Section II, it is

possible to combine TNFs and electric harmonics using a

Fig. 4. Air gap pulsating torque ripple IM 6MW

graphical representation called Campbell Diagram in or-der to provide a quick overview of the critical operatingspeeds (Fig. 5). On the x-axis they are represented the f

mot

variations while on the y-axis we find the overall harmoniccontents transmitted to the shaft. The intersection pointbetween the TNFs lines and the f

excit (m,±,k) lines identifiesoperation points (critical speeds) where the coupling torqueand the related torsional mode become amplified. If thesystem works around these speeds, the risk of a fatigue shaftfailure is dramatically increased. For the i TNF , the criticalspeeds are defined as in (7).

⌦

(i)crit

=f

res

n

rat

n

k

f

line

n

k = 6th, 12th, 18th, ... (7)

where ⌦

(i)crit

is the motor speeds that excites the i TNF ; fres

is the i TNF ; nk is the order of the inverter supply harmonics(6, 12 or 18); n

rat

is the rated motor speed.

Fig. 5. Campbell Diagram for a 6MW IM with three operating regions

Fig. 5 shows the Campbell Diagram for the consideredMV application. According to the Section II analysis it ispossible to focus on the 1stTNF only. The higher TNFs

and related critical speeds are only reported for graphicalcompleteness. In Fig. 5 it is possible to see that criticalspeeds are mainly excited at quite low speeds so they canbe a problem during the start-up and/or when the operatingspeed range is located at quite low speed.

B. Critical Speed Sensitivity AnalysesEven if with Campbell Diagram it easy to find where the

⌦

(i)crit

are located, it is also important to analyze the amplitudeof mechanical vibrations at each ⌦

(i)crit

or, in other words, thedamping factor ⇠.

Fig. 6. Damping influences at critical speeds

This damping factor is not only related to the mechanicaldamping associated to the shaft proprieties ⇠

mech

= ⇠

res

, butit is also influenced by the electrical damping ⇠

elet

related tothe drive itself (Fig. 6). This damping factor come from themotor electrical characteristics (⇠

mot

) and from the electricaldrive working principle (⇠

conv

) defined by the control design.Previously, the damping coefficient at the resonance wasassociated to the poles of the mechanical transfer functionG31(s). Now the closed-loop control strategy changes thedamping behavior at the resonance because the closed-looptransfer function has at denominator more terms in additionto G31(s) such as the speed control and the inner torque looptransfer functions. These additional terms are related to theelectrical damping mentioned above so it is possible to definehere an overall process damping coefficient ⇠

P

as in (8) andshown in Fig. 7.

⇠

P

= ⇠ (⇠elet

(⇠mot

, ⇠

conv

) , ⇠mech

) (8)

To find how to combine ⇠

mech

and ⇠

elet

, it is necessary toanalyze how it changes the overall factor due to the closed-loop control. Hence, the latency generated in the controlstructure could have an high impact in the vibrations behaviordue to the influence on ⇠

P

.

Fig. 7. Damping definitions inside a process

IV. CONTROL DESIGN AND STABILITY ANALYSIS

Nowadays the most used industrial control architectureis based on an augmented closed-loop solution as in Fig. 9.

The feedback control is used to stabilize the control loopand to reject to the torque load acting on the system. Thefeedback control would be designed to reach both goodspeed reference-tracking and good load torque-rejection, butit is not possible to reach both with this simple structure.For this reason, the architecture is modified improving asmuch is possible the load-torque rejection performance ofthe feedback control and then using an additional feedforwardcontrol only to optimize the command-tracking performance(Fig. 8). This architecture is called 2DOF-control [7].

Fig. 8. Command-tracking step response comparison

A. Industrial Control Design ProcedureConsidering a speed control schema for an induction

motor, the speed loop can be closed using a speed estimatorfor b

⌦

mot

or using a sensor as shown in Fig. 9. The innertorque loop can present different implementation accordingthe drive manufacturer and its needs. However, in terms oftorsional excitation it is reasonable to assume a converterspectrum as explained in Section II. Thus, we can callT (s) the overall inner torque loop modelled as a complexfunction from m

ref

to m

mot

that is based on (9) and definingf

mot

= n

pp

60 ⌦

mot

.

m

mot

= |mref

| (1 + sin (2⇡ |6fmot

|) ) 6th

+sin (2⇡ |12fmot

|) ) 12th

+sin (2⇡ |18fmot

|)) ) 18th(9)

For the following analysis, the feedback speed controllerR(s) has been considered as a standard PI-type, while thefeedforward controller C(s) is defined in (10). C(s) iscomputed in order to have an overall command transferfunction with a first-order dynamic.

R(s) = k

p

+k

i

s

C(s) =�k

i

s+ k

p

(Jmot

+ J

load

)�1(10)

The common guidelines for tuning the controllers are re-ported in [7], [8]. It is clear that the speed control can interactwith torsional modes if the control bandwidth includes thetorsional resonance frequencies in its range. Theoretically agood tuning keeps under control these phenomena in orderto have the resonance peak !

res

in L(s) under the 0db axisavoiding critical amplification effects (11).

L(s) = (R(s) + C(s))T (s)G31(s) (11)

Using the overall open-loop transfer function L(s), tostudy the torsional issues it is more interesting to find the

Fig. 9. 2DOF speed control architecture

command tracking transfer function (12) and the couplingtorque transfer function (13).

F

comm

(s) =⌦

mot

⌦

ref

=L(s)

1 + L(s)(12)

F

coup

(s) =m

coupling

⌦

ref

=(R(s) + C(s))T (s)G51(s)

1 + L(s)(13)

B. Latency Impact in Vibrations SuppressionIn the real applications, the control system and the

estimators are implemented in a Digital Signal Processor(DSP) or in microcontroller board and for these reasons theyare affected by delays and latencies due to the samplingtime of the signals and the processing time itself of thediscrete environment (e.g. a control variable can pass throughmany time-layers with different sampling time during thecomputation). So, the implementation itself can producedelays in the closed-loop computation and this can lead toa stability problem. For example, if there is a time delaybetween the torque reference m

ref

and the actual motortorque m

mot

and/or in the speed estimation that provideb⌦

mot

, the mechanical oscillations can not be suppressed andthey continue to spread into the closed loop path. So, even ifthe controller is well tuned, it operates in a underperformedway due to the presence of latencies that decrease the overallclosed-loop stability and reactivity. Referring to Fig. 9, theclosed-loop path follows the sequence (14) that representseach single encircle of the feedback-loop.

(⌦ref

� b⌦

mot

) ) m

ref

) m

mot

) ⌦

mot

) b⌦

mot

m

coupling

(14)

Giving a speed ramp as ⌦

ref

, m

mot

drives through oneof the critical speeds. This implies a TNF excitation andan oscillation in terms of m

coupling

, ⌦mot

and ⌦

load

. Thecoupling torque is much more sensitive to the torsional modebecuase of F

coup

(s) and the amplitude of the oscillationsare higher. Therefore, also b

⌦

mot

contains oscillations thatare feeding back to the controller through the error. R(s)partially damps these oscillations that appears in m

ref

and

further in m

mot

and provide to damp the effects on ⌦

mot

andm

coupling

. Now, b⌦

mot

still contains oscillations but if R(s) iswell tuned and the amount of delay is small, the oscillationsin m

ref

are recursively reduced up to delete them. Hence,the presence of delays extends this loop idea increasing theeffort of R(s) and consequently the time-decay to dumpthese oscillations. If the amount of time-delay is too highthe system become even unstable and it can be possible tohave a divergence in the oscillations amplitude for m

coupling

and b⌦

mot

. Considering an overall delay T

tot

acting into thesystem, in the frequency domain it is defined by a linearlydecreasing phase-shift as

��e

�j!T

tot

�� = �1 '(!) = �!T

tot

.

Fig. 10. Latency influence on L(s) changing Ttot

C. Feedback-loop Stability: Nyquist CriterionIn order to identify the stability limit of the system it

is possible to use the Nyquist diagrams of L(s) changingT

tot

and using these results to analyse the command-trackingtransfer function F

comm

(s). This criterion indicates a stablesystem if L(s) does not encircle the critical point locatedat �1 + j0. A longer distance between L(s) curve and�1 + j0 indicates a more robust feedback loop. Assuminga correct design of the controller, it is possible to observethe displacement behaviour when T

tot

is increased by usingL(s), L(s)e�sT1

, L(s)e�sT2, ... where T1 T2 ... . In

this way, using Fig. 10 it is possible to define the criticaltime delay T

cr

where the characteristic hits the �1+j0 point(T

tot

⇠= 10ms). It is possible to assume that the system is:

• stable if Ttot

< T

cr

. L(s) doesn’t encircle �1+ j0. Allthe perturbation acting in the system will be damp fasteras higher is the distance from this point (Fig. 11)

Fig. 11. Stable behavior

• at limit of stability if T

tot

= T

cr

. L(s) hits the �1 +j0 point. The system start to oscillate with a persistentoscillation or with a slowly decreasing in presence of aperturbation (Fig. 12)

Fig. 12. Limit of stability behavior

• unstable if T

tot

> T

cr

. Every kind of perturbationsproduces a divergent time response (Fig. 13)

Fig. 13. Unstable behavior

V. PROCESS DAMPING CHARACTERISTICS

A. Sources of Time DelaysUntil now, it has been considered a system affected by

a generalized T

tot

. There are several elements defining T

tot

(15). The main sources of time-delays in electrical drives arelocated into the torque-control loop, the speed controller andthe speed-estimation in the estimator unit [9].

T

tot

= T

s

+ T

⌦

+ T

m

+ T

filter

(15)

where: Ts

is the speed computation delay coming from digitaloperations (S&H, differentiating), T

⌦

is the computationaldelay of the speed controller necessary to sampling the input

and actualizing the output, T

m

is the computational delayof the inner torque control loop for the same reason of thespeed control, T

filter

is the delay introduced by the additionalfilters located around the loop and especially in the estimatorunit. If a speed sensor (e.g. an encoder) is used, the latenciesimpact on the speed-measurement can be smaller but stillpresent due to the filtering action may introduced to reducethe noisy of the encoder position.

B. Critical Speeds Dynamic: Latencies Effect

In terms of control action, it is useful to evaluate thecontrol performance using the step response, but to validatethe tuning parameter and the overall performances it shouldbe introduced the latency impact on the critical speed dy-namics. A speed reference ramp as in Fig. 14 is a goodrepresentation of the initial start-up and/or of the transientbetween the operating point changes: at critical speeds thecoupling torque amplification is smaller with a smaller slopeprofile [1]. In time-domain these effects can be analysedusing the relationship between ⇠

P

and the oscillations timedecay t

decay

introduced as t

decay

⇠ (⇠P

!

res

)�1. However,the definition of t

decay

is based on ⇠

P

. As already explained,closing the speed and torque loops yield a more complexdenominator of F

comm

(s) and F

coup

(s), defining a new ⇠

P

.As previously demonstrated, the latencies can also affectthis damping. In particular, F

coup

(s), considering the delays,becomes e

F

coup

(s) as indicated in (16).

F

coup

(s) )T

tot

eF

coup

(s) =R(s)T (s)G51(s)e�sT

tot

1 +R(s)T (s)G31(s)e�sT

tot

| {z }⇠⇠

P

(16)Fig. 15 shows the bode diagram of (16) where it is possibleto see that increasing the time delay T

tot

, ⇠P

decreases andthe phase is shifted. If the delay is small, e

F

coup

(s) is verysimilar to the one without delays and ⇠

P

is not very differentfrom ⇠

mech

. However, if the value of the delay is increased,the resonance peak starts to be positive (exceed 0dB axis).This means that the oscillations in m

coupling

starts to beamplified until reaching the highest magnitude value for thecritical time delay T

cr

. After this point, the system stabilityis lost. In general, the relation between peaks magnitudeand the time-delay is not linear and it is a function of themechanical and electrical parameter as shown in Fig. 16. Infirst approximation, it can be used the effects on the peaksamplitude to describe this behaviour as in (17).

" T

tot

)# ⇠

P

)"��� eF

coup

���db

, ⇠

P

⇠ 1��� eFcoup

���db

(17)

Fitting the simulation data based on different T

tot

througha Matlab optimization tools are obtained many damping-latency behaviors for different ⇠

elet

and ⇠

mech

(Fig. 16).Based on Fig. 16, it is possible to highlight that if the layoutof the plant is such that ⇠

mech

is dominant against the

Fig. 14. Effects of time-delay on the critical speeds decay

others effects (e.g. grey line) ⇠

P

remains similar to thisvalue even if T

tot

is increasing until reaching T

cr

. On theother side, when ⇠

elet

and ⇠

mech

are very similar, or at leastcomparable, then the effect of the time delay variations havea huge impact.

Fig. 15. Latency influence on resonance peak amplitude of eFcoup

(s)

Many example can be written, but all of these consid-erations are related to the specific conditions of the overallsystem (e.g. the mechanical coupling, the converter setting,the operating points, the inertia). When ⇠

elet

is dominat (e.g.orange line) the ⇠

P

effects are in agreement with [3].

VI. CONCLUSIONS

In this paper, a new approach to relate the overall damp-ing of a process with the control latencies T

tot

has beenpresented. This underline that the mechanical oscillationsdamping is not only related to the mechanical side but itdepends on the electrical side and mainly on the quality of thecontrol behaviour, so the process damping is a time-variant

Fig. 16. Process damping-latency relationship

coefficient. This dependency is stronger if it is higher theamount of delay, so the latency is, in some sense, an indexof the interactions between the electrical and the mechanicalsides. To evaluate these interactions, a descriptive method toanalyze the process damping ⇠

P

effects on a complex VSDdrive-line has been presented. This will be for sure a keypoint for future development against these kind of issues.

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Mattia Rossi is a Research Assistant at Politecnico di Milano. He receivedthe B.Sc., M.Sc. degrees in Control Engineering from Politecnico di Milanoin 2013 and 2015-Marco Mauri is an Assistant Professor in Electrical Machines and Drivesat Politecnico di Milano. He received the M.Sc., Ph.D. degrees in ElectricalEngineering from Politecnico di Milano in 1998 and 2002-Maria Stefania Carmeli is an Assistant Professor in Electrical Machinesand Drives at Politecnico di Milano. She received the M.Sc., Ph.D. degreesin Electrical Engineering from Politecnico di Milano in 1997 and 2000-Francesco Castelli-Dezza is a Full Professor in Electrical Machines andDrives at Politecnico di Milano. He received the M.Sc., Ph.D. degrees inElectrical Engineering from the Politecnico di Milano in 1986 and 1990