Closed-loop Control System for the Reliability of IntelligentMechatronic Systems

Tobias Meyer1 and Walter Sextro2

1,2 University of Paderborn, Paderborn, Germanytobias.meyer@uni-paderborn.dewalter.sextro@uni-paderborn.de

ABSTRACT

So-called reliability adaptive systems are able to adapt theirsystem behavior based on the current reliability of the system.This allows them to react to changed operating conditions orfaults within the system that change the degradation behavior.To implement such reliability adaptation, self-optimizationcan be used. A self-optimizing system pursues objectives, ofwhich the priorities can be changed at runtime, in turn chang-ing the system behavior.

When including system reliability as an objective of the sys-tem, it becomes possible to change the system based on thecurrent reliability as well. This capability can be used to con-trol the reliability of the system throughout its operation pe-riod in order to achieve a pre-defined or user-selectable sys-tem lifetime. This way, optimal planning of maintenance in-tervals is possible while also using the system capabilities totheir full extent.

Our proposed control system makes it possible to react tochanged degradation behavior by selecting objectives of theself-optimizing system and in turn changing the operating pa-rameters in a closed loop. A two-stage controller is designedwhich is used to select the currently required priorities of theobjectives in order to fulfill the desired usable lifetime.

Investigations using a model of an automotive clutch systemserve to demonstrate the feasibility of our controller. It isshown that the desired lifetime can be achieved reliably.

1. INTRODUCTION

Self-optimizing mechatronic systems are a class of intelli-gent technical systems that are able to autonomously adapttheir behavior if user requirements or operating conditionschange (Gausemeier, Rammig, Schafer, & Sextro, 2014). Tothis end, the current situation is monitored and the objectives

Tobias Meyer et. al. This is an open-access article distributed under the termsof the Creative Commons Attribution 3.0 United States License, which per-mits unrestricted use, distribution, and reproduction in any medium, providedthe original author and source are credited.

of the system are determined. Using model based multiob-jective optimization, for which a model of the dynamical be-havior of the system is used, optimal system configurationsare calculated before operation of the system. To adapt thesystem behavior during operation, the self-optimizing systemselects among these optimal system configurations.

In order to use self-optimization to ensure that the require-ments regarding reliability of the system are met, a suitableselection process has to be implemented. To adapt the sys-tem behavior advantageously with regard to system reliabil-ity, it has to be possible to lower work load or wear on criticalcomponents by selecting appropriate optimal system config-urations. Thus it is also necessary to include system degra-dation in the objective functions used for the multiobjectiveoptimization.

To control the remaining useful lifetime, the whole systemhistory has to be taken into account as well. This could notbe achieved by directly including remaining useful lifetime inthe model used for multiobjective optimization, as then eachobjective function evaluation would require a simulation ofthe whole system lifetime. Such a simulation requires a lot ofcomputing effort, rendering this approach impossible. Thusa process to take the system history into account separatelyduring operation is required. For this, our presented self-optimization based remaining useful lifetime controller canbe used.

2. MAINTENANCE PLANNING

The big advantage of actively controlling the reliability ofa system becomes apparent if the whole life-cycle includingmaintenance is considered. Within the scope of this section,it is assumed that after maintenance, a system is as-good-as-new. Traditionally, maintenance was conducted as either cor-rective of preventive maintenance (Birolini, 2007). In correc-tive maintenance, system functionality is reestablished once afailure occurs. This strategy is cheap at first, but once a failureoccurs and the system is unavailable, maintenance has to beconducted as soon as possible, making the repair expensive. It

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0%

100%

time

RU

L

usable lifetime until failure

usable lifetime until maintenance

corrective maintenance

condition based maintenance

preventive maintenance

wasted lifetimedue to earlymaintenance

system not usabledue to unscheduledmaintenance

Figure 1. Maintenance planning techniques and their effecton usable lifetime.

also comes with the risk of catastrophic failures which makeit unsuitable for many systems. This approach maximizes theusable lifetime, as can be seen in Fig. 1. Availability, how-ever, is limited due to unnecessarily long unscheduled main-tenance.

Preventive maintenance, on the other hand, allows a high avail-ability of the system by retaining system functionality. Thisis achieved by conducting maintenance before a failure oc-curs, making the maintenance schedulable and thus highlyefficient. Usually, suitable maintenance intervals are deter-mined using stochastic models for large fleets of systems (Joo,Levary, & Ferris, 1997). This approach has the advantageof achieving high availability with planned maintenance in-tervals, but usable lifetime until maintenance is lower thanusable lifetime until failure. This increases the cost of opera-tion due to earlier maintenance than necessary. Also it is bestsuited for large fleets of identical systems and can hardly beimplemented for unique machinery.

In order to overcome these drawbacks, condition based main-tenance can be used. According to (Jardine, Lin, & Ban-jevic, 2006), a condition based maintenance program con-sists of three steps: Data acquisition, data processing andmaintenance decision making. In the first two steps, the cur-rent state of the system is assessed. After evaluation, effi-cient maintenance policies are recommended. A conditionbased maintenance program is comprised of two importantaspects: Diagnostics and prognostics. In diagnostics, exist-ing faults are detected, isolated and identified before they

ω1ω2 Θ2

FNμ

Frictionplates

Engine Drivensystem

Figure 2. Basic structure of clutch system.

lead to a failure. Prognostics, on the other hand, deals withthe prediction of future faults. The main objective is to es-timate the time until a fault occurs or the probability of itoccuring. Using this information, the system can be operatedwithout wasting usable lifetime for overly cautious mainte-nance intervals and also without requiring unscheduled main-tenance. While this is advantageous over corrective and pre-ventive maintenance, it remains a reactive method in whichthe system degradation drives the scheduling of maintenanceoperations and which makes planning of inspection and main-tenance complex (Chena & Trivedi, 2005).

By combining information about the current system reliabil-ity with a feedback to system operation, it becomes possibleto adjust system behavior according to its current reliability.This allows reversal of the usual approach. It now becomespossible to schedule maintenance operations with the systemadapting its behavior and its degradation accordingly. Theproposed closed loop control allows for such operation.

3. APPLICATION EXAMPLE

A single plate dry clutch has already been introduced as ap-plication example in (Meyer, Sondermann-Wolke, Kimotho,& Sextro, 2013) and is used again in this contribution. Thistype of clutch is commonly utilized in passenger vehicles toconnect an internal combustion engine to the drivetrain. Thebasic outline of the clutch system is shown in Fig. 2. It con-sists of two friction plates with coefficient of friction µ, ofwhich the input plate is connected to the engine while theoutput plate is connected to the driven system, e.g. a gear-box. The input and the output plates are rotating at speedsω1 = 1 rad

s and ω2 respectively. To engage the clutch, bothplates are pressed against each other by the force FN , thustransmitting torque Tf from the input plate to the output plateand in turn applying this torque to the driven system.

The system dynamics can be modelled with

Tf (t) = FN (t) · µ (∆ω (t)) · reff , (1)

ω2 (t) =1

Θ2· (Tf (t)− d2 · ω2 (t)) , (2)

µ (∆ω) = µ0 ·2

π· arctan

(∆ω

ω

)(3)

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0 0.5 1 1.5 2 2.50

5

10

15

20

25

30

f2

f1

k = 1f1,1

= 3.81f2,1

= 2.04tr,1

= 2.64 sα = 1.864

k = 84f1,84

= 28.3f2,84

= 0.0226tr,84

= 9.96 sα = 1254

α1

1

84 k = 49f1,49

= 9.77f2,49

= 0.0564tr,49

= 9.36 sα = 173.2

49

k = 40f1,40

= 6.15f2,40

= 0.182tr,40

= 6.89 sα = 33.86

40

Figure 3. Pareto front of clutch system with two objectivefunctions: f1: minimize wear and f2: Minimize accelera-tions, i.e. maximize comfort. Note that the duration of anactuation cycle tr has a great effect on both objectives.

where µ0 = 1 is the nominal coefficient of friction, ∆ω =ω2−ω1 is the difference in revolutionary speed of the plates,ω = 0.1 rad

s is the accuracy parameter, reff = 1 m is theeffective radius of the plates, Θ2 = 1 kg

m2 is the moment ofinertia of driven system, d2 = 1N ·m · s

rad is the damping factorof the driven system. Arbitrary values, which do not model aparticular system, were chosen to demonstrate the proposedcontrol method.

Also in (Meyer et al., 2013) it was shown that using multi-objective optimization techniques, a control trajectory for theactuation force FN (t) can be computed to actuate the clutchsystem. Multiobjective optimization techniques attempt tominimize user defined objective functions by adapting sys-tem parameters. Typically, it is not possible to minimize mul-tiple objective functions at once, but instead as one objectivefunction value is lowered, another objective function valuerises. This leads to the so-called Pareto front, which con-sists of all optimal compromises between multiple objectivefunctions. To each point on the Pareto front, system parame-ters are given in the Pareto set. To compute Pareto front andPareto set, a genetic algorithm which comes with the Matlabglobal optimization toolbox has been used.

The required objective functions are included in a full modelof the system dynamics. For our system, the objective func-tions are f1, which represents the power loss in the clutch Pfand in turn corresponds to the wear rate of the clutch plates,and f2, which represents e.g. comfort of vehicle passengers:

f1 =

∫ t0+tr

t0

(Pf (t))2

d t =

∫ t0+tr

t0

(TF (t) ·∆ω (t))2

d t,

f2 =

∫ t0+tr

t0

(ω2 (t))2

d t.

020

4060

80 0

5

10

0

20

40

60

80

100

tk

FN,k(t)

Figure 4. Pareto set of clutch system with 84 possible actua-tion trajectories FN (t).

To compute the values of these objective functions, the dy-namical model of the system is simulated over the periodt = t0 . . . t0 + tr using trajectories for FN (t) as simulationinput.

The duration of the actuation cycle and the shape of the trajec-tory are the optimization parameters. To include these in theoptimization procedure, the trajectory was subdivided into 16sections with equal durations. For the trajectory to begin witha completely disengaged clutch and end with a completely en-gaged clutch, FN (t0) = 0 N and FN (t0 + tr) = 100 N areassumed. The optimization parameters are then the total du-ration of the actuation cycle tr and the shape computed by us-ing 15 intermediate values FN

(t0 + 1

16 · i · tr), i = 1 . . . 15.

Linear interpolation is used between these values. This way,the Pareto front shown in Fig. 3 with the corresponding Paretoset shown in Fig. 4 is obtained. A short total duration ofthe actuation cycle yields low energy losses but high accel-erations, as opposed to a long duration, which yields inverseresults. Each trajectory is a trade-off between these two ob-jectives.

4. CONTROLLING THE RELIABILITY

In prior works (Meyer et al., 2013), a basic controller forthe reliability of the clutch system was presented. However,the approach outlined therein was limited in its effectivenesssince it did not take the inherent non-linearities and deviationsbetween multiobjective optimization model and real systeminto account. It was not capable of handling deviations thatrequired a great change from the nominal working point. Theapproach presented in the remainder of this contribution over-comes these drawbacks and offers better generalizability toother engineering problems.

A two-stage controller design has been favored for the possi-blity to be designed separately for high-frequency perturba-

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Generation ofRUL trajectory

s-trf.

Dynamic system

Sys

tem

re

qu

ire

me

nts

Sys

tem

p

ara

me

ters

P

αdes

RULdes

Current remaininguseful lifetime RUL

ParetoController

RULController

αuse

-1 -1( )s r -trf.

z1

1 z1

z-1z

ΔRUL

-

-

αcur

GRUL -s ¹-trf.

obj.eval.

r-trf.

Figure 5. Full two-stage control loop.

tions on the inner loop and for low-frequency perturbationson the outer loop.

While priorities of objectives of a self-optimizing system maybe selected arbitrarily, the system behavior does not neces-sarily reflect this immediately. On the one hand, an adapta-tion usually takes some time to take full effect; on the otherhand the system model used for multiobjective optimizationand the real system might deviate from one another, thus if aworking point is chosen based an pre-calculated optimal sys-tem configurations, which are based on the system model, theactual system might behave differently. This leads to differ-ences between desired objectives and achieved objectives.

To overcome these shortcomings, Kruger et al. developed aclosed loop control for the objectives of a self-optimizing sys-tem (see (Kruger, Remirez, Kessler, & Trachtler, 2013)), col-loquially called “Pareto controller”. The purpose of this con-troller is to ascertain a pre-selected system configuration isactually being used, despite of perturbations or deviations be-tween optimization model and actual system. To this end, thedesired system configuration is selected with a so-called α-parameterization, which can be defined individually for eachsystem. Suggestions are made, e.g. to use a Simplex-basedmethod or to calculate the ratio among two objectives. In thecourse of this paper, we define the α-parameterization as fol-lows, it is also included in Fig. 3:

α =f1

f2.

The desired parameterization value αdes is used as controllerinput. The current value of the α-parameterization, αcur isrequired for the controller to calculate the used value αusedaccording to the difference between αcur and αdes. Onceαused has been calculated, the parameters of the system aredetermined by the so-called s-transform and set in the sys-tem. After a certain time, the resulting system behavior isevaluated to determine the current value αcur of the α-pa-rameterization.

It is assumed that the behavior adaptation and evaluation ofthe actual system behavior takes some time to take full effect.For this reason, the Pareto controller works in discrete timeon a slow time scale, where one discrete time step is the con-stant time period required for the full behavior adaptation andevaluation process. For this reason, in the abstract model ofthe system, the output is delayed by the unit delay 1

z .

This Pareto controller is used as inner loop of the full con-trol loop. It is not able to take the full lifetime informationinto account and serves the purpose of reliably achieving thedesired system behavior.

The outer loop, on the other hand, is responsible for control-ling the remaining useful lifetime. For this, an abstract modelof the system adaptation process is required. As the innerloop already controls the desired behavior, the outer loop doesnot need to take actual system parameters into account but in-stead relies on using the α-parameterization as system input.System output and controlled variable is the remaining use-ful lifetime RUL. The reference input is denoted by RULdes.However, the relationship between α and RUL is highly non-linear. The difference in remaining useful lifetime ∆RUL (α)over a single actuation cycle i can, however, be approximatedusing the system model. This is called the r-transform:

∆RUL (α) = r (s (α)) .

To obtain the current remaining useful lifetime, an integralelement z

z−1 in the dynamic system, and a unit delay 1z for the

evaluation of the current remaining useful lifetime are added,as shown in Fig. 5.

As controller for the remaining useful lifetime, a P controllerwas chosen. An integral element is not required to correctfor steady state errors due to the integrating properties of thewear process. It calculates the r-transformed desired α-pa-rameterization r (s (αdes)) according to:

GRUL =r (s (αdes))

RULdes − RUL= Kp,RUL (4)

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This discrete controller can be implemented in the same dis-crete time used for the Pareto controller. The controller out-put is then converted by the inverse r-transform s−1

(r−1)

togive αdes.

The reference input generated for the RUL-controller needsto be strictly monotonically decreasing. If it was not, an actu-ation cycle with no or even negative wear would be required,which is physically impossible. The chosen reference inputbegins with RULdes (new system) = 100% and ends withRULdes (end of specified lifetime) = 0%. Linear interpo-lation is chosen for intermediate cycles. The reference inputcan be altered during operation in case of changed require-ments. An adaptation of system behavior is then conductedby means of the control loop.

5. SETUP OF THE CONTROLLER FOR THE APPLICATIONEXAMPLE

When controlling the remaining useful lifetime, the systembehavior is adapted by changing system objectives. However,it needs to be ascertained that these objectives are met. Aswas mentioned in the basic introduction of the control loopin section 4, a specifically designed closed loop control byKruger et al. (Kruger et al., 2013) is used. This control loopas well as the RUL-controller that builds on it are workingin discrete time, their stepsize is big compared to the systemdynamics. Since the clutch system has discrete events, onestep corresponds to one full actuation cycle. Due to this, thestepsize of both controllers is 1 cycle.

5.1. Pareto controller

The basic idea of the closed loop Pareto controller is to definethe desired system behavior using a so-called α-parameteri-zation. The value of this parameterization is used as referenceinput αdes for the controller. The actual current value αcur iscomputed from signals or measured variables of the system.

At first, the α-parameterization needs to be defined. For theclutch system, which pursues two objectives only, the frac-tion of both objective values is used, i.e. α = f1

f2. This ap-

proach has several advantages over more complex parameter-izations, e.g. the Simplex-based parameterization suggestedin (Kruger et al., 2013). First, it is very simple to calculate,thus requiring low computational time. Second, and moreimportantly, no knowledge about the Pareto front, such as anapproximating function, number of known points or values atthe edges, is required. This makes evaluating the currentlyachieved value αcur independent of any assumptions aboutother possible working points.

The α-value needs to be transformed into a set of parametersto be used by the actual system. For this, the s-transform isused. It determines the desired Pareto point from the Paretofront and selects the Pareto set, which contains all system pa-

rameters, accordingly. For the clutch system, linear interpo-lation between pre-calculated Pareto points is used. This isdone in three steps: At first, the two Pareto points closest tothe desired α-parameterization αdes are searched. In the nextstep, the two sets of parameters are selected from the Paretoset Pset. Last, linear interpolation is used for each pair ofparameters to obtain the final parameter.

To determine the closest Pareto point, the α-paramterizationvalue for each pre-calculated Pareto point is calculated. Forthis, k = 1 . . . n, k ∈ N, n ∈ N Pareto points are assumed:

αk =f1,k

f2,k.

The following two steps are conducted at runtime. At first, kclosest to the currently desired value αdes is searched:

mink

(|αk − αdes|) .

Once this is known, linear interpolation among two pointswith α-values closest to the desired value αdes is conductedto find system parameters W from the Pareto set Pset:

P (αdes) =

(Pset,k+Pset,k+1)·αdes

αk+αk+1,

if 1 < k < n and|αk − αk−1| < |αk − αk+1|,

(Pset,k−1+Pset,k)·αdes

αk−1+αk,

if 1 < k < n and|αk − αk−1| > |αk − αk+1|,

Pset,k, else.

The advantage of this approach is that even though a limitednumber of Pareto points is known from numerical multiob-jective optimization, a close approximation for intermediatevalues can be found. This is important in subsequent steps,since all controllers developed herein have continuous outputvalues and expect the system, i.e. s-transform, clutch system,objective evaluation, and s−1-transform, to accept such andwork continuously as well.

With linearly interpolating between Pareto points, it is as-sumed that all computed possible solutions Pset to the op-timization problem are similar. Proof that this assumptionholds is difficult, but clear indications can be seen in Fig. 4.

The s−1-transform, on the other hand, is very simple oncecurrent values of the system objectives f1,cur and f2,cur aredetermined by evaluating measured variables or signals fromthe system:

αcur =f1,cur

f2,cur.

With these transformations all set, the actual controller canbe parameterized. It was created according to (Kruger et al.,2013) without modifications. The controller parameters werechosen as Kp = 0.05 and Ki = 0.05.

The controller reference input is the desired α-parameteriza-tion αdes. It is set by the outer loop which controls the re-

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maining useful lifetime of the system and induces a behavioradaptatation by changing αdes.

5.2. RUL controller

The purpose of the outer control loop is to determine the cur-rently required desired α-parameterization αdes from the de-sired remaining useful lifetime RULdes and the current re-maining useful lifetime RUL.

At first, the remaining useful lifetime RUL needs to be de-termined. This is highly application-specific. A model-basedapproach has been selected to estimate the remaining usefullifetime of the friction plates. It is based on the assump-tion that clutch plate wear is proportional to friction energyEf (Fleischer, 1973). For each actuation cycle i with timespan t = t0,i . . . t0,i + tr, where tr is the duration of the ac-tuation cycle, the wear w (i) occuring during this cycle is:

w (i) = pf ·∆Ef (i) = pf ·∫ t0,i+tr

t0,i

Pf (t) d t

= pf ·∫ t0,i+tr

t0,i

TF (t) ·∆ω (t) d t. (5)

The proportionality factor is assumed to be pf = 1 for normalwear behavior. Due to e.g. errors in manufacturing or materi-als, it might deviate, thus requiring a changed operating pointin order to fulfill the specified lifetime.

To estimate the remaining useful lifetime, all actuation cyclesneed to be taken into account. To do so, the sum of the wearoccuring in each cycle w (i) is summed over all prior m cy-cles, i.e. i = 1 . . .m, i ∈ N,m ∈ N. The remaining usefullifetime RUL for the next cycle m+ 1 can then be estimatedby taking the maximum amount of wear wmax of the clutchinto account. This results in the following relation:

RUL (m+ 1) = 1−(∑m

i=1 w (i)

wmax

). (6)

To convert the RUL-controller output to a desired value of theα-parameterization, the inverse r-transform s−1

(r−1)

needsto be defined next. Since ∆RUL (α) can not easily be com-puted analytically, the main cause of wear needs to be deter-mined. As was shown in eqns. 5 and 6, the remaining use-ful lifetime mainly depends on the friction energy ∆Ef , thus∆RUL (α) ∼ ∆Ef .

To setup the inverse r-transform, the friction energy for eachpre-calculated α-parameterization ∆Ef (α) is computed bysimulating the system model for one full clutch cycle. Theresulting relationship between α-parameterization and ∆Efis shown in Fig. 6.

Using a least-squares approach, an approximating functionwas fitted to obtain a computationally effective s−1

(r−1)-

2 4 6 8 10 12 14 160

200

400

600

800

1000

1200

1400

1600

Friction energy ΔEf per clutch cycle

Valu

e of

α p

aram

eter

izat

ion

Simulation resultsApproximation

Figure 6. Compensation of nonlinear behavior.

transform. An exponential ansatz was chosen:

αapprox = q1 · eq2·∆Ef .

The parameterized approximating function (q1 = 0.3714,q2 = 0.5536) is also shown in Fig. 6.

The objective-based controller for the remaining useful life-time is implemented according to eq. 4. As proportional gainparameter, Kp,RUL = 1000 was chosen.

6. SIMULATION RESULTS

To evaluate the feasibility of the proposed approach, simula-tions that span the whole lifetime of the clutch system wereconducted. For this, a model of the dynamic behavior of theclutch system according to eqns. 1, 2 and 3 was used.

An artifical fault was introduced into the system model: Af-ter 200 regular clutch cycles, the wear proportionality factorwas changed from pf = 1 to pf = 2. This way, the simu-lated wearing process was accelerated; the plates wear twiceas fast as they did previously. As can be seen in Fig. 7, thesystem behavior is adapted accordingly. At first, a slight de-viation between desired and obtained RUL can be observed;however, the system lasts for the required 500 cycles.

In another test of the behavior adaptation process, the require-ments for the system were changed at 200 cycles. The systemis now required to last for 600 cycles instead of 500 cycles,as was the initial requirement. As can be seen in Fig. 8, theadaptation process enables the system to successfully adaptits behavior to changed requirements.

As was shown, an adaptation to either changed system degra-dation processes or to changed requirements is possible. Thecontrolled system fulfills the desired properties regarding re-liability.

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0 100 200 300 400 5000

0.5

1

RUL

Desired RULStatic systemReliability−controlled

0 100 200 300 400 5000

200

400

600

Cycles

α−p

aram

eter

izat

ion

DesiredUsedCurrent

Figure 7. System behavior if a fault occurs. At 200 cycles,the proportionality factor pf was changed to simulate a clutchsystem wearing twice as fast as was anticipated for a normalsystem.

The adaptation to accelerated wear processes and changeduser requirements comes at the expense of degrading perfor-mance of the system. In case of the clutch system, the value ofthe α-parameterization is lowered for both adaptations. Thisleads to lower, i.e. better values of the objective minimizewear and to higher, i.e. worse values of the objective mini-mize accelerations. As can be seen in Fig. 4, the main dif-ference between different working points is the duration ofthe actuation trajectory. A system running in nominal oper-ating mode, i.e. before 200 cycles are reached, has an actu-ation duration of approximately 9.5 s, giving a comfort valuef2 = 0.039. If changed user requirements are to be taken intoaccount, the actuation duration is shortened to approximately8.9 s, lowering the comfort value to f2 = 0.064. In order tocompensate accelerated wear processes, the selected workingpoint requires an even faster actuation duration of approxi-mately 6.9 s at a comfort value f2 = 0.25. These lower val-ues signify a quicker and less comfortable acceleration ma-neuver, which is required to react on these great variations insystem behavior or requirements. Even though the differencein comfort value suggests severely limited operating poten-tial, the benefit of reaching pre-defined reliability goals willin most cases outweigh the loss in comfort.

7. CONCLUSION & OUTLOOK

The behavior adaptation process of an intelligent system ismodelled abstractly. A two-stage control loop was designedwith the inner loop controlling the desired system behaviorwhereas the outer loop controls the remaining useful lifetime.To this end, an existing controller for the inner system behav-ior is implemented. For the outer loop, a new controller isadded. Simulation results show, that the adaptation of the

0 100 200 300 400 500 6000

0.5

1

RUL

Desired RULStatic systemReliability−controlled

0 100 200 300 400 500 6000

200

400

600

Cycles

α−p

aram

eter

izat

ion

DesiredUsedCurrent

Figure 8. System behavior for changed requirements. At 200cycles, the system requirements are changed; it is now ex-pected to sustain 600 actuation cycles.

system behavior based on the remaining useful lifetime suc-cessfully adapts the behavior if either the system behavior orthe requirements change. In both cases, the desired usefullifetime can be accomplished.

While simulations show that the system degrades as desired,experimental validation is still required. Since the behavioradaptation and experiments that span the whole system life-time are complex, the setup of a dedicated test rig is currentlybeing pursued.

ACKNOWLEDGMENT

This research and development project is funded by the Ger-man Federal Ministry of Education and Research (BMBF)within the Leading-Edge Cluster Competition “it’s OWL” (in-telligent technical systems OstWestfalenLippe) and managedby the Project Management Agency Karlsruhe (PTKA). Theauthors are responsible for the contents of this publication.

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Kruger, M., Remirez, A., Kessler, J. H., & Trachtler, A.(2013, June). Discrete objective-based control for self-optimizing systems. In American control conference(acc), 2013 (p. 3403-3408).

Meyer, T., Sondermann-Wolke, C., Kimotho, J. K., & Sextro,W. (2013). Controlling the remaining useful lifetimeusing self-optimization. Chemical Engineering Trans-actions, 33, 625-630. doi: 10.3303/CET1333105

BIOGRAPHIES

Tobias Meyer studied mechanical engineering and mecha-tronics at the University of Paderborn. Since 2011 he is withthe research group Mechatronics and Dynamics at the Univer-sity of Paderborn. His research focusses on the dependabilityof intelligent self-optimizing systems.

Walter Sextro studied mechanical engineering at the LeibnizUniversity of Hanover and at the Imperial College in London.Afterwards, he was development engineer at Baker HughesInteq in Celle, Germany and Houston, Texas. Back as re-search assistant at the University of Hanover he was awardedthe academic degree Dr.-Ing. in 1997. Afterward he habil-itated in the domain of mechanics under the topic Dynam-ical contact problems with friction: Models, Methods, Ex-periments and Applications. From 2004-2009 he was profes-sor for mechanical engineering at the Technical University ofGraz, Austria. Since March 2009 he is professor for mechan-ical engineering and head of the research group Mechatronics

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