σPA = relative standard deviationϕ = general variableΩ = control signal, V
I. Introduction
I N RECENT years, plasma actuators have proven to be anattractive and promising alternative to conventional flow-control
devices [1], and therefore enjoy increasing importance for variousflow-control scenarios in the community [2,3]. The variety ofinvestigated flow-control applications ranges from velocities of a fewmeters per second (e.g., [4]) to supersonic conditions (e.g., [5]).However, it is commonly assumed in the flow-control communitythat the actuator dischargemanipulates the airflow, but not vice versa.The dielectric-barrier-discharge plasma-actuator performance isinfluenced by numerous thermodynamic and kinematic environ-mental parameters. The effect of changing ambient conditions(humidity [6–8], temperature [8,9], and ambient pressure [9–15]) onthe discharge intensity has been documented in several publications.Changes of these background conditions act differently on the
plasma-actuator performance. An increase in relative humidity, forinstance, monotonously reduces the power consumption, but firstleads to a flow-rate augmentation of the resulting wall jet at moderatehumidity levels before an overall decrease occurs for both quantities.Similar nontrivial interrelationships are observed when the ambientpressure changes. The close interrelation between breakdownvoltageand ambient pressure is well known from the Paschen curves [16]. Inconsequence, above the Stoletow point [17], any reduction ofpressure increases the discharge intensity. In contrast, the transferredmomentumdoes not changemonotonouslywith decreasing pressure,
*Postdoctoral Associate, Flughafenstr. 19; currently Mechanical andManufacturing Engineering, University of Calgary, Calgary, AB, Canada;[email protected]. Member AIAA (Corresponding Author).
†Masters Student, Center of Smart Interfaces, Flughafenstr. 19.‡Research Assistant, Center of Smart Interfaces, Flughafenstr. 19;
[email protected]. Member AIAA.§Research Assistant, Center of Smart Interfaces, Flughafenstr. 19;
[email protected]. Member AIAA.¶Professor, Institute of Fluid Mechanics and Aerodynamics, Center of
but rather a (local [15]) maximum is observed for the induced thrustbelow ambient condition before it decreases under further pressurereductions. Changes in altitude for any aerial vehicle imply simulta-neous changes of all state variables, in which decreasing pressure andtemperature act competitively on the discharge performance. Inaddition, the aerodynamic influence of the freestream velocity on thegas-discharge intensity has recently been identified to significantlyreduce the actuator performance [18–20]. Obviously, the variety ofpossible combinations of promoting and diminishing effects on thedischarge intensity limits the predictability of environmental influ-ences on the plasma-actuator performance.Kriegseis et al. [21,22] introduced a performance-characterization
procedure, which is based on an improved interpretation of voltage–charge cyclograms (Lissajous figures) and a light-emission analysisof the discharge domain.With these new diagnosis approaches, it hasbeen possible to quantify the performance drop of plasma actuatorsfor different airflow speeds (up to 30% [19,20]). Assuming aninitially optimized plasma-actuator setup, precisely adjusted powerlevel, and perfectly matched impedance of the electrical circuit, theseenvironmental influences on the discharge result in a detuned setup ofthe plasma actuator, which consequently operates at unnecessarilyhigh energy requirements. The more important consequence is asignificantly reduced control authority of the plasma actuator as aflow-control device. To ensure a constant plasma-actuator perfor-mance during operation, a real-time and in situ evaluation of theperformance is desirable.The present study addresses this requirement with a real-time-
characterization approach, which allows a closed-loop performancecontrol of the electrical plasma-actuator setup. Because of the closed-loop character of the proposed control concept, a compensation forany performance changes can be successfully achieved without adetailed knowledge about the complex interrelationship between theinvolved thermodynamic and kinematic environmental parameters.In the first step, the relevant performance-identifying approaches
[21,22] are modified such that the required data are continuouslyacquired and processed to provide an online evaluation basis asproposed by Kriegseis et al. [23]. Then, in the second step, anyidentified performance changes can be counteracted in a closed-loopcircuit, based on the known interrelations of the involved quantities.The novel tool is tested and optimized by applying it to an artificialflow situation of changing pressure andMach number in a blowdownwind tunnel. However, the main objective of the present study was tooutline the potential of the presented closed-loop-control concept fordischarge-based aerodynamic flow control in general, rather than anoptimization of one particular closed-loop-controller design for anartificial test case in a blowdown wind tunnel.
II. Experimental Procedure
The experiments were conducted in the blowdown wind tunnel ofthe Technische Universität Darmstadt. This wind tunnel is designedto operate at Mach numbers in the range of 0.4 < M < 4. Thedimensions of the test section are 150 × 150 mm2. The plasmaactuator consisting of two copper electrodes (w1 � 2.5 mm,w1 � 10 mm) and a Kapton dielectric (d � 0.4 mm) was mountedon the side window of the test section, as shown in Fig. 1. Toretroactively verify the online evaluation of the performance, similarto previous investigations [19–21], a complementary metal-oxidesemiconducter camera (Phantom V12.1, 512 × 512 pixels, 24 fps;Nikon 105 mm, AF Micro-Nikkor f/2.8D) was used to record thespatiotemporal light emission of the discharge during the power-consumption analysis.The electrical control circuit, as shown in Fig. 1b, was built up
using a computer-based digital oscilloscope (Picotech PicoScope4424, four channels, 2500 points per channel, 10 MS/s) to record theoperating voltage V (TESTEC HVP-15HF, 1000:1) and the voltageVp across the charge probe capacitorCp � 22 nF (LeCroy PP006A,10:1). The operating voltage V was generated by a high-voltagetransformer circuit board (GBS Elektronik, Minipuls 2 [24]), whichwas driven by an external laboratory power supply (Voltcraft VSP2410, variable output 0–24 V dc) and a function generator [GW
Instek, SFG-2004, fixed frequency (sine): f � 12.0 kHz]. For moredetails about the chosen high-voltage transformer-circuit-boardworking principle, the reader is referred to the manufacturer’s webpage [24].The governing equation to calculate the power consumption PA
from Lissajous figures (see Fig. 2a) is
PA � fIQ dV � f
K
XKk�1
IkCpVp dV (1)
in which CpVp � Q is the charge crossing the actuator [22].Equation (1) represents the average ofK discharge cycles. It has beendemonstrated by Kriegseis et al. [21] that changes of the plasmalength and corresponding discharge light-emission distribution onthe dielectric are a robust means to quantify changes of the actuatorperformance (i.e., power consumption PA and thrust production F).Therefore, the simultaneously recorded light-emission data are usedsubsequently to retroactively validate the online diagnostic tool bymeans of the temporal plasma-length evolutionΔx�t� as discussed inSec. III.A. The gray-value analysis of the light-emission images leadsto the (chordwise) plasma length:
Δx � xmax�G�x� > Gb� − xmin�G�x� > Gb� (2)
in whichGb andGp are the gray values of the background and light-emission peak, respectively. A typical result of the gray-valueanalysis is shown qualitatively in Fig. 2b.Reproducible airflow conditions were achieved, operating the
blowdown wind tunnel at a constant valve position, thus generating ablowdown from initiallyM � 0.85 (cruise flight) to quiescent air atchanging pressure levels (p � 0.9–1.5 bar). The resulting timetraces of the state variables static and total pressurep,pt are shown inFig. 3, alongside the Mach numberM.In Fig. 3, three characteristic times are highlighted for p�t1� �
pmax, p�t2� � p0, p�t3� � pmin with the purpose of distinguishingpressure and air-speed effects on the discharge performance. For thesake of completeness, the interdependency of pressure and Machnumber is stated, that is,
p
pt��γ − 1
2M2 � 1
� γ1−γ
(3)
a) Wind-tunnel test section b) Detail: closed-loop circuit
Fig. 1 Sketch of experimental setup: a) wind-tunnel test section and
overhead camera (CAM); and b) detailed view of electrical plasma-actuator setup and closed-loop circuit comprising a function generator(FG), power supply (PS), high-voltage (HV) transformer, notebookcomputer (NB), and plasma actuator.
a) Power consumption b) Plasma length
Fig. 2 Qualitative example results of a) electric measurements for theLissajous figure and b) gray-value analysis of the light-emission images(according to Kriegseis et al. [21,22]).
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in which γ is the isentropic exponent of gas (γ � 1.4 fordiatomic gases).
III. Online Diagnostic and Control Approach
The recorded data of operating voltage V and probe voltage Vpwere continually acquired by the notebook computer from the digitaloscilloscope. The consumed power PA for monitoring or controllingpurposes was computed from voltage–charge cyclograms. Based onEq. (1), the evaluation algorithm calculates the power consumptionfor every time step tj according to
PjA � fItj
tj−1Q dV with Q � CpVp (4)
When using the diagnostic tool in the closed-loop-control mode, thealgorithm furthermore comparesPjAwith a preset power levelP
�A, and
calculates the deviation
ΔPjA � PjA − P�A (5)
as the relevant control error. The control signal for the next time steptj�i is estimated based on a proportional–integral derivative (PID)control algorithm:
Ωj�1 � Kp�ΔPjA� �1
Ti
Ztj
0
�ΔPjA� dt� Kdd�ΔPjA�
dt(6)
This type of controller has been chosen for the ease of adjusting thecontroller gains for robust and stable controller characteristics.After the output Ωj�1 has been calculated, it is fed into the controlinput of the power supply, where it is transformed directly into thecorresponding voltage for the high-voltage transformer (see Fig. 1b).For all experiments, the quiescent-air operating conditions of
f � 12 kHz, V � 10 kV, and p0 � 1.028 bar resulted in an initialpower consumption PA � P�A � 7.1 W for t < 0. The experimentsand corresponding basic parameter settings are listed in Table 1.
A. Proof of Concept
In a preliminary proof of concept by Kriegseis et al. [23], twoexperiments (ExpA, ExpB) were conducted to demonstrate thecapabilities and the two operating modes of the online diagnostictool, and to verify the validity of the close correlation of powerconsumption and resulting plasma length across the entire range ofrapidly changing environmental conditions during the experimentalruns. This set of experiments is briefly reviewed in the following toexplain the control concept. The advanced control concept and theachieved results are discussed in Secs. III.B and IV, respectively.Notethat the wind-tunnel blowdown for the preliminary experimentsExpA and ExpB was slightly faster than for the main experimentsExp1–Exp5, which does not affect the qualitative comparability ofthe discussed results for the characteristic times t1 − t3.In the first experiment (ExpA — monitoring mode), the
performance changes for a preset power consumption of P�A �7.1 Wweremonitored online according to Eq. (4) in time intervals ofΔt � tj − tj−1 ≈ 0.5 s. Because the hardware/software interfaceswere preimplemented in LabVIEW, but the source code of theLissajous-figure analysis was implemented in MATLAB, for thepreliminary proof of concept, every time step required the time-consuming communication between both software packages. Inthe second experiment (ExpB — controlling mode), a simpleproportional-derivative (PD) control algorithm according to Eq. (6)remote controlled the laboratory power supply of the electricalplasma-actuator setup, thus closing the control loop. The results areshown in Fig. 3. Because of the large time steps of the controller(Δt ≈ 0.5 s), the integral term of Eq. (6) had to be set to zero in thepreliminary control concept.The light-emission data of ExpA and ExpB are used to
retroactively validate the online diagnostic tool by means of thetemporal plasma-length evolution Δx�t� based on the closecorrelation of Δx and PA according to Kriegseis et al. [21].In Fig. 4a, the results of the monitoring experiment (ExpA) are
depicted. They clearly reveal the impact of the transient flowconditions on the actuator power PA. Immediately after the wind-tunnel valve was opened at t � 0, a power peak occurred due to aninitial expansion wave passing the test section, which was followedby a significant performance drop (PA � 4.8 W) once the blowdownscenario was fully developed at t1 under adverse pressure conditionsat maximum airflow speed (see Table 2). For decreasing Machnumber and pressure at t2, a constantly reduced performance(PA � 4.9 W) was observed, solely due to the impact of high-speedairflow (M � 0.75) at ambient-pressure conditions p0, which agreeswith the reports of Barckmann et al. [20] andKriegseis et al. [19]. Theinfluence of theminimum pressure at t3 exceeded the adverse airflowimpact (M � 0.69), which resulted in an increased performancePA � 8.7 W as compared to the preset initial value P�A � 7.1 W.This augmentation is in good agreement with the reports of Abe et al.[14] and Bénard et al. [12,25]. Thereafter, for t > t3, all quantitiesasymptotically returned to their initial values again. The plasmalength Δx of the simultaneously recorded light emissions,retroactively determined according to Kriegseis et al. [21], furtherconfirms the correctness of the online characterization of the powerconsumption.
Fig. 3 Transient flowconditions during experimentation.Time traces of
static and total pressure p, pt, Mach numberM; characteristic times arelabeled t1, t2, t3.
Table 1 List of conducted experiments and corresponding basic parameter settingsa
Experiment number Controller concept Time step Δt, ms Characteristictimes, s
aConstant settings: f � 12 kHz, V � 10 kV, P�A � 7.1 W, and p0 � 1.028 bar.bProportional derivative.cProportional–integral.
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For identical initial and airflow conditions, the results of theclosed-loop-control experiment (ExpB) are shown in Fig. 4b. Thecontrol algorithm failed for the very strong initial power oscillation ofthe passing expansion wave. Thereafter, the performance drop wasidentified at t1 and the algorithm counteracted this drop, as shown bythe slope of the control signal Ω. At t � 5.5 s, the control algorithmcollapsed for a single time step and caused a power overshoot due toan erratic signal. Apart from this peak, the algorithm successfullyconducted a closed-loop control of the power variations, which againis confirmed by the results for the plasma length Δx.
B. Advanced Control Circuit
To develop a more effective control algorithm, it is necessary toreduce the size of the control loop (i.e., minimize Δt). To eliminatethe time-consuming communication between both softwarepackages, the source code for the Lissajous-figure analysis wastranslated from MATLAB to LabVIEW. In addition, a programparallelizing multiple tasks has been developed to optimize thecomputational time for each time step. This program uses pipeliningtechnology and is especially powerful on multicore processors.The data acquisition of the digital oscilloscope samples the two
channels (V and Vp) in block mode with 250 data points at a samplerate of 1 MS∕s. These data points are filtered using a Savitzky–Golayfilter [26], and then separated cyclewise (K � 1) into individualLissajous figures with 83 data points each. For each block, the powerconsumption is calculated from Eq. (1), based on which the newremote signal of the closed-loop control circuit is estimated accordingto Eq. (6). The basic tasks processed for each iteration aresummarized in Table 3. Furthermore, the table shows the average run
time of the tasks for a standard dual-core laptop computer (2.2 GHz,4 GB RAM).For an optimized pipelining program, all parallelized tasks have to
be distributed over the available CPU cores to minimize theoverall run time.Obviously, the data acquisition (task 1) takesmost ofthe time. Therefore, at the same time as the current data block isacquired using CPU#1, the program performs all other computations(tasks 2–5) with the previous data block using CPU#2 as sketched inFig. 5. In total, the program needs about Δt � 17.3 ms to perform acomplete cycle of data acquisition and computations for 250data points per channel at a sampling rate of 1 MS∕s, which isan improvement of one order of magnitude with respect toconsumed time.As the repetition rate of the controller was increased, the system
dynamics also changed. Practice showed that the PD controller usedbefore was not suitable for the given noise level, as the Δt reductionresulted in higher noise gradients. Consequently, a proportional–integral (PI) controller based on Eq. (6) was chosen.To determine the controller gains, the open-loop step responsewas
analyzed using the Ziegler–Nichols step-response method [28]. Inthe literature, there are different ways shown for determining thecontroller gainsKp and Ti. Åström and Hägglund [29] determine thesystem latency with the help of a line of best fit through the point ofthe highest slope of the process variable, whereas the PID ControlToolkit user manual from National Instruments [30] uses a referencepoint of the process variable, which has 63.2%of themaximumvalueof the process variable.Additionally, the time gapΔt between twomeasurements is still in
the same order of magnitude as the system latency (see Fig. 6), suchthat an accurate determination of the system latency beyond thetemporal resolution of the control circuit is impossible. For the stepresponse shown in Fig. 6, this led to a proportional gain Kp rangingfrom 0.2 to 1, and an integral time Ti ranging from 0.05 to 0.1.Therefore, these values served as a first starting point for tuning thecontroller gains manually. Based on this semimanual procedure, itwas possible to implement a PI controller with reduced overshoot,minimized steady-state error, and suppressed oscillations.
IV. Results
Five experiments were conducted with the advanced controlalgorithm based on the PI-control concept. Exp1 was operated inmonitoring mode to provide a reference for the discharge-performance variations. Subsequently, four experiments in thecontrol mode (Exp2–Exp5) were conducted (see Table 1).
a) Monitoring mode (ExpA) b) Controlling mode (ExpB)
Fig. 4 Proof-of-concept results of consumed power PA, operating voltage V, plasma length Δx and remote-control signal Ω for a) monitoring andb) controlling modes of operation (cp. Table 2).
Table 2 Measured data at characteristic timesa
p, bar M PA, W V, kV Δx, mm Ω, Vt < 0 1.03 0 7.2m;c 10.0m;c 2.9m;c 0.89c
t3 � 14.5 s 0.89 0.69 8.7m 7.2 10.3m 9.8c 3.3m 2.8c 0.78c
aThe superscript m means monitoring mode (ExpA), whereas cmeans controlling mode (ExpB); (cp. time traces in Figs. 3and 4).
Table 3 List of tasks to be processed duringeach performance-control iteration and
corresponding (average) run time
Task Description Average run time, ms
1 Data acquisition 15.92 Filtering 0.83 Data separation 0.34 Power computation 0.15 Control computations 0.1
Fig. 5 Timing diagram for the pipelined performance-control circuitrunning on two CPU cores (according to NI Developer Zone [27]).
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A. Monitoring/Controlling
Figure 7a shows the result of the new monitoring experiment(Exp1). The improvement of the diagnostic tool due to the increasedsampling rate is clearly visible even in the monitoring mode.At the first instant of time after the wind-tunnel valve is opened
at t � 0, the typical actuator power peak can be recognized inthe diagram due to the passing expansion wave. Thereafter, thesignificant power drop occurred at t1 (PA � 3.7 W) under adversepressure and airflow conditions. At t2, the performance reductionsolely due to airflow influence is less pronounced (PA � 6.1 W),before the favorable pressure conditions lead to an increasedperformance of PA � 9.6 W at t3. The wind-tunnel valve is closedat t � 43 s.The results of Exp2 (controlling mode) are shown in Fig. 7b as a
direct comparison to Exp1. Both initial performance peak andsubsequent drop are reduced significantly as the controlled mimicsthe respective slopes with opposite signs. At t ≈ 7 s, the variations ofenvironmental conditions are entirely compensated, that is, theremaining control error ΔPjA is minimized.Qualitatively, the slope of the control signal Ω of the controlled
case directly mirrors the slope of the power PA of theuncontrolled case.
B. Parameter Optimization
Although considered an artificially strong change of theenvironmental conditions, the extreme performance gradients inthe time span between t � 0 and t1 emerged as an excellent test-casescenario for further control-circuit-optimization efforts. In particular,an interval J was defined, which was used to determine the relativestandard deviation:
σPA �1
P�A
������������������������������������������1
J − 1
XJj�1�PjA − P�A�
2
vuut (7)
of the controlled cases as a measure of control success. Differentcombinations of control parameters Kp and Ti were implemented in
the control algorithm (6), as listed in Table 4 together with therespective values of σPA . The results of all experiments are shownin Fig. 8.The reduction of the control error is reflected directly in the
standard deviation, which is 24.22% for the open-loop (monitoring)experiment Exp1, and has been reduced to 1.7% for the optimizedclosed-loop controller in experiment Exp5. However, the success ofcontrol is highly dependent on the choice of the control parameters. Ahigher control gain Kp increases the speed of the controller, but
Fig. 6 Open-loop step response of the control circuit; control signal Ω � process variable, power consumption PA � control variable.
a) Monitoring mode (Exp1) b) Controlling mode (Exp2)Fig. 7 Results of consumed power PA and control signal Ω for a) monitoring and b) controlling modes of operation (advanced PI-control concept).
Table 4 List of control parametersKp andTi as used forequation (6)
aRelative standard deviation σPA for the chosen intervalJ of tmax − tmin � 10 s (cp. Fig. 8).
Fig. 8 Comparison of the actuator power consumptionPA for differentcombinations of control parameters Kp and Ti as used for Eq. (6);considered evaluation interval J is indicated by arrows (cp. Table 4).
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comes at the cost of an increasing actuating variable, which isnaturally limited. The influence of the controller gain can be seen inthe beginning of the experiment at the difference of Exp4 incomparison to Exp5, in which the first performance drop is reducedfrom Pmin
A � 4.43 W to PminA � 5.57 W by an increase of Kp.
Figure 8 also yields that a reduction of Ti enhances the controlperformance by decreasing the steady-state error, but this alsodecreases the stability margin of the controller. For the value of Tichosen to low the controller shows heavy oscillations, whichtherefore leads to instability.
V. Conclusions
The present work successfully demonstrates a counteraction ofchanging environmental conditions (i.e., changes of pressure leveland airflow speed) on the resulting plasma-actuator performance.Continuing in the direction of previous studies, a novel online
characterization approach is introduced, allowing an in situ conditionmonitoring of the discharge performance. Moreover, this new toolfeatures a closed-loop control circuit, which assures constant plasma-actuator performance independently of the environmental con-ditions. A proportional–integral control algorithm is successfullyimplemented, closing the loop between discharge measurements andpower supply of the electric setup. Based on the relative performanceΠ as evaluation measure, the slope of the control signal Ω of thecontrolled casewas identified to directlymirror the slope of the powerPA of the uncontrolled case.From this result, the conclusion can be drawn that by means of
steadily processed real-time performance data, it is possible toachieve a constant plasma-actuator performance during operationunder fluctuating and transient flow conditions. This is an importantinsight implying significant consequences, because beyond thecommon purpose of favorably manipulating the airflow, anyadvanced dielectric-barrier-discharge-based flow-control systemwill necessarily require an appropriate closed-loop performancecontrol of the discharge device.The first successful incorporation of the closed-loop control
circuit for in-flight experiments on a full-sized motorized gliderwas demonstrated recently by the authors. Application of the onlinecontrol tool assures constant control performance of the actuatordespite variations of the environmental conditions (relative humidity,temperature, density) during transition control experiments. Furtherenhancements of the closed-loop control system for flight applicationare projected.
Acknowledgments
The authors gratefully acknowledge the financial support by theGerman Research Foundation (Deutsche Forschungsgemeinschaft)under grant EXC 259.
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