Active Compressor Surge Control System by Using Piston Actuation: Implementation and Experimental Results*

11th IFAC Symposium on Dynamics and Control of 11th IFAC Symposium on Dynamics and Control of 11th Symposium on and Process including Biosystems 11th IFAC IFACSystems, Symposium on Dynamics Dynamics and Control Control of of 11th IFAC Symposium on Dynamics and Control of Process Systems, including Biosystems Process Systems, including Biosystems June 6-8,Systems, 2016. NTNU, Trondheim, Norway Available online at www.sciencedirect.com Process including Biosystems Process Systems, including Biosystems June 6-8, 2016. NTNU, Trondheim, Norway June 6-8, 2016. NTNU, Trondheim, Norway June June 6-8, 6-8, 2016. 2016. NTNU, NTNU, Trondheim, Trondheim, Norway Norway

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IFAC-PapersOnLine 49-7 (2016) 347–352

Active Compressor Surge Control System Active Compressor Surge Control System Active Compressor Surge Control System Active Compressor Surge Control System by Using Piston Actuation: Implementation by Using Using Piston Piston Actuation: Actuation: Implementation Implementation by  by Usingand Piston Actuation:Results Implementation Experimental  and Experimental Results and Experimental Results and Experimental Results  Nur Uddin, Jan Tommy Gravdahl Nur Uddin, Jan Tommy Gravdahl Nur Uddin, Jan Tommy Gravdahl Nur Uddin, Jan Tommy Nur Uddin, Jan Tommy Gravdahl Gravdahl Dept. of of Engineering Engineering Cybernetics Cybernetics Dept. Dept. Cybernetics Dept. of of Engineering Engineering Cybernetics Norwegian University University of Science Science and and Technology (NTNU), (NTNU), Dept. of Engineering Cybernetics Norwegian of Technology Norwegian University of Science and Technology (NTNU), Norwegian University of Science and (NTNU), O.S. Bragstads plass 2D, Trondheim, Norway N-7491 N-7491 Norwegian University of2D, Science and Technology Technology (NTNU), O.S. Bragstads plass Trondheim, Norway O.S. Bragstads plass 2D, Trondheim, Norway N-7491 O.S. Bragstads plass 2D, Trondheim, Norway N-7491 (e-mail: [email protected], [email protected]) O.S. Bragstads plass 2D, [email protected]) Trondheim, Norway N-7491 (e-mail: [email protected], (e-mail: (e-mail: [email protected], [email protected], [email protected]) [email protected]) (e-mail: [email protected], [email protected]) Abstract: A novel implementation and experimental test results of piston actuated active Abstract: A A novel novel implementation implementation and and experimental experimental test test results results of of aaa piston piston actuated actuated active active Abstract: Abstract: A novel implementation and experimental test results of a piston actuated active surge control system (PAASCS) on a laboratory scale pipeline-compressor system are presented. Abstract: A novel implementation and experimental test results of a piston actuated active surge control system (PAASCS) on a laboratory scale pipeline-compressor system are presented. surge control system (PAASCS) on aa laboratory scale pipeline-compressor system are presented. surge control system (PAASCS) on laboratory scale pipeline-compressor system are presented. The experimental test is done to prove the concept of stabilizing compressor surge by surge control system (PAASCS) on a laboratory scale pipeline-compressor system are presented. The experimental experimental test test is is done done to to prove prove the the concept concept of of stabilizing stabilizing compressor compressor surge surge by by The The experimental test is done to prove the concept of stabilizing compressor surge by dissipating the plenum energy using a piston actuation. The PAASCS’s controller is applying The experimental test energy is done to aprove concept The of stabilizing by dissipating the plenum plenum using pistonthe actuation. PAASCS’s compressor controller is is surge applying dissipating the energy using a piston actuation. The PAASCS’s controller applying dissipating the aa piston The PAASCS’s controller is ψ-control introduced in (Uddin and Gravdahl, 2016), which uses feedback from pressure dissipating the plenum plenum energy using piston actuation. actuation. The only PAASCS’s controller is applying applying ψ-control introduced introduced in energy (Uddinusing and Gravdahl, Gravdahl, 2016), which which only uses feedback feedback from pressure ψ-control in (Uddin and 2016), only uses from pressure ψ-control introduced in (Uddin and Gravdahl, 2016), which only uses feedback from pressure measurements at the compressor discharge and in the plenum. Practical aspects of implementing ψ-control introduced in (Uddin and Gravdahl, 2016), which only uses feedback from pressure measurements at the compressor discharge and in the plenum. Practical aspects of implementing measurements at the compressor discharge and in the plenum. Practical aspects of implementing measurements at the compressor discharge and in the plenum. Practical aspects of implementing the PAASCS are presented including: flow measurement, generating a compressor map based measurements at the compressor discharge and in the plenum. Practical aspects of implementing the PAASCS PAASCS are are presented presented including: including: flow flow measurement, measurement, generating generating aa compressor compressor map map based based the the PAASCS are presented including: flow measurement, generating a compressor map based on a compressor performance test, piston design, and the test setup. The experimental test the are performance presented including: flow design, measurement, a compressor map based on aaPAASCS compressor test, piston piston and the thegenerating test setup. setup. The experimental experimental test on compressor performance test, design, and test The test on a compressor performance test, piston design, and the test setup. The experimental test results show that the PAASCS is able to stabilize surge and prove the concept of PAASCS with on a compressor performance test, piston design,surge and and the prove test setup. The experimental test results show that the PAASCS is able to stabilize the concept of PAASCS with results show the PAASCS is to surge and and prove the of PAASCS PAASCS with results show that that the PAASCS PAASCS is able able to stabilize stabilize surge prove the concept concept of with the advantage of ψ-control which stabilizes compressor surge by using feedback from pressure results show that the is able to stabilize surge and prove the concept of PAASCS with the advantage advantage of ψ-control ψ-control which stabilizes compressor surge by using using feedback from pressure pressure the of which stabilizes compressor surge by feedback from the advantage of ψ-control which stabilizes compressor surge by using feedback from pressure measurements only. the advantage only. of ψ-control which stabilizes compressor surge by using feedback from pressure measurements measurements only. measurements only. measurements only. © 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Compressor, active surge control, pitot tube flow measurement, linear actuator, Keywords: Compressor, active active surge surge control, control, pitot pitot tube tube flow flow measurement, measurement, linear linear actuator, actuator, Keywords: Compressor, Keywords: Compressor, active surge control, control, pitot pitot tube tube flow flow measurement, measurement, linear linear actuator, actuator, hardware in the loop test, experimental. Keywords: Compressor, active surge hardware in the loop test, experimental. hardware in the loop test, experimental. hardware in the loop test, experimental. hardware in the loop test, experimental. 1. INTRODUCTION is stabilizing surge by increasing the upstream pressure 1. INTRODUCTION INTRODUCTION is stabilizing surge by increasing the upstream pressure 1. is stabilizing surge by increasing the upstream pressure 1. is surge by the upstream pressure to increase the upstream energy, while the downstream 1. INTRODUCTION INTRODUCTION is stabilizing stabilizing surge by increasing increasing the upstream pressure to increase the upstream energy, while the downstream to increase the upstream energy, while the downstream to increase the upstream energy, while the downstream energy dissipation ASCS is stabilizing surge by flowing A centrifugal compressor operating area is commonly to increase the upstream energy, while surge the downstream energy dissipation ASCS is stabilizing by flowing A centrifugal compressor operating area is commonly energy dissipation ASCS is stabilizing surge by flowing A centrifugal compressor operating area is commonly energy dissipation ASCS is stabilizing surge by flowing extra fluid out from the plenum to decrease the downA centrifugal compressor operating area is commonly shown by a compressor map, where the compressor openergy dissipation ASCS is stabilizing surge by flowing A centrifugal compressor operating areacompressor is commonly extra fluid out from the plenum to decrease the downshown by a compressor map, where the opextra fluid out from the plenum to decrease the downshown by a compressor map, where the compressor opextra fluid out from the plenum to decrease the downstream energy. Two general state feedback control law shown by a compressor map, where the compressor operation at low mass flows is limited by a surge line. The extra fluid out from the plenum to decrease the downshown by a compressor map, where the compressor opstream energy. Two general state feedback control law eration at low mass flows is limited by a surge line. The stream energy. Two general state feedback control law eration at low mass flows is limited by a surge line. The stream energy. Two general state feedback control law for the both ASCS types were introduced by Uddin and eration at low mass flows is limited by a surge line. The operating area on the left side of the surge line is unstable stream energy. Two general state feedback control law eration at low mass flows is limited by a surge line. The for the both ASCS types were introduced by Uddin and operating area on the left side of the surge line is unstable for the both ASCS types were introduced by Uddin and operating area on the left side of the surge line is unstable for the both ASCS types were introduced by Uddin and Gravdahl (2016), and named φ-control for the upstream operating area on the left side of the surge line is unstable and will lead to surge, while it is stable operating area for the both ASCSand types wereφ-control introduced by Uddin and operating area to on surge, the leftwhile side of the surge line is unstable Gravdahl (2016), named for the upstream and will lead it is stable operating area Gravdahl (2016), and named for the and will lead to surge, while it Compressor is stable operating area Gravdahl (2016),and and named φ-control φ-control for stream the upstream upstream energy injection ψ-control for the down energy and will lead to while is on the of the line. surge is an (2016), and named φ-control for the upstream and willright lead side to surge, surge, while it Compressor is stable stable operating operating area energy injection and ψ-control for the down stream energy on the the right side of the the line.it surge is isarea an Gravdahl energy injection and ψ-control for the down stream energy on right side of line. Compressor surge an energy injection and ψ-control for the down stream energy dissipation. Both control laws make the closed loop system on the right side of the line. Compressor surge is an aerodynamic instability in the compression system and energy injection and ψ-control for the down stream energy on the right side of the line. Compressor surge is an dissipation. Both control laws make the closed loop system aerodynamic instability in the compression system and dissipation. Both control laws make the closed loop system aerodynamic instability in the compression system and dissipation. Both control laws make the closed loop system globally asymptotically stable (GAS) and the advantage aerodynamic instability in the compression system and results in an axisymmetric oscillation of the compressor dissipation. Both control laws make the closed loop system aerodynamic instability in the compression system and globally asymptotically stable (GAS) and the advantage results in in an an axisymmetric axisymmetric oscillation oscillation of of the the compressor compressor globally asymptotically stable (GAS) and the advantage results globally asymptotically stable (GAS) and of them are the minimum sensor requirement. The φresults in an oscillation the compressor mass flow the compressor pressure. is asymptotically stable (GAS) and the the advantage advantage results in and an axisymmetric axisymmetric oscillation ofThe theinstability compressor of them are the minimum sensor requirement. The φmass flow flow and the compressor compressor pressure.of The instability is globally of them are the minimum sensor requirement. The φmass and the pressure. The instability is of them are the minimum sensor requirement. The φcontrol requires feedback from the compressor mass flow mass flow and the compressor pressure. The instability is physically indicated by pressure fluctuation, reversal flow, of them are the minimum sensor requirement. The φmass flow and the compressor pressure. The reversal instability is control requires feedback from the compressor mass flow physically indicated by pressure fluctuation, flow, control requires feedback from the compressor mass flow physically indicated by pressure fluctuation, reversal flow, control requires feedback from the compressor mass flow measurement only, while the ψ-control requires feedback physically indicated by pressure fluctuation, reversal flow, temperature fluctuation and followed by severe vibration. control requires feedback from the compressor mass flow physically indicated by pressure fluctuation, reversal flow, measurement only, only, while while the the ψ-control ψ-control requires requires feedback feedback temperature fluctuation fluctuation and and followed followed by by severe severe vibration. vibration. measurement temperature measurement only, while ψ-control requires feedback from pressure measurements the compressor temperature fluctuation and followed severe Compressor surge leads to especially measurement only, while the the at ψ-control requires discharge feedback temperature fluctuation andcompressor followed by bydamage severe vibration. vibration. pressure measurements at the compressor discharge Compressor surge surge leads to to compressor damage especially from from pressure measurements at the compressor discharge Compressor leads compressor damage especially from pressure measurements at the compressor discharge and in the plenum only. Compressor surge leads to compressor damage especially at the rotating parts, for examples: compressor blades, from pressure measurements at the compressor discharge Compressor surgeparts, leadsfor to compressor damage especially and in the plenum only. at the rotating examples: compressor blades, and at the rotating parts, for examples: compressor blades, and in in the the plenum plenum only. only. at the rotating parts, for compressor shaft bearing, and also pipeline and structure (Gravin the plenum only. at theand rotating parts, for examples: examples: compressor blades, shaft and bearing, and also also pipeline and and structure blades, (Grav- and Piston actuated active surge control system (PAASCS) shaft and bearing, and pipeline structure (GravPiston actuated active surge control system (PAASCS) shaft and bearing, and also pipeline and structure (Gravdahl and Egeland, 1999). Piston actuated active surge control system (PAASCS) shaft and bearing, and also pipeline and structure (Gravdahl and Egeland, 1999). Piston actuated active surge control system (PAASCS) was in introduced by Uddin and Gravdahl (2011b). It is Piston actuated active surgeand control system (PAASCS) dahl and Egeland, 1999). was in introduced by Uddin Gravdahl (2011b). It is dahl and Egeland, 1999). was in introduced by Uddin and Gravdahl (2011b). It is dahl and Egeland, 1999). was in introduced by Uddin and Gravdahl (2011b). It is in the class of ASCS with downstream energy dissipation. A method to stabilize surge by using a state feedback conwas in introduced by Uddin and Gravdahl (2011b). It is in the class of ASCS with downstream energy dissipation. A method to stabilize surge by using a state feedback conin the class of ASCS with downstream energy dissipation. A method to stabilize surge by using a state feedback conin the class of ASCS with downstream energy dissipation. Theoretical works to improve the PAASCS performance A method to stabilize surge by using a state feedback control was introduced by Epstein et al. (1986). The method in the class of ASCS with downstream energy dissipation. A method to stabilize surge by using a state feedback conTheoretical works works to to improve improve the the PAASCS PAASCS performance performance trol was was introduced introduced by by Epstein Epstein et et al. al. (1986). (1986). The The method method Theoretical trol Theoretical works to improve PAASCS performance have been done by: introducing integral action to eliminate trol was by al. The is known as active surge control (ASCS). Several works to improve the the PAASCS performance trol was introduced introduced by Epstein Epstein etsystem al. (1986). (1986). The method method have been done by: introducing integral action to eliminate is known known as active active surge surge controlet system (ASCS). Several Theoretical have been done by: introducing integral action to eliminate is as control system (ASCS). Several have been done by: introducing integral action to eliminate piston drift (Uddin and Gravdahl, 2011a), and introducing is known as active surge control system (ASCS). Several actuators have been applied in the ASCS as summarized in have been done by: introducing integral action to eliminate is known as active surge control system (ASCS). Several piston drift (Uddin and Gravdahl, 2011a), and introducing actuators have been applied in the ASCS as summarized in piston drift (Uddin and Gravdahl, 2011a), and introducing actuators have been applied in the ASCS as summarized in piston drift (Uddin and Gravdahl, 2011a), and introducing a back-up system by using blow-off mechanisms (Uddin actuators have been applied in the ASCS as summarized in (Willems and de Jager, 1999; Uddin and Gravdahl, 2015), piston drift (Uddin and Gravdahl, 2011a), and introducing actuators havede been applied inUddin the ASCS as summarized in aa back-up system by using blow-off mechanisms (Uddin (Willems and Jager, 1999; and Gravdahl, 2015), back-up system by using blow-off mechanisms (Uddin (Willems and de Jager, 1999; Uddin and Gravdahl, 2015), aaand back-up system by using blow-off mechanisms (Uddin and Gravdahl, 2012b) and by using surge avoidance system (Willems and de Jager, 1999; Uddin and Gravdahl, 2015), for examples: movable plenum wall, close couple valve, back-up system by using blow-off mechanisms (Uddin (Willems and de Jager, 1999; Uddin and Gravdahl, 2015), Gravdahl, 2012b) and by using surge avoidance system for examples: movable plenum wall, close couple valve, and Gravdahl, 2012b) and by using surge avoidance system for examples: movable plenum wall, close couple valve, and Gravdahl, 2012b) and by using surge avoidance system (SAS) (Uddin and Gravdahl, 2012a) for fail-safe operation. for examples: movable plenum wall, close couple valve, drive torque, active magnetic bearing, and piston actuand Gravdahl, 2012b) and by 2012a) using surge avoidance system for examples: movable plenumbearing, wall, close couple valve, (SAS) (Uddin and Gravdahl, for fail-safe operation. drive torque, active magnetic and piston actu(SAS) (Uddin and Gravdahl, 2012a) for fail-safe operation. drive torque, active magnetic bearing, and piston actu(SAS) (Uddin and Gravdahl, 2012a) for fail-safe operation. drive torque, active magnetic bearing, and piston actuation. Based on how the actuators work to stabilize surge, (Uddin and Gravdahl, 2012a) for fail-safe operation. drive torque, active magnetic bearing, and piston surge, actu- (SAS) ation. Based on how the actuators work to stabilize This paper presents the implementation and the experation. Based on how the actuators work to stabilize surge, paper presents the implementation and the experation. Based on how the work stabilize surge, the ASCS can classified in two types: upstream This paper presents the implementation and the experation. Based onbe how the actuators actuators work to to stabilizeenergy surge, This the ASCS can be classified in two types: upstream energy This paper presents the implementation and the experimental test results of a PAASCS on a laboratory scale This paper presents the implementation and the experthe ASCS can be classified in two types: upstream energy imental test results of a PAASCS on a laboratory scale the ASCS can be classified in two types: upstream energy injection and downstream energy dissipation (Uddin and imental test results of a PAASCS on a laboratory scale the ASCS can be classified in two types: upstream energy injection and downstream energy dissipation (Uddin and imental test results of a PAASCS on a laboratory scale pipeline-compressor system running at a constant comimental test results of a PAASCS onata alaboratory scale injection and downstream energy dissipation (Uddin and pipeline-compressor system running constant cominjection and downstream energy dissipation (Uddin and Gravdahl, 2015). The upstream energy injection ASCS system running at a constant cominjection and downstream energy energy dissipation (Uddin and pipeline-compressor Gravdahl, 2015). The upstream injection ASCS pipeline-compressor system running at a constant compressor speed. An experimental test setup is built in pipeline-compressor system running at a constant comGravdahl, 2015). The upstream energy injection ASCS pressor speed. An experimental test setup is built Gravdahl, 2015). The upstream energy injection ASCS  pressor speed. speed. An experimental experimental test setup setup is built built in in Gravdahl, 2015). The upstream energy injection ASCS The authors acknowledge the financial support of Siemens Oil pressor An test is in Compressor laboratory at Departement of Engineering  pressor speed. An experimental test setup is built in The authors acknowledge the financial support of Siemens Oil Compressor laboratory at Departement of Engineering  The authors acknowledge the financial support of Siemens Oil  Compressor laboratory at Departement of Engineering and Gas Solutions Offshore through the Siemens-NTNU research The authors acknowledge the financial support of Siemens Oil  Compressor laboratory at Departement of Engineering Cybernetics, NTNU. The PAASCS control law is applying The authors acknowledge the financial support of Siemens Oil Compressor laboratory at Departement of Engineering and Gas Solutions Offshore through the Siemens-NTNU research Cybernetics, NTNU. The PAASCS control law is applying and Gas Solutions Offshore through the Siemens-NTNU research Cybernetics, collaboration project. and Gas Offshore Cybernetics, NTNU. NTNU. The The PAASCS PAASCS control control law law is is applying applying and Gas Solutions Solutions Offshore through through the the Siemens-NTNU Siemens-NTNU research research collaboration project. Cybernetics, NTNU. The PAASCS control law is applying

collaboration project. collaboration collaboration project. project. Copyright © 2016, 2016 IFAC 347 Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © IFAC (International Federation of Automatic Control) Copyright © 2016 IFAC 347 Copyright © 2016 IFAC 347 Copyright © 2016 IFAC 347 Peer review under responsibility of International Federation of Automatic Copyright © 2016 IFAC 347Control. 10.1016/j.ifacol.2016.07.323

IFAC DYCOPS-CAB, 2016 348 June 6-8, 2016. NTNU, Trondheim, Norway Nur Uddin et al. / IFAC-PapersOnLine 49-7 (2016) 347–352

Table 1. Major components of test setup.

Ls

Component Compressor Pressure sensor Mass flow sensor Valve Pipeline Plenum Control board Piston

us

ws Piston

pt Station A

pA

pi wi

pc

pd wd

Vp , p p

Station B

wt

pB

Inlet

T M 

Motor

Compressor

Plenum

Throttle

Lc

Fig. 1. Piston actuated active surge control system. the ψ-control. The control gain is determined by using the test setup parameters and a compressor map. The pt compressor map is obtained through a compressor perpi p Station A Station B d V p , palgorithm pc p pA p formance test. The control law is written in B wi wt wd Inlet Matlab and Simulink and embedded in a dSpace board to build a hardware in loop simulation. The PAASCS is T M  Throttle Plenum Compressor to see the performance tested experimentally of the system Motor in stabilizing surge. The test is started by running the Lc compressor at a constant speed and reducing the flow by closing an outlet valve (throttle) such that the compressor is entering surge while the PAASCS is inactive. The PAASCS is then activated after the compressor is in surge. The surge is shown by pressures oscillation sensed by pressure sensors at the compressor discharge and in the plenum. This is the first experimental confirmation of actively stabilizing compressor surge by using piston actuation. 2. SYSTEM DYNAMICS AND CONTROL

Detail Supercharger Vortech V-1 S-Trim Race M Druck PTX 610 Endress+Hauser t-mass 65F80 Siemens PN 10 Polypropylene pipe with diameter 75mm Cylindrical vessel dSpace DS1103 See Section 3.3

where ρ is the fluid density, As is the piston cross-sectional area, and Ls is the piston position. To simplify the surge control design, we ignore the piston dynamic and assume that the piston will generate a mass flow ws following a a20 c reference signal. Define constants B1 = A Lc and B2 = Vp , and substitute them into (1) and (2) such that results in: w˙ i = B1 (pc − pp )

(4)

p˙p = B2 (wi − wo − ws ). (5) The PAASCS is in the class of downstream energy dissipation ASCS (Uddin and Gravdahl, 2011b) such that the ψ-control introduced in (Uddin and Gravdahl, 2016) is applicable. Theorem 1. The ψ-control states that an equilibrium point of (4) and (5) is globally asymptotically stable (GAS) 1 if ws = wu , where wu = −ku (pc − pp ) with 2B B2 k m < ku <   ∂pp  ∂pc  2B1 and kn = ∂wo  . B2 kn , km = ∂wi  max

min

The stability proof can be found in (Uddin and Gravdahl, 2016). The surge control requires ws to behave as wu , and it is the task of a piston as the actuator of PAASCS. 3. LABORATORY TEST SETUP

A model of PAASCS is shown in Figure 1. The PAASCS model is a modification of the Greitzer compressor model (Greitzer, 1976) by adding a piston. The assumptions in the Greitzer model are applied in the PAASCS model. The pA and pB are the ambient pressures and assumed to be equal, and fluid pressures in the system are measured relative to the ambient pressure. It is assumed that pressure drop along the ducts in the system are neglected. Therefore, the compressor discharge pressure (pd ) is equal to the compressor pressure rise (pc ), and the compressor discharge mass flow (wd ) is equal to the inlet mass flow (wi ). Dynamic equations of the PAASCS model are given as follows (Uddin and Gravdahl, 2011b):

The concept of PAASCS is implemented and tested on a laboratory scale pipeline-compressor system at Compressor Laboratory in Department of Engineering Cybernetics, NTNU. A PAASCS test setup is built as shown in Figure 2. Major components in the setup are listed in Table 1 and most of the components have been used in an experimental work on compressor surge control using torque drive (Bøhagen, 2007). Fluid pressures in the setup are measured relative to the ambient pressure.

Ac (pc − pp ) (1) Lc a2 (2) p˙p = 0 (wi − wo − ws ), Vp where Ac is the compressor duct cross-sectional area, Lc is the effective length of the equivalent compressor duct, pp is the plenum pressure, a0 is the speed of sound, Vp is the plenum volume, wo is the outlet mass flow, and ws is the piston mass flow. The outlet mass flow is the set point of the desired compressor operating mass flow. A compressor operating point is an equilibrium point where w˙ i = 0 and p˙p = 0. The piston mass flow is defined by: dLs , (3) ws = ρAs dt

The mass flow sensor used in the setup is Endress+Hauser t-mass 65F80-AE2AG1AAAAAA. It is a high performance mass flow sensor for industrial gases and compressed air. The sensor is configured to measure mass flow at a range of 0 to 0.26 kg/s. The sensor has high accuracy with measurement error 2% of the measured value (Endress+Hauser, 2015). However, the sensor response is quite slow such that it is only applicable for measuring steady flow and not for measuring unsteady flow. Because surge is unsteady flow, we measure mass flow using a pitot tube as an alternative solution. The pitot tube is installed at the compressor inlet duct and equipped with two pressure sensors to measure the total pressure (pt ) and the static pressure (ps ). The mass flow is calculated by following equation:  w ¯ = Ac 2ρ(pt − ps ), (6)

w˙ i =

348

3.1 Mass flow measurement

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Nur Uddin et al. / IFAC-PapersOnLine 49-7 (2016) 347–352

349

680 cm 1 phase AC

Fc2 37 cm

155 cm outlet valve

Fc1

M2

M1

73 cm

100 cm d=20 cm

PT7,8

20 cm

XT

PT3,4 PT5,6

100 cm

piston

MF plenum compressor 40 cm

PT1,2

90 cm door

380 cm

343 cm

20 cm 17 cm

Matlab Simulink dSpace ControlDesk

3 phases AC : power supply line Fc: frequency converter

M : AC Motor

Signal converters & dSpace

door

: signal lines MF: mass flow sensor

: pipeline PT : pressure sensor

XT: position sensor

Fig. 2. Compression system with PAASCS test setup at Compressor Laboratory, Dept. of Engineering Cybernetics, NTNU. where w ¯ is the calculated mass flow and Ac is the inlet pipe cross-sectional area. The fluid density (ρ) is assumed to be constant and equal to the ambient air density. The calculated mass flow is corrected by calibrating the mass flow measurement using pitot tube with the mass flow measurement using the mass flow sensor. The corrected mass flow is given as follows: w = 0.45w ¯ − 0.0035, (7) where w is the corrected mass flow. The main reasons for this correction are misalignment of pitot tube and incorrect air density. The pitot tube mass flow measurement provides a much faster response than the mass flow sensor. 3.2 Compressor Performance Test A compressor map of the test setup is obtained through a compressor performance test. The performance test is done by running the compressor at a constant speed for several operating points and recording data of the compressor mass flow and the compressor discharged pressure for each operating points. The compressor mass flow is measured using the pitot tube and calculated using (7). The operating point is changed by adjusting the throttle opening. A test was done by running the compressor at 23978 RPM for eight operating points. The initial operating point is 349

at throttle opening 40% and reduced gradually at 5% for the other seven operating points. The operating points are labelled sequentially by alphabet A to H. The test results show that the compressor is operating stable at the operating points A to G (throttle opening 40% to 10%), but not at the operating point H (throttle opening 5%). Figure 3 shows the compressor states for operating points A to G. The compressor entered surge at operating point H as shown in Figure 4. The compressor surge is shown by oscillations of the compressor mass flow, the compressor discharge pressure, and the plenum pressure. The mass flow measurement is not accurate because reversal flows (negative flows) were physically observed during surge in the performance test, but the measurement output is not negative. The surge phenomenon is therefore presented by pressure oscillations in this study. A further study on flow measurement during surge using a pitot tube is suggested. A compressor map for stable compressor operating points are obtained by approximating the compressor states of the seven operating points (A to G) by a cubic function as shown by ”Approximation 1 ” in the Figure 3. The peak point of curve ”Approximation 1” is the surge point. The compressor map for unstable compressor operating points are estimated by a cubical function introduced in (Moore and Greitzer, 1986) and given as follows:

IFAC DYCOPS-CAB, 2016 350 June 6-8, 2016. NTNU, Trondheim, Norway Nur Uddin et al. / IFAC-PapersOnLine 49-7 (2016) 347–352

0.68

21.5

G

21

F

1.00

Approximation 1 Pd Approximation 2

E D

Linear actuator

0.075 0.20

C

20

pressure (kPa)

19.5

% Approximation 2 Pc0=20250; H=190; W=0.011; wi=−0.02:0.001:0.022; Pc=Pc0+H*(1+1.5*(wi/W−1)−0.5*(wi/W−1).^3);

Position sensor

26287 rpm

19

0.35

20.5

B

18.5 18

Fig. 5. Piston design.

%Aprroximation 1 wi=0.022:0.001:0.1; Pc = 11580*wi.^3 − 2534*wi.^2 + 94.43*wi +19.97;

17.5

0.35 0.20

A

17 16.5 16 −0.02

0

0.02

0.04

mass flow (kg/s)

0.06

0.08

0.1

Fig. 3. Compressor map obtained by a performance test.

mass flow (kg/s)

0.03 0.025 0.02

Fig. 6. Piston unit.

0.015

pressor surge as shown in Figure 4. The mass flow of the surge point is equal to 2W . The value of pc0 is approximated by subtracting 2H from the pressure of the surge point. The estimated compressor performance curve at unstable operating area is shown by ”Approximation 2” in Figure 3.

0.01 0.005 500

501

502

time (s)

503

504

pressure (kPa)

21 20.8 20.6

3.3 Piston

20.4 20.2 20 19.8 500

Pp Pd 501

502

503

504

502

503

504

time (s)

opening throttle (%)

9 8 7 6 5 4 3 500

501

time (s)

Fig. 4. Compressor is surge at operating point H with throttle setting 5%.   1 w 3  3  wi i (8) −1 − −1 pc (wi ) = pc0 + H 1 + 2 W 2 W where pc0 is the shut-off value of the axisymmetric characteristic, W is the semi-width of the cubic axisymetric compressor characteristic, and H is the semi-height of the cubic axisymetric compressor characteristic; consult (Moore and Greitzer, 1986) for more detailed definitions. The value of H is approximated by the amplitude of the compressor discharged pressure oscillation during com350

A piston as the actuator of PAASCS is required to have sufficient power and speed to generate mass flow ws to stabilize compressor surge. Based on the compressor map, the piston must be able to work at pressure 21 kPa. The piston mass flow is determined by the piston cross-sectional area and the piston speed. To minimize the length of the piston, the piston should have a larger cross-sectional area. By considering further applications of the piston, we decided to have a piston with diameter 0.2 m. The piston was designed as shown in Figure 5. The piston is driven by a linear actuator Servomech UAL4RV2C500 which has maximum speed 0.44 m/s, maximum displacement 0.5 m, and maximum force 1700 N (Servomech, 2015). The piston displacement is sensed by a spring loaded potentiometer Multicomp SP1-50 Transducer. The piston displacement is set up in the range of ± 0.25 m. The piston was manufactured by the workshop staff at Engineering Cybernetics, NTNU as shown in Figure 6. The piston dynamics is obtained through a closed loop system identification using the data of the piston displacement and the input signal. Figure 7 shows a block diagram of the closed loop system identification where Lsref is the position input as the reference signal, Ls is the piston displacement, ks1 is a proportional control gain, ks2 is the position sensor gain which is a conversion factor from meter to volt, and Gs is the piston transfer function. An initial test by exciting the piston using a step function reference signal showed that the piston movement is very

IFAC DYCOPS-CAB, 2016 June 6-8, 2016. NTNU, Trondheim, Norway Nur Uddin et al. / IFAC-PapersOnLine 49-7 (2016) 347–352

Lsref

k s2 Conversion factor meter to volt

+ −

us

ks1 Controller

Gs ( s )

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5. EXPERIMENTAL RESULTS

Ls

An experimental test is performed to test the PAASCS performance. The compressor is running at 24335 RPM and the throttle opening is reduced to 5% such that the compressor enters surge as shown by the pressure oscillations since t = 475 seconds in Figure 9. The PAASCS controller is then turned on at t = 482 seconds and is suppressing the pressure oscillations. It results in stabilizing the compressor surge. The PAASCS controller is then turned off at t = 513 seconds and as can be seen the compressor is driven back to surge.

Piston

k s2 Position Sensor

Fig. 7. Block diagram of piston system identification.

slow. Therefore, a proportional controller, ks1 = 10, is dL ⎛ dL ⎞ wu applied ⎟ + of ks2 is 6.17 usThe experimental Ls results in Figure ws the Compression 0 +to get a faster response. 1 The⎜⎝ dtvalue 9 show that piston dt ⎠ s PID G s As volt/m, which was kobtained through a calibration of the s (is )not following the referenceρsignal u velocity given bySystem the ρ A piston position sensor. Processings the data −of the piston Piston − Piston surge controller. An investigation of the piston using the Surge Time Controller input and the piston displacement using Matlab Toolbox Controller derivative closed loop system identification data shows that piston for System Identification results in a model with transfer bandwidth is about 1.2 Hz. The piston bandwidth is quite k s2 G f ( s ) lows compared function: to the surge frequency which is 3.5 Hz. This 0.251 Ls (s) Filter indicates that the piston response is quite slow to follow Position Time = (9) derivative Sensor Gs (s) = the reference signal. us (s) s(s + 5.405) s

s

ref

pc −

The piston was also experience with some drift. Integral control was recommended by (Uddin and Gravdahl, 2011a) to eliminate the piston drift. It has been applied in this experimental test but it does not give to much 4. PAASCS IMPLEMENTATION improvement Piston in this experiment. The slow response of the piston is the main reason of it. ⎛ dL ⎞ dL ⎜ dtof⎟ PAASCS implementation block wu diagram + ⎝ ⎠ u Lfaster ws piston 0 + Figure 8 shows 1 dt actuator for the s expected s d Compression Surge Piston Linear It is that a linear ρ As and theController values of parameters in the ktest setup are given s2 System Controller Actuator dt ρ A would lead to better performance. Nevertheless, surge was s the block − in Table 2. The algorithms in Conversion − diagram are stabilized with the current Time actuator. factor derivative Conversion Table 2. PAASCS meter toParameters volt factor Test Setup 6. CONCLUSION AND FURTHER WORKS mass flow to where Ls is the piston displacement in meters and us is the piston input voltage in volts.

s

s

ref

Parameter a0 Lc ρ

Value velocity Unit 340 m/s 0.8 m 1.2041 kg/m3

Parameter Vp Ac As

Value 0.12 0.0038 0.0314

Unit 3 Filter m m2 m2

d ks2 Andt implementation and experimental test of PAASCS were done and the results were presented. The PAASCS is Time Position derivative able to stabilize Sensor compressor surge and prove the concept of PAASCS. The PAASCS by using ψ-control makes the implemented in a Simulink model and embedded into a implementation simple as only requiring feedback from dSpace board DS1103 to build a hardware in the loop pressure measurements. Pressure Sensor (HIL) simulation. The dSpace board has a 20-channelsFilter digital to analog converter (DAC) and an 8-channels Recommendation of further works to improve the PAASSC analog to digital converter (ADC) as the interfaces to are given as follows. The performance of PAASCS can be improved by using a better linear actuator with higher connect with actuators and sensors, respectively. bandwidth. The measurement of piston velocity can be The surge control gain ku is calculated by using Theorem 1 improved by using velocity sensor instead of using the time 2B1 2B1 where B2 km < ku < B2 kn . By using (8), compressor derivative of the position sensor output. The mass flow map in Figure 3, and the test setup parameters, it can measurement by using pitot tube can be improved by con3H be obtained km = 2W = 2.5909 × 104 Pa.s/kg, kn = sidering that the air density is varying instead of assuming  2pp  = 3.3684 × 105 Pa.s/kg, B1 = 0.0047, and B2 = it as a constant. The air density can be approximated as wo  min a function of temperature. Another solution for the mass 963330. The calculation results in 2.555 × 10−4 < ku < flow measurement is by using an observer as introduced in 3.3 × 10−3 . We choose ku = 4 × 10−4 for the experimental (Bøhagen and Gravdahl, 2002). test. The output of the surge controller is wu which is a reference mass flow for the piston. Since we only have a ACKNOWLEDGEMENTS position sensor in the piston, the reference mass flow is 1 . The The authors would like to thank to Per Inge Snildal converted to velocity with a conversion factor ρA s velocity is a reference velocity for the piston. An inner and Terje Haugen for constructing the piston, and Rune closed loop with a piston controller is required to assure Mellingseter for the electrical installation. that the piston movement follows the reference velocity. REFERENCES The piston controller is a PID controller with kp = 120, ki = 5, and kd = 1. The Filter 1 is a first-order low-pass Bøhagen, B. (2007). Active surge control of centrifugal Butterworth filter with passband frequency 20π rad/s and compression systems: Theoretical and experimental rethe Filter 2 is a first-order low-pass Butterworth filter with sults of drive actuation. Ph.D. thesis, Norwegian Unipassband frequency 60π rad/s. versity of Science and Technology.

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Gf (s) Filter

s

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Time derivative

Position Sensor

IFAC DYCOPS-CAB, 2016 June 6-8, 2016. NTNU, Trondheim, Norway Nur Uddin et al. / IFAC-PapersOnLine 49-7 (2016) 347–352 352

Piston 0 +

ku

−

Surge Controller

wu

1 ρ As

⎛ dLs ⎞ ⎜ dt ⎟ ⎝ ⎠ref

Conversion factor mass flow to velocity

k s2

Conversion factor meter to volt

+

us

PID control

−

Gs ( s )

Ls

Piston Controller

d dt

dLs dt

ρ As

ws

Compression System

pc − pp

Time derivative

d dt

ks2

Time derivative

Position Sensor

Filter 1

Pressure Sensor

Filter 2

Fig. 8. PAASCS block diagram.

pc − pp (Pa)

pressure (kPa)

Control ON 18 17.5 17 16.5 475

pp

pc

480

485

490

495 500 time (s)

505

510

515

520

480

485

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495 500 time (s)

505

510

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495 500 time (s)

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495 500 time (s)

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495 500 time (s)

505

510

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520

200 0 −200

piston velocity (m/s)

475 0.1 0 −0.1 475

reference

actual

s

u (volt)

10 0

piston position (m)

−10 475 0.08 0.06 0.04 0.02 0 475

Fig. 9. Experimental result of PAASCS. Bøhagen, B. and Gravdahl, J.T. (2002). On active surge control of compressors using a mass flow observer. In Proceedings of the 41st IEEE Conference on Decision and Control, volume 4, 3684–3689. IEEE. Endress+Hauser (2015). Technical information proline t-mass 65f, 65i thermal mass flowmeter. URL https://portal.endress.com/wa001/dla/5000009/ 2467/000/03/TI00069DEN_1314.pdf. [Online; accessed 20-October-2015]. 352

Epstein, A.H., Williams, J.E.F., and Greitzer, E.M. (1986). Active suppression of compressor instabilities. In Proc. of AIAA 10th Aeroacoustic Conference, 86-1994. Seattle. Gravdahl, J.T. and Egeland, O. (1999). Compressor surge and rotating stall: Model and control. Springer Verlag, London. Greitzer, E.M. (1976). Surge and rotating stall in axial flow compressor, part I: Theoritical compression system model. J. Engineering for Power, 98, 190–198. Moore, F.K. and Greitzer, E.M. (1986). A theory of post stall transients in an axial compressors system: Part I-Development of equation. J. Engineering for Gas Turbine and Power, 108, 68–76. Servomech (2015). Mechanical linear actuators catalogue. URL http://www.servomech.com. [Online; accessed 20-October-2015]. Uddin, N. and Gravdahl, J.T. (2011a). Piston-actuated active surge control of centrifugal compressor including integral action. In Proc. of the 11th International Conference on Control Automation and System. Gyeonggido, South Korea. Uddin, N. and Gravdahl, J.T. (2012a). A compressor surge control system: Combination active surge control and surge avoidance. In Proc. of the 13th International Symposium on Unsteady Aerodynamics, Aeroacoustics, and Aeroelasticity of Turbomachinery (ISUAAAT). Tokyo, Japan. Uddin, N. and Gravdahl, J.T. (2012b). Introducing backup to active compressor surge control system. In Proc. of the 2012 IFAC Workshop on Automatic Control in Offshore Oil and Gas Production, 263–268. Trondheim, Norway. Uddin, N. and Gravdahl, J.T. (2011b). Active compressor surge control using piston actuation. In ASME 2011 Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control, 69–76. Virginia, US. Uddin, N. and Gravdahl, J.T. (2015). Bond graph modeling of centrifugal compression systems. SIMULATION, 91(11), 998–1013. Uddin, N. and Gravdahl, J.T. (2016). Two general state feedback control laws for compressor surge stabilization. submitted to The 24th Mediterranean Conference on Control and Automation. Willems, F. and de Jager, B. (1999). Modeling and control of compressor flow instabilities. Control Systems, IEEE, 19(5), 8 –18.