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Hydraulic Actuation System modeling for developmental Gas Turbine Engine

This document presents a hydraulic actuation system modeling using bond graph techniques. It summarizes the modeling of a two-stage servo valve and hydraulic actuator. The key steps are: 1. The two-stage servo valve and hydraulic actuator are modeled using bond graphs. Differential equations are derived from the bond graphs. 2. The differential equations are transformed into state-space form. 3. Simulation results are analyzed for the electro-hydraulic system model under conditions of underlap and critical lap servo. The document outlines the component modeling using bond graphs, derivation of differential equations, and state-space representations to analyze the hydraulic actuation system dynamics.

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Hydraulic Actuation System Modeling for Developmental Gas Turbine Engine Presented by N . Premnath 31607104 M.tech Instrumentation 4th Semester. Internal Guide Dr. Neena Jaggi HOD, Professor Dept of Physics NIT Kurukushetra. External Guide Mr. V.G.Sanjawadmath Scientist ‘G’. Mr. Santhosh Muthe Scientist ‘D’ GTRE, DRDO, Bangalore FINAL VIVA VOCE 2016-2018 DEPARTMENT OF PHYSICS NATIONAL INSTITUTE OF TECHNOLOGY KURUKSHETRA
Contents:  Introduction  Literature Review  Block Diagram of EHAS  Goals  Bond Graph Techniques  Comparison of bond graph elements with block diagram  Schematic Diagram of Two Stage Servo Valve  Modeling of Two Stage Servo Valve using Bond graph  Differential equations and State space form of Two Stage Servo Valve  Schematic Diagram of Hydraulic Actuator  Modeling Hydraulic Actuator using Bond graph  Differential equations and State space form of Hydraulic Actuator  Controller Design  Results and Discussion
Literature Review: Effects Result References Oil is returned from the valve to the tank through a low pressure return pipe. Simulation results show that dynamic behavior is mainly depends on the proper conditions of the seals. Richard Poley, 2005 Internal leakage and friction forces are present in the hydraulic cylinder Fuzzy logical control is to produce control signals that are not only proportionally dependent on control error. B.Sulc, J.A. Jan, 2002 Friction and internal leakage model were integrated into the electro-hydraulic actuator model. Sliding mode control technique, the nonlinearities and uncertainties i.e. friction and internal leakage has been fully compensated. M. F. Rahmat, Zulfatman, A.R.Husain, Y. m. Sam, July 2011.
Literature Review: Effects Result References Excess pump fluid is discharged to tank from relief valve and pressure drops due to throttling in proportional valve. This cause waste of energy. System uncertainties are considered and a robust H∞ control synthesis approach is used to control the position of the system. Ahsan Saeedzadeh, S. Mehdi Rezaei, Mohammad Zareinejad oct 2016. Leakage flow between the spool valve and body considerably dominates the orifice flow through the valve. It should be accounted in controller design. Erylmaz and Wilson, 2000.
Introduction:  An Electro-Hydraulic Actuation Systems are widely used in different industrial application.  It is used wherever high magnitude forces are exerted.  It is a closed loop system which consists of Two Stage Servo Valve, double acting hydraulic cylinder and reservoir.  It is used to control the position of the aircraft, and etc,.
Block Diagram of EHAS: TWO STAGE SERVO VALVE HYDRAULIC ACTUATOR CONTROLLER Demand Input (mm) - + Supply Pressure (KPa) Input Current for valve is(mA) Flow rate (Qx) (m3 /s) Flow rate (Qy) (m3 /s) Acutator Position (mm) Negative Feedback
Goals:  The Physical structure and operating principle of the Electro-Hydraulic Actuation system are analyzed first.  Modeled the Two Stage Servo Valve and Hydraulic Actuator using Bond Graph Technique in presence of Underlap servo and Critical lap servo.  Mathematical differential equations are derived from the Bond Graph of Two Stage Servo Valve and Hydraulic Actuator.  Generated the State Space representation from the Differential equations of the Two Stage Servo Valve and Hydraulic Actuator.  Analyzed the Electro-Hydraulic System model under condition of Underlap Servo and Critical lap Servo by simulating in MATLAB/Simulink environment.
Bond Graph Technique:  Bond Graph is the technique which is used to represent the any system in the single graphical model.  In Bond Graph technique, the flow of energy for the systems never change.  The basic components of Bond Graph technique consists of ‘effort’ represented as ‘e’, ‘flow’ indicated as ‘f’, Resistive elements as ‘R’, Capacitive elements as ‘C’, and Inertance elements as ‘I’.  Two types of sources are available in Bond Graph, they are ‘Source effort’ indicated as ‘Se’ and ‘Source flow’ represented as ‘Sf ‘.  There are types of junctions are available in Bond Graph, they are ‘0-Junction’ and ‘1-Junction’.  Special bond graph element introduced in the Bond Graph technique which is the hidden edge of the Tetron State Variables, known as ‘Memristor’.
 Resistive Element: 𝑒 = 𝑅 𝑓 𝑓 = 1 𝑅 𝑒  Inertial Element: 𝑓 = 1 𝐼 𝑒 𝑑𝑡 𝑒 = 𝐼 𝑓 R e f R f e I f e I f e
 Capacitance Element: 𝑒 = 1 𝐶 𝑓 𝑒 = 1 𝐶 𝑓 𝑑𝑡  Transformer Element: 𝑒2 = 𝑛 𝑒1, 𝑓1 = 𝑛 𝑓2  Gyrator Element: 𝑒1 = 𝑟 𝑓2, 𝑒2 = 𝑟 𝑓1 C f e C f e TF e1 f1 e2 f2 n e2 f2 GY f1 e1 r
 0 Junction: 𝑒3 = 𝑒1 = 𝑒2 𝑓3 = 𝑓1 − 𝑓2  1 Junction: 𝑓1 = 𝑓2 = 𝑓3 𝑒3 = 𝑒1 − 𝑒2  Source effort:  Source flow: 0 e1 f1 e2 f2 e3f3 f2 e2 1 f1 e1 f3 e3 e f Seea: e f Sffa:
Special Elements:  The memristor, is proposed as a new bond graph element, on an equal footing with R, L and C, and having some unique modeling capabilities for nonlinear systems.  If the resistance value can be controlled by an external signal, the resistor is named as a Modulated Resistor, in mnemonic represented as MR.  There should be dynamic change in the resistive either charge or impulse controlled, when the momentum and displacement change. This has been represented as the ‘Memristor’.
C I ∫dt ∫dt e f p q R Memristor Tetron of state with memristor Momentum Displacement p = ∫e dt q = ∫f dt Displacement vs Momentum
Comparison of bond graph elements with block diagram: I I C f e f e f e R e f R f e f2 e2 1 f1 e1 f3 e3 0 e1 f1 e2 f2 e3f3 C f e GY e1 f1 f2 e2 r e2 f2 GY f1 e1 r f2 e2 TF f1 e1 n TF e1 f1 e2 f2 n R ef 1/R ef 1/C ef C ef I ef 1/I ef 1/n e2e1 1/nf1 f2 n e2e1 nf1 f2 r e2f1 re1 f2 1/r e2f1 1/re1 f2 e1 e3 e2 f1 f3 f2 + - + - f1 f2 f3 e1 e2 e3 Bond Graph Block Diagram Bond Graph Block Diagram
Schematic Diagram of Two Stage Servo Valve: Qx Qy PBPA Pln Prn θfl QnrQnl PiPi PiPi Pt Stage 1 Stage 2 xsp Torque Motor Flapper Nozzle Spool Qal QblQlfe Qlre Moog’s Two Stage Servo Valve
Construction of Two Stage Servo Valve:  Two Stage Servo Valve consists of two stages, First stage is Torque motor, Flapper nozzle and the Second stage is Spool Valve.  First Stage, the sleeve is wounded with armature coil which is placed between the permanent magnet with an air gap.  In Second Stage, the spool valve movement is based on the input current for the servo valve.  The change of the angle of flapper, which control the movement of the spool valve and also the flow rate of servo valve.  Small input current is control the flow rate of servo valve which happens only Electro Hydraulic Servo Valve.
Torque motor of Two Stage Servo Valve: N N SS is is xfl Permanent Magnet b a  The relationship for Tmotor , Torque of the Motor for Two Stage Servo Valve [Merritt], is given by 𝑇 𝑚𝑜𝑡𝑜𝑟 = 𝐾 𝑚 θ 𝑓𝑙 + 𝐾𝑖 𝑖𝑠 Where, Tmotor = Torque of the motor Km and Ki = Intensity control constant(Nm/A) and Rotational angle constant(Nm/rad) θ 𝑓𝑙 = Flapper angle (rad) is = input current (mA)
Modeled Two Stage Servo Valve using Bond Graph: 1 1 0 TF 1/lrc 1/3Ksl TF: lfc Bfl Jfl Tmotor TF: Anfl1/Anfl:TF 00 1 Pi Rn 0 1 1 MR MR Pt 1Pi TF: Asp1/Asp:TF 1 0 1 0 1101 Pt Pi Pi Port A Port B MR MR MR MR PA PB msp Qb1 Qa1 Qlfe Qlre θfl xsp Rn CnCn PLn PRn Qnr Qnl xfl Fsl Bsp . . . Stage 1 Stage 2 1/Ktalt 2 θfl . θfl . θfl . θfl . θfl . e2 e3 e4 e5 e6 Fsl q10 Fslq9 Fsl xsp . xsp . xsp .xsp .xsp .xsp . xsp . xsp . xsp . e23 e22e21 e20 e19 e18 e17 e16 Qa1e24 e25 Qlfe e26 Qlre Qb1 e27 Qa1 PA PA Qlfe Qlfe Pt Pt Qlre Qlre PB PB Qb1 xfl .xfl . xfl . xfl . xfl .e1 e9 e8 e12 e13 PRn PRn PLn PLn Qnr Qnre10 q4 Qnl Qnle11 q6 PLn q8 PLn q5 PLn q7 PRn PRn PRn q3 q5 q5 Pt Pt q3 q3 q3 e14 e15
Differential equation of Two Stage Servo Valve: 𝜃 𝑓𝑙 = 1 𝐽 𝑓𝑙 (−𝐵𝑓𝑙 𝜃 𝑓𝑙 + 𝑙𝑟𝑐 𝐹𝑠𝑙 + 𝐾 𝑚 − 𝑙2 𝑡𝑎 𝐾𝑡𝑎 𝑙 𝑓𝑐 𝑥𝑓𝑙 − 𝑙𝑓𝑐 𝐴 𝑛 + 𝐴𝑛𝑓𝑙 ∆𝑃 + 𝐾𝑖 𝑖 𝑠) 𝐹 𝑠𝑙 = −3𝑙𝑟𝑐𝐾𝑠𝑙 𝜃 𝑓𝑙 + 3𝐾𝑠𝑙 𝑥 𝑠𝑝 𝑥 𝑓𝑙 = 𝑙𝑓𝑐 𝜃 𝑓𝑙 𝑥 𝑠𝑝 = − 1 𝑚 𝑠𝑝 𝐹𝑠𝑙 − 𝐵 𝑠𝑝 𝑚 𝑠𝑝 𝑥 𝑠𝑝 + 𝐴 𝑠𝑝 𝑚 𝑠𝑝 ∆𝑃 − 2 𝐴𝑖 𝑚 𝑠𝑝 𝑃𝑖 ∆𝑃 = − 2 𝐴 𝑛𝑓 𝑙𝑓𝑐 𝐶 𝑛 𝜃 𝑓𝑙 − 2𝐴𝑠𝑝 𝐶 𝑛 𝑥 𝑠𝑝 − 1 𝐶 𝑛 𝑅𝑛 ∆𝑃
State Space form of Two Stage Servo Valve: 𝜃 𝑓𝑙 𝐹 𝑠𝑙 𝑥 𝑓𝑙 𝑥 𝑠𝑝 ∆𝑃 = −𝐵𝑓𝑙 𝐽 𝑓𝑙 𝑙 𝑟𝑐 𝐽 𝑓𝑙 𝐾 𝑚 𝑙2 𝑡𝑎 𝐾𝑡𝑎 𝐽 𝑓𝑙 0 −𝑙𝑓𝑐 𝐴 𝑛 + 𝐴𝑛𝑓𝑙 𝐽 𝑓𝑙 −3𝑙𝑟𝑐𝐾𝑠𝑙 0 0 3𝐾𝑠𝑙 0 𝑙 𝑓𝑐 0 0 0 0 0 −1 𝑚 𝑠𝑝 0 −𝐵𝑠𝑝 𝑚 𝑠𝑝 𝐴 𝑠𝑝 𝑚 𝑠𝑝 −2 𝐴 𝑛𝑓 𝑙 𝑓𝑐 𝐶 𝑛 0 0 −2𝐴𝑠𝑝 𝐶 𝑛 −1 𝐶 𝑛 𝑅 𝑛 𝜃 𝑓𝑙 𝐹 𝑠𝑙 𝑥 𝑓𝑙 𝑥 𝑠𝑝 ∆𝑃 + 𝐾𝑖 𝐽 𝑓𝑙 0 0 0 0 0 0 0 0 −2𝐴𝑖 𝑚 𝑠𝑝 𝑖 𝑠 𝑃𝑖
 The flow rates which is given as input to the actuator, 𝑄 𝑥 = 𝑐𝑑 𝑑𝑟 𝑥𝑠𝑝 2 𝑝 (𝑃𝑖 − 𝑃𝐴) 𝑄 𝑦 = 𝑐𝑑 𝑑 𝑟 𝑥𝑠𝑝 2 𝑝 (𝑃𝐵 − 𝑃𝑡) Where, Qx and Qy = Flow rates(m3/s) 𝑝 = Density of the oil(Kg/m3) Pi = Supply Pressure(Pa) cd = Discharge coefficient xsp = Position of spool (m) PA and PB = Pressure of servovalve(Pa) Pt = Tank Pressure(Pa)
Schematic Diagram of Hydraulic Actuator: Pi Pt ui Qx Qy Qle P1 P2Api xpi xsp Hydraulic pump Tank Two stage servo valve Hydraulic cylinder Ml Ksp Bda Load Qe1 Qe2
Construction of Hydraulic Actuator:  In an Electro Hydraulic Actuation System, using the Hydraulic Actuator to control the position of aircraft.  Double Acting Cylinder used as the Hydraulic Actuator.  The double acting cylinder consists of piston which is controlled by the difference of the pressures across it.  The piston is used to control the constant load.  The flow from the servo valve is used to adjust the piston of the double acting cylinder in Hydraulic actuator.
Modeled Hydraulic Actuator using Bond Graph: 0 TF 1 TF 0 1 1 1 1 1/Ksp Ml Bda mr Ff Rle1 Rle2 Cp1 Cp2 P1 P2 Rin Qx Qy Api 1/Api P1 P1 P1 P3 P2 P2 P2 P4 P1-P2 P1 P2 F1 F2 F3 F F4 F5 F6 xpi . xpi . xpi . xpi . xpi . xpi .xpi . xpi . Ff q7 q7 q2 q3 q1 q3 q6 q8 q8 q3 q4
Differential Equations of Hydraulic Actuator: 𝑃1 = − 1 𝑅𝑖𝑛 + 1 𝑅𝑙𝑒1 1 𝐶 𝑝1 𝑃1 + 1 𝑅𝑖𝑛 𝐶𝑝1 𝑃2 − 𝐴 𝑝𝑖 𝐶 𝑝𝑖 𝑥 𝑝𝑖 𝑃2 = − 1 𝑅𝑖𝑛 𝐶 𝑝1 𝑃1 − 1 𝑅𝑖𝑛 + 1 𝑅𝑙𝑒2 1 𝐶𝑝2 𝑃2 + 𝐴 𝑝𝑖 𝐶 𝑝𝑖 𝑥 𝑝𝑖 𝑥 𝑝𝑖 = 𝐴 𝑝𝑖 𝑀𝑙 +𝑚𝑟 𝑃1 − 𝐴 𝑝𝑖 𝑀𝑙 +𝑚𝑟 𝑃2 + 𝐵 𝑑𝑎 𝑀𝑙 +𝑚𝑟 𝑥 𝑝𝑖 − 1 𝑀𝑙 +𝑚𝑟 𝐹 𝑓
Where, 𝐶 𝑝1 = 𝑉 𝑜 + 𝑥 𝑝𝑖 β 𝑜 and 𝐶 𝑝2 = 𝑉 𝑜 − 𝑥 𝑝𝑖 β 𝑜 Vo= Volume of the hydraulic fluid, the piston at the position of middle (m3) βo = Bulk modulus of the hydraulic fluid (Nm2) xpi = Displacement of the actuator (m) Differential Equations of Hydraulic Actuator:
State Space form of Hydraulic Actuator: 𝑃1 𝑃2 𝑥 𝑝𝑖 = −( 1 𝑅𝑖𝑛 + 1 𝑅𝑙𝑒1 ) 1 𝐶 𝑝1 1 𝑅𝑖𝑛 𝐶 𝑝1 − 𝐴 𝑝𝑖 𝐶 𝑝1 1 𝑅𝑖𝑛 𝐶 𝑝2 −( 1 𝑅𝑖𝑛 + 1 𝑅𝑙𝑒2 ) 1 𝐶 𝑝2 − 𝐴 𝑝𝑖 𝐶 𝑝2 𝐴 𝑝𝑖 𝑀𝑙 + 𝑚𝑟 −𝐴 𝑝𝑖 𝑀𝑙 + 𝑚𝑟 𝐵 𝑑𝑎 𝑀𝑙 + 𝑚𝑟 𝑃1 𝑃2 𝑥 𝑝𝑖 + 1 𝐶 𝑝1 0 0 0 0 −1 𝐶 𝑝2 0 0 0 0 𝐾 𝑠𝑝 𝑀𝑙 +𝑚𝑟 −1 𝑀𝑙 +𝑚𝑟 𝑄 𝑥 𝑄 𝑦 𝑥 𝑝𝑖 𝐹 𝑓
Controller Design:  One form of Controller widely used in industrial process control is PI controller.  The Transfer Function of controller is , Gc(S) = Kpr + Kint/S Where, Kpr = Proportional Gain Kint = Integral Gain  The Controller have been tuned for the Electro hydraulic actuation system, to bring the actuator to the desired position.  The Tuned parameter of controller is, Kpr = 0.1 mA/mm, Kint = 0.0001mA/mm.s
Simulation Model of the Electro Hydraulic Actuation System: • The Sampling Time of an Electro Hydraulic Actuation System is 0.0001sec
Step Response for Closed Loop System: Results:
Input Current for Servo Valve of Closed Loop System:
Pressure Difference across the Hydraulic Actuator under Closed Loop System:
Flow rates of Servo Valve Under Condition of Underlapped and Critical lapped Systems:
Open Loop Frequency of System:
Closed Loop Frequency of System:
Discussion of Results:  Open loop and Closed loop frequency responses for system with Critical lap and a system with Underlapped spool configuration are obtained.  Closed loop position response indicates, Under lapped system is having more Overshoot than the Critical lapped system and it’s rise time is lesser than that of the critically lapped system.  Closed loop current response indicates, the power required for under lapped system is more than that of the critically lapped system.  The open loop bandwidth, closed loop bandwidth, rise time and settling time, closed loop currents are tabulated.
Comparison Under lapped and Critically lapped Systems: PARAMETER UNDER LAP CRITICAL LAP Rise Time (s) 0.1399 0.3241 Settling Time (s) 6.1146 6.0413 Open loop Bandwidth (Hz) 15.45 3.029 Closed loop Bandwidth (Hz) 2.562 1.092
Conclusions:  Basic bond graph elements are used in constructing the Electro Hydraulic Actuation System.  Two Stage Servo Valve and Hydraulic actuator are modeled separately and two different state space representation are obtained.  Under lapped configuration is obtained by introducing increased flow.  Performance simulations results indicate the results are in line with physical behavior.
Future Scope:  Electro Hydraulic Servo Valve with overlapped spool configuration need to be modeled with some modifications to the basic bond graph elements.  Fidelity of the model can be enhanced considering all three configuration namely Critical lap, Under lap and Over lap.  Improves the Controller for the Configuration of Under lap.
References:  H.Paynter, Analysis and Design of engineering systems, MIT Press, 1961.  Jan F. Broenink, Introduction to Physical Systems Modelling with Bond Graph, Control Laboratory, University of Twente.  M.H.Toufigi, S.H.Sati, F.Najafi, Modeling and Analysis of a Mechantronic Actuator System by using Bond Graph Methodology, IEEE 2007.  Karnopp.D.C, Margolis.D and Rosenbergy.R, System dynamics: A unified approach, 2nd edition, New York, Wiley 1990.  Amalendu Mukherjee, Ranjit Karmakar, Arun Kumar Samantaray, Bond graph in modeling, simulation and fault Identification, I.K.International.  Javier A.Kypuros, System Dynamics and Control with Bond Graph Modeling, CRC Press.  Chua.L, Memistor- The Missing Circuit Element, 2nd edition, New York, Wiley, 1990.  Attila KOVARI, Influence of cylinder leakage on dynamic behavior of electrohydraulic servo system, IEEE, 2009.  H.E.Merrit, Hydraulic control systems, John Wiley and Sons, 1967.  Moog’s Documentation of Two Stage Servo Valve.
 Keiwan Kashi and Dirk Soffker. Model–based estimation of force and displacement of a hydraulic cylinder. 2002.  Berzen.W. Non linear modelling and control of hydraulic cylinders. IEEE Mediterranean Conference on Control and Systems, 1998.  T.H.Ho and K.K.Ahn. Design and control of a closed–loop hydraulic energy– regenerative system. 22:444– 458, 2012.  Richard Poley. Dsp control of electro–hydraulic servo actuators. Texas Instruments Application Report, 2005.  Muvengei.M , Kihiu.J. Bond graph modeling of interactuator interactions in multi cylinder hydraulic system. International Journal of Aerospace and Mechanical Engineering, 5(3):147–156, 2011.  J.Zaborszky , H.J.Harrington. A describing function for mulitiple nonlinearities present in electrohydraulic control valves. IEEE Transcations, pages 183–190, 1957.  P.K.C.Wang. Mathematical models for time domain design of electrohydraulic servomechanisms. IEEE Transcations, pages 252–260, 1961.  Nosikievic.P. Modelling and system identification. Montanex a.s, 1999.  B. Sulc , J.A.Jan. Non linear modelling and control of hydraulic actuators. Acta Polytechnica, 42(3):41–47, 2002.  Ilyas Istif , Ahmet Sagirifi , Kenan Kutlu. Bond graph modeling and position control of an electrohydraulic elevator, 6th Biennial Conference on Engineering Systems Design and Analysis, pages 1–6, 2002. Conference on Robotics and Mechatronics, pages 234– 239, 2016.
 Esmaeil Ghasemi , S.Ali Jazayeri , S.Ali A.Moosavian. Model improvement for a servovalve with force feedback and back pressure. IEEE Transactions, 2008.  Attila KOVARI. Influence of cylinder leakage on dynamic behavior of electrohydraulic servo system. IEEE Transactions, pages 375–379, 2009.  M.F.Rahmat , Zulfatman , A.R.Husain , K.Ishaque , Y.M.Sam , R.Ghazali , S.Md Rozali. Modeling and controller design of an industrial hydraulic actuator system in the presence of friction and internal leakage. International Journal of the Physical Sciences, 6(14):3502–3516, 2011.  Farid Arvani , Geoff Rideout , Nick Krouglicof , Steve Butt. Bond graph modeling of a hydraulic vibration system: Simulation and control. IMAACA, 2011.  Damic. V , Cohodar.M , Kulenovic.M. Modeling and simulation of hydraulic systems by bond graphs. International DAAM Symposium, 23(1):591–594 2012.  So-Nam Yun , Jung-Ho Park , Sung-Soo Lee , Choong-Mok Yoo. Hydraulic circuit analysis for the electro hydrostatic actuator system. International Conference on Control, Automation and Systems, pages 178–181, 2016.  Thoma J.U. Introduction to bond graphs and their applications. Pergamon Press, Oxford., 1975.  Liming Yu , Yudong Zhang , Hongfei Liu. Performance analysis and optimization design of dissimilar redundant hybrid electro hydraulic actuation system. International Conference on Aircraft Utility Systems, pages 98–104, 2016.  Karnopp D.C. , Rosenberg R.C. System dynamics, a unified approach. John Wiley & Sons, New York., 1975.
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Hydraulic Actuation System modeling for developmental Gas Turbine Engine

  • 1.
    Hydraulic Actuation System Modelingfor Developmental Gas Turbine Engine Presented by N . Premnath 31607104 M.tech Instrumentation 4th Semester. Internal Guide Dr. Neena Jaggi HOD, Professor Dept of Physics NIT Kurukushetra. External Guide Mr. V.G.Sanjawadmath Scientist ‘G’. Mr. Santhosh Muthe Scientist ‘D’ GTRE, DRDO, Bangalore FINAL VIVA VOCE 2016-2018 DEPARTMENT OF PHYSICS NATIONAL INSTITUTE OF TECHNOLOGY KURUKSHETRA
  • 2.
    Contents:  Introduction  LiteratureReview  Block Diagram of EHAS  Goals  Bond Graph Techniques  Comparison of bond graph elements with block diagram  Schematic Diagram of Two Stage Servo Valve  Modeling of Two Stage Servo Valve using Bond graph  Differential equations and State space form of Two Stage Servo Valve  Schematic Diagram of Hydraulic Actuator  Modeling Hydraulic Actuator using Bond graph  Differential equations and State space form of Hydraulic Actuator  Controller Design  Results and Discussion
  • 3.
    Literature Review: Effects ResultReferences Oil is returned from the valve to the tank through a low pressure return pipe. Simulation results show that dynamic behavior is mainly depends on the proper conditions of the seals. Richard Poley, 2005 Internal leakage and friction forces are present in the hydraulic cylinder Fuzzy logical control is to produce control signals that are not only proportionally dependent on control error. B.Sulc, J.A. Jan, 2002 Friction and internal leakage model were integrated into the electro-hydraulic actuator model. Sliding mode control technique, the nonlinearities and uncertainties i.e. friction and internal leakage has been fully compensated. M. F. Rahmat, Zulfatman, A.R.Husain, Y. m. Sam, July 2011.
  • 4.
    Literature Review: Effects ResultReferences Excess pump fluid is discharged to tank from relief valve and pressure drops due to throttling in proportional valve. This cause waste of energy. System uncertainties are considered and a robust H∞ control synthesis approach is used to control the position of the system. Ahsan Saeedzadeh, S. Mehdi Rezaei, Mohammad Zareinejad oct 2016. Leakage flow between the spool valve and body considerably dominates the orifice flow through the valve. It should be accounted in controller design. Erylmaz and Wilson, 2000.
  • 5.
    Introduction:  An Electro-HydraulicActuation Systems are widely used in different industrial application.  It is used wherever high magnitude forces are exerted.  It is a closed loop system which consists of Two Stage Servo Valve, double acting hydraulic cylinder and reservoir.  It is used to control the position of the aircraft, and etc,.
  • 6.
    Block Diagram ofEHAS: TWO STAGE SERVO VALVE HYDRAULIC ACTUATOR CONTROLLER Demand Input (mm) - + Supply Pressure (KPa) Input Current for valve is(mA) Flow rate (Qx) (m3 /s) Flow rate (Qy) (m3 /s) Acutator Position (mm) Negative Feedback
  • 7.
    Goals:  The Physicalstructure and operating principle of the Electro-Hydraulic Actuation system are analyzed first.  Modeled the Two Stage Servo Valve and Hydraulic Actuator using Bond Graph Technique in presence of Underlap servo and Critical lap servo.  Mathematical differential equations are derived from the Bond Graph of Two Stage Servo Valve and Hydraulic Actuator.  Generated the State Space representation from the Differential equations of the Two Stage Servo Valve and Hydraulic Actuator.  Analyzed the Electro-Hydraulic System model under condition of Underlap Servo and Critical lap Servo by simulating in MATLAB/Simulink environment.
  • 8.
    Bond Graph Technique: Bond Graph is the technique which is used to represent the any system in the single graphical model.  In Bond Graph technique, the flow of energy for the systems never change.  The basic components of Bond Graph technique consists of ‘effort’ represented as ‘e’, ‘flow’ indicated as ‘f’, Resistive elements as ‘R’, Capacitive elements as ‘C’, and Inertance elements as ‘I’.  Two types of sources are available in Bond Graph, they are ‘Source effort’ indicated as ‘Se’ and ‘Source flow’ represented as ‘Sf ‘.  There are types of junctions are available in Bond Graph, they are ‘0-Junction’ and ‘1-Junction’.  Special bond graph element introduced in the Bond Graph technique which is the hidden edge of the Tetron State Variables, known as ‘Memristor’.
  • 9.
     Resistive Element: 𝑒= 𝑅 𝑓 𝑓 = 1 𝑅 𝑒  Inertial Element: 𝑓 = 1 𝐼 𝑒 𝑑𝑡 𝑒 = 𝐼 𝑓 R e f R f e I f e I f e
  • 10.
     Capacitance Element: 𝑒= 1 𝐶 𝑓 𝑒 = 1 𝐶 𝑓 𝑑𝑡  Transformer Element: 𝑒2 = 𝑛 𝑒1, 𝑓1 = 𝑛 𝑓2  Gyrator Element: 𝑒1 = 𝑟 𝑓2, 𝑒2 = 𝑟 𝑓1 C f e C f e TF e1 f1 e2 f2 n e2 f2 GY f1 e1 r
  • 11.
     0 Junction: 𝑒3= 𝑒1 = 𝑒2 𝑓3 = 𝑓1 − 𝑓2  1 Junction: 𝑓1 = 𝑓2 = 𝑓3 𝑒3 = 𝑒1 − 𝑒2  Source effort:  Source flow: 0 e1 f1 e2 f2 e3f3 f2 e2 1 f1 e1 f3 e3 e f Seea: e f Sffa:
  • 12.
    Special Elements:  Thememristor, is proposed as a new bond graph element, on an equal footing with R, L and C, and having some unique modeling capabilities for nonlinear systems.  If the resistance value can be controlled by an external signal, the resistor is named as a Modulated Resistor, in mnemonic represented as MR.  There should be dynamic change in the resistive either charge or impulse controlled, when the momentum and displacement change. This has been represented as the ‘Memristor’.
  • 13.
    C I ∫dt ∫dt e f p q R Memristor Tetronof state with memristor Momentum Displacement p = ∫e dt q = ∫f dt Displacement vs Momentum
  • 14.
    Comparison of bondgraph elements with block diagram: I I C f e f e f e R e f R f e f2 e2 1 f1 e1 f3 e3 0 e1 f1 e2 f2 e3f3 C f e GY e1 f1 f2 e2 r e2 f2 GY f1 e1 r f2 e2 TF f1 e1 n TF e1 f1 e2 f2 n R ef 1/R ef 1/C ef C ef I ef 1/I ef 1/n e2e1 1/nf1 f2 n e2e1 nf1 f2 r e2f1 re1 f2 1/r e2f1 1/re1 f2 e1 e3 e2 f1 f3 f2 + - + - f1 f2 f3 e1 e2 e3 Bond Graph Block Diagram Bond Graph Block Diagram
  • 15.
    Schematic Diagram ofTwo Stage Servo Valve: Qx Qy PBPA Pln Prn θfl QnrQnl PiPi PiPi Pt Stage 1 Stage 2 xsp Torque Motor Flapper Nozzle Spool Qal QblQlfe Qlre Moog’s Two Stage Servo Valve
  • 16.
    Construction of TwoStage Servo Valve:  Two Stage Servo Valve consists of two stages, First stage is Torque motor, Flapper nozzle and the Second stage is Spool Valve.  First Stage, the sleeve is wounded with armature coil which is placed between the permanent magnet with an air gap.  In Second Stage, the spool valve movement is based on the input current for the servo valve.  The change of the angle of flapper, which control the movement of the spool valve and also the flow rate of servo valve.  Small input current is control the flow rate of servo valve which happens only Electro Hydraulic Servo Valve.
  • 17.
    Torque motor ofTwo Stage Servo Valve: N N SS is is xfl Permanent Magnet b a  The relationship for Tmotor , Torque of the Motor for Two Stage Servo Valve [Merritt], is given by 𝑇 𝑚𝑜𝑡𝑜𝑟 = 𝐾 𝑚 θ 𝑓𝑙 + 𝐾𝑖 𝑖𝑠 Where, Tmotor = Torque of the motor Km and Ki = Intensity control constant(Nm/A) and Rotational angle constant(Nm/rad) θ 𝑓𝑙 = Flapper angle (rad) is = input current (mA)
  • 18.
    Modeled Two StageServo Valve using Bond Graph: 1 1 0 TF 1/lrc 1/3Ksl TF: lfc Bfl Jfl Tmotor TF: Anfl1/Anfl:TF 00 1 Pi Rn 0 1 1 MR MR Pt 1Pi TF: Asp1/Asp:TF 1 0 1 0 1101 Pt Pi Pi Port A Port B MR MR MR MR PA PB msp Qb1 Qa1 Qlfe Qlre θfl xsp Rn CnCn PLn PRn Qnr Qnl xfl Fsl Bsp . . . Stage 1 Stage 2 1/Ktalt 2 θfl . θfl . θfl . θfl . θfl . e2 e3 e4 e5 e6 Fsl q10 Fslq9 Fsl xsp . xsp . xsp .xsp .xsp .xsp . xsp . xsp . xsp . e23 e22e21 e20 e19 e18 e17 e16 Qa1e24 e25 Qlfe e26 Qlre Qb1 e27 Qa1 PA PA Qlfe Qlfe Pt Pt Qlre Qlre PB PB Qb1 xfl .xfl . xfl . xfl . xfl .e1 e9 e8 e12 e13 PRn PRn PLn PLn Qnr Qnre10 q4 Qnl Qnle11 q6 PLn q8 PLn q5 PLn q7 PRn PRn PRn q3 q5 q5 Pt Pt q3 q3 q3 e14 e15
  • 19.
    Differential equation ofTwo Stage Servo Valve: 𝜃 𝑓𝑙 = 1 𝐽 𝑓𝑙 (−𝐵𝑓𝑙 𝜃 𝑓𝑙 + 𝑙𝑟𝑐 𝐹𝑠𝑙 + 𝐾 𝑚 − 𝑙2 𝑡𝑎 𝐾𝑡𝑎 𝑙 𝑓𝑐 𝑥𝑓𝑙 − 𝑙𝑓𝑐 𝐴 𝑛 + 𝐴𝑛𝑓𝑙 ∆𝑃 + 𝐾𝑖 𝑖 𝑠) 𝐹 𝑠𝑙 = −3𝑙𝑟𝑐𝐾𝑠𝑙 𝜃 𝑓𝑙 + 3𝐾𝑠𝑙 𝑥 𝑠𝑝 𝑥 𝑓𝑙 = 𝑙𝑓𝑐 𝜃 𝑓𝑙 𝑥 𝑠𝑝 = − 1 𝑚 𝑠𝑝 𝐹𝑠𝑙 − 𝐵 𝑠𝑝 𝑚 𝑠𝑝 𝑥 𝑠𝑝 + 𝐴 𝑠𝑝 𝑚 𝑠𝑝 ∆𝑃 − 2 𝐴𝑖 𝑚 𝑠𝑝 𝑃𝑖 ∆𝑃 = − 2 𝐴 𝑛𝑓 𝑙𝑓𝑐 𝐶 𝑛 𝜃 𝑓𝑙 − 2𝐴𝑠𝑝 𝐶 𝑛 𝑥 𝑠𝑝 − 1 𝐶 𝑛 𝑅𝑛 ∆𝑃
  • 20.
    State Space formof Two Stage Servo Valve: 𝜃 𝑓𝑙 𝐹 𝑠𝑙 𝑥 𝑓𝑙 𝑥 𝑠𝑝 ∆𝑃 = −𝐵𝑓𝑙 𝐽 𝑓𝑙 𝑙 𝑟𝑐 𝐽 𝑓𝑙 𝐾 𝑚 𝑙2 𝑡𝑎 𝐾𝑡𝑎 𝐽 𝑓𝑙 0 −𝑙𝑓𝑐 𝐴 𝑛 + 𝐴𝑛𝑓𝑙 𝐽 𝑓𝑙 −3𝑙𝑟𝑐𝐾𝑠𝑙 0 0 3𝐾𝑠𝑙 0 𝑙 𝑓𝑐 0 0 0 0 0 −1 𝑚 𝑠𝑝 0 −𝐵𝑠𝑝 𝑚 𝑠𝑝 𝐴 𝑠𝑝 𝑚 𝑠𝑝 −2 𝐴 𝑛𝑓 𝑙 𝑓𝑐 𝐶 𝑛 0 0 −2𝐴𝑠𝑝 𝐶 𝑛 −1 𝐶 𝑛 𝑅 𝑛 𝜃 𝑓𝑙 𝐹 𝑠𝑙 𝑥 𝑓𝑙 𝑥 𝑠𝑝 ∆𝑃 + 𝐾𝑖 𝐽 𝑓𝑙 0 0 0 0 0 0 0 0 −2𝐴𝑖 𝑚 𝑠𝑝 𝑖 𝑠 𝑃𝑖
  • 21.
     The flowrates which is given as input to the actuator, 𝑄 𝑥 = 𝑐𝑑 𝑑𝑟 𝑥𝑠𝑝 2 𝑝 (𝑃𝑖 − 𝑃𝐴) 𝑄 𝑦 = 𝑐𝑑 𝑑 𝑟 𝑥𝑠𝑝 2 𝑝 (𝑃𝐵 − 𝑃𝑡) Where, Qx and Qy = Flow rates(m3/s) 𝑝 = Density of the oil(Kg/m3) Pi = Supply Pressure(Pa) cd = Discharge coefficient xsp = Position of spool (m) PA and PB = Pressure of servovalve(Pa) Pt = Tank Pressure(Pa)
  • 22.
    Schematic Diagram ofHydraulic Actuator: Pi Pt ui Qx Qy Qle P1 P2Api xpi xsp Hydraulic pump Tank Two stage servo valve Hydraulic cylinder Ml Ksp Bda Load Qe1 Qe2
  • 23.
    Construction of HydraulicActuator:  In an Electro Hydraulic Actuation System, using the Hydraulic Actuator to control the position of aircraft.  Double Acting Cylinder used as the Hydraulic Actuator.  The double acting cylinder consists of piston which is controlled by the difference of the pressures across it.  The piston is used to control the constant load.  The flow from the servo valve is used to adjust the piston of the double acting cylinder in Hydraulic actuator.
  • 24.
    Modeled Hydraulic Actuatorusing Bond Graph: 0 TF 1 TF 0 1 1 1 1 1/Ksp Ml Bda mr Ff Rle1 Rle2 Cp1 Cp2 P1 P2 Rin Qx Qy Api 1/Api P1 P1 P1 P3 P2 P2 P2 P4 P1-P2 P1 P2 F1 F2 F3 F F4 F5 F6 xpi . xpi . xpi . xpi . xpi . xpi .xpi . xpi . Ff q7 q7 q2 q3 q1 q3 q6 q8 q8 q3 q4
  • 25.
    Differential Equations ofHydraulic Actuator: 𝑃1 = − 1 𝑅𝑖𝑛 + 1 𝑅𝑙𝑒1 1 𝐶 𝑝1 𝑃1 + 1 𝑅𝑖𝑛 𝐶𝑝1 𝑃2 − 𝐴 𝑝𝑖 𝐶 𝑝𝑖 𝑥 𝑝𝑖 𝑃2 = − 1 𝑅𝑖𝑛 𝐶 𝑝1 𝑃1 − 1 𝑅𝑖𝑛 + 1 𝑅𝑙𝑒2 1 𝐶𝑝2 𝑃2 + 𝐴 𝑝𝑖 𝐶 𝑝𝑖 𝑥 𝑝𝑖 𝑥 𝑝𝑖 = 𝐴 𝑝𝑖 𝑀𝑙 +𝑚𝑟 𝑃1 − 𝐴 𝑝𝑖 𝑀𝑙 +𝑚𝑟 𝑃2 + 𝐵 𝑑𝑎 𝑀𝑙 +𝑚𝑟 𝑥 𝑝𝑖 − 1 𝑀𝑙 +𝑚𝑟 𝐹 𝑓
  • 26.
    Where, 𝐶 𝑝1= 𝑉 𝑜 + 𝑥 𝑝𝑖 β 𝑜 and 𝐶 𝑝2 = 𝑉 𝑜 − 𝑥 𝑝𝑖 β 𝑜 Vo= Volume of the hydraulic fluid, the piston at the position of middle (m3) βo = Bulk modulus of the hydraulic fluid (Nm2) xpi = Displacement of the actuator (m) Differential Equations of Hydraulic Actuator:
  • 27.
    State Space formof Hydraulic Actuator: 𝑃1 𝑃2 𝑥 𝑝𝑖 = −( 1 𝑅𝑖𝑛 + 1 𝑅𝑙𝑒1 ) 1 𝐶 𝑝1 1 𝑅𝑖𝑛 𝐶 𝑝1 − 𝐴 𝑝𝑖 𝐶 𝑝1 1 𝑅𝑖𝑛 𝐶 𝑝2 −( 1 𝑅𝑖𝑛 + 1 𝑅𝑙𝑒2 ) 1 𝐶 𝑝2 − 𝐴 𝑝𝑖 𝐶 𝑝2 𝐴 𝑝𝑖 𝑀𝑙 + 𝑚𝑟 −𝐴 𝑝𝑖 𝑀𝑙 + 𝑚𝑟 𝐵 𝑑𝑎 𝑀𝑙 + 𝑚𝑟 𝑃1 𝑃2 𝑥 𝑝𝑖 + 1 𝐶 𝑝1 0 0 0 0 −1 𝐶 𝑝2 0 0 0 0 𝐾 𝑠𝑝 𝑀𝑙 +𝑚𝑟 −1 𝑀𝑙 +𝑚𝑟 𝑄 𝑥 𝑄 𝑦 𝑥 𝑝𝑖 𝐹 𝑓
  • 28.
    Controller Design:  Oneform of Controller widely used in industrial process control is PI controller.  The Transfer Function of controller is , Gc(S) = Kpr + Kint/S Where, Kpr = Proportional Gain Kint = Integral Gain  The Controller have been tuned for the Electro hydraulic actuation system, to bring the actuator to the desired position.  The Tuned parameter of controller is, Kpr = 0.1 mA/mm, Kint = 0.0001mA/mm.s
  • 29.
    Simulation Model ofthe Electro Hydraulic Actuation System: • The Sampling Time of an Electro Hydraulic Actuation System is 0.0001sec
  • 30.
    Step Response forClosed Loop System: Results:
  • 31.
    Input Current forServo Valve of Closed Loop System:
  • 32.
    Pressure Difference acrossthe Hydraulic Actuator under Closed Loop System:
  • 33.
    Flow rates ofServo Valve Under Condition of Underlapped and Critical lapped Systems:
  • 34.
  • 35.
  • 36.
    Discussion of Results: Open loop and Closed loop frequency responses for system with Critical lap and a system with Underlapped spool configuration are obtained.  Closed loop position response indicates, Under lapped system is having more Overshoot than the Critical lapped system and it’s rise time is lesser than that of the critically lapped system.  Closed loop current response indicates, the power required for under lapped system is more than that of the critically lapped system.  The open loop bandwidth, closed loop bandwidth, rise time and settling time, closed loop currents are tabulated.
  • 37.
    Comparison Under lappedand Critically lapped Systems: PARAMETER UNDER LAP CRITICAL LAP Rise Time (s) 0.1399 0.3241 Settling Time (s) 6.1146 6.0413 Open loop Bandwidth (Hz) 15.45 3.029 Closed loop Bandwidth (Hz) 2.562 1.092
  • 38.
    Conclusions:  Basic bondgraph elements are used in constructing the Electro Hydraulic Actuation System.  Two Stage Servo Valve and Hydraulic actuator are modeled separately and two different state space representation are obtained.  Under lapped configuration is obtained by introducing increased flow.  Performance simulations results indicate the results are in line with physical behavior.
  • 39.
    Future Scope:  ElectroHydraulic Servo Valve with overlapped spool configuration need to be modeled with some modifications to the basic bond graph elements.  Fidelity of the model can be enhanced considering all three configuration namely Critical lap, Under lap and Over lap.  Improves the Controller for the Configuration of Under lap.
  • 40.
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  • 43.