April 07, 2003 Presented by: PATRICK OPDENBOSCH HUSCO Electro-Hydraulic Poppet Valve Project Review George W. Woodruff School of Mechanical Engineering

AGENDA 1.Components 2.Opening Sequence 3.Related Work 4.Mathematical Modeling 5.Control Schemes 6.Future Work 7.Conclusions

Outlet Input Main Poppet Main Spring Solenoid Core Pilot Inlet Control Chamber Pilot Spring 1. COMPONENTS Feed Line

2. OPENING SEQUENCE

Performance Limitations of a Class of Two-Stage Electro-hydraulic Flow Valves 1 Done by: Rong Zhang. Dr. Andrew Alleyne. Eko Prasetiawan. 3. RELATED WORK (1) Zhang, R.,Alleyne, A., and Prasetiawan, E., “Performance Limitations of a Class of Two-Stage Electro-hydraulic Flow Valves”, International Journal of Fluid Power, April Figure 3.1 Vickers EPV-16 Valvistor

. Valve Modeling: States: Output: Figure 3.2 Electro-proportional flow valve (3.1) (3.2) (3.3)

Jacobian Linearization and Model Reduction : (3.4) (3.5) (3.6) (3.7) Assumptions:

Figure 3.4 Flow valve identification test setup (3.8) Figure 3.3 Simplified Second Order Model

Figure 3.5 Time domain experimental validation Figure 3.6 Root-locus of a Valvistor-controlled system Main Results: Pilot flow introduces open-loop zeros that limit the closed-loop bandwidth. Pilot flow can be re-routed to tank trading performance by efficiency. Open-loop zeros can be moved leftwards by altering valve parameters.

4. MATHEMATICAL MODELING Flow Distribution: QaQa Q2Q2 QbQb Q1Q1 QpQp uvuv

xmxm PaPa PpPp DrDr Q2Q2 (4.2) xmxm PbPb Q1Q1 (4.1) QpQp PpPp PbPb xmxm xpxp (4.3) PaPa

 : Fluid density V: Chamber volume  : Equivalent length of pilot inside control volume  : Bulk modulus Q2Q2 QpQp xmxm xoxo a m,1 xpxp Compressibility: small (4.4) (4.5) (4.6) (4.7) (4.9) (4.10) (4.8)

Second Order Systems: Pilot Dynamics (from equilibrium state): (4.11)

Main Poppet Dynamics (from equilibrium state): (4.12) a m,1 : Poppet’s Large area a m,s : Poppet’s Small area

(4.14) (4.13) Letting: and EHPV State Space Representation about Equilibrium Point

Reduced Order EHPV State Space Representation about Equilibrium Point (4.16) (4.15) From (4.10): 0 Then, solving for X 3 and substituting in (4.14):

5. CONTROL SCHEMES Jacobian Linearization Input-output Linearization +BLBL CLCL ALAL Int uy + BLBL

Jacobian Linearization: (5.1) (5.2) (5.3) Assumption: Incompressible fluid:

Figure 5.1 Output flow for PWM input about nominal value.

Figure 5.2 Control diagram. K ALAL CLCL L ALAL CLCL BLBL F KiRQbQb Int Dist Integral Controller Plant Observer

Input-Output Linearization (Model Reduction): (5.4) (5.5) Assumption: Pilot dynamics are fast and can be considered as the Input to the system (i.e. x p =W)

(5.6) (5.7) Equation 5.7 gives a direct mapping between fictitious input V and output flow.

6. FUTURE WORK Complete control scheme for jacobian linearized system. Extend input-ouput linearization theory to full order system. Compare simulation results to experimental results. Perform system parameter identification (hardware) Determine control solutions to EHPV operational problems

7. CONCLUSIONS Review of valve components and opening sequence Determination of valve limitations: Pilot flow introduces open-loop zeros Re-route flow to tank (efficiency/performance) Alter valve parameters Evaluation of 5 th order EHPV mathematical model Control alternatives: Jacobian linearized system Input-Output linearization