Auto-Calibration and Control Applied to Electro-Hydraulic Valves

1. Auto-Calibration and Control Applied to Electro-Hydraulic Valves A Ph.D. Thesis Proposal Presented to the Faculty of the George Woodruff School of Mechanical Engineering at the Georgia Institute of Technology By PATRICK OPDENBOSCH Committee Members: Nader Sadegh (Co-Chair, ME) Wayne Book (Co-Chair, ME) Chris Paredis (ME) Bonnie Heck (ECE) Roger Yang (HUSCO Intl.)

2. PRESENTATION OUTLINE • INTRODUCTION • PROBLEM STATEMENT • OBJECTIVES • REVIEW OF MOST RELEVANT WORK • PROPOSED RESEARCH • PRELIMINARY WORK • EXPECTED CONTRIBUTIONS • CONCLUSION

3. INTRODUCTION • CURRENT APPROACH • Electronic control • Use of solenoid Valves • Energy efficient operation • New electrohydraulic valves • Conventional hydraulic spool valves are being replaced by assemblies of 4 independent valves for metering control High Pressure Low Pressure Spool Valve Spool piece Spool motion Piston Piston motion

4. INTRODUCTION • CURRENT APPROACH • Electronic control • Use of solenoid Valves • Energy efficient operation • New electrohydraulic valves • Conventional hydraulic spool valves are being replaced by assemblies of 4 independent valves for metering control Valve motion Low Pressure High Pressure Piston motion

5. INTRODUCTION • ADVANTAGES • Independent control • More degrees of freedom • More efficient operation • Simple circuit • Ease in maintenance • Distributed system • No need to customize Valve motion Low Pressure High Pressure Piston motion

6. INTRODUCTION • METERING MODES • Standard Extend • Standard Retract • High Side Regeneration • Low Side Regeneration • DISADVANTAGES • Nonlinear system • Complex control Valve motion Low Pressure High Pressure Piston motion

7. INTRODUCTION Adjustment Screw Coil Cap • POPPET ADVANTAGES • Excellent sealing • Less faulting • High resistance to contamination • High flow to poppet displacement ratios • Low cost and low maintenance Modulating Spring Input Current Coil Armature Pilot Pin Control Chamber Armature Bias Spring U.S. Patents (6,328,275) & (6,745,992) Pressure Compensating Spring Main Poppet Forward (Side) Flow Reverse (Nose) Flow

8. INTRODUCTION Adjustment Screw Coil Cap • Electro-Hydraulic Poppet Valve (EHPV) • Poppet type valve • Pilot driven • Solenoid activated • Internal pressure compensation • Virtually ‘zero’ leakage • Bidirectional • Low hysteresis • Low gain initial metering • PWM current input Modulating Spring Input Current Coil Armature Pilot Pin Control Chamber Armature Bias Spring U.S. Patents (6,328,275) & (6,745,992) Pressure Compensating Spring Main Poppet Forward (Side) Flow Reverse (Nose) Flow

9. INTRODUCTION • VALVE CHARACTERIZATION Flow Conductance Kv or

10. INTRODUCTION • FORWARD MAPPING • REVERSE MAPPING Side to nose Forward Kv at different input currents [A] Nose to side Reverse Kv at different input currents [A]

11. MOTIVATION Need to control valve’s KV Currently done by inversion of the steady-state input/output characteristics Requires individual offline calibration CHALLENGES Online learning of steady state and transient characteristics Online estimation of individual Kv. ADVANTAGES No individual offline calibration Design need not be perfect and ‘sufficiently fast’ Maintenance scheduling can be implemented from monitoring and detecting the deviations from the normal pattern of behavior. INTRODUCTION

12. PRESENTATION OUTLINE • INTRODUCTION • PROBLEM STATEMENT • OBJECTIVES • REVIEW OF MOST RELEVANT WORK • PROPOSED RESEARCH • PRELIMINARY WORK • EXPECTED CONTRIBUTIONS • CONCLUSION

13. PROBLEM STATEMENT • PURPOSE • Develop a general theoretical framework for auto-calibration and control of general nonlinear systems. It is intended to explore the feasibility of the online learning of the system’s characteristics while improving its transient and steady state performance without requiring much a priori knowledge of such system. • APPLICATION • This framework is applied to a hydraulic system composed of electro-hydraulic valves in an effort to study the applicability of having a self-calibrated system.

14. PRESENTATION OUTLINE • INTRODUCTION • PROBLEM STATEMENT • OBJECTIVES • REVIEW OF MOST RELEVANT WORK • PROPOSED RESEARCH • PRELIMINARY WORK • EXPECTED CONTRIBUTIONS • CONCLUSION

15. THEORETICAL Development of a general formulation for control of nonlinear systems with parametric uncertainty and time-varying characteristics Development of a formulation for auto-calibration of nonlinear systems Study of learning dynamics online along with fault diagnosis Improve Kv control of EHPV’s EXPERIMENTAL Analysis and validation on the effectiveness of the proposed method Study of the accuracy of the auto-calibration and possible drift problems Development of computationally efficient algorithms Development of a nonlinear observer for state estimation for unmeasurable states OBJECTIVES

16. PRESENTATION OUTLINE • INTRODUCTION • PROBLEM STATEMENT • OBJECTIVES • REVIEW OF MOST RELEVANT WORK • PROPOSED RESEARCH • PRELIMINARY WORK • EXPECTED CONTRIBUTIONS • CONCLUSION

17. RELEVANT WORK REVIEW Sadegh (1995) • The plant is linearized about a desired trajectory • A Nodal Link Perceptron Network (NLPN) is employed in the feedforward loop and trained with feedback state error • The control scheme needs the plant Jacobian and controllability matrices – obtained offline • Approximations of the Jacobian and controllability matrices can be used without loosing closed loop stability.

18. RELEVANT WORK REVIEW Sadegh (1998) • Nodal Link Perceptron Network (NLPN) • Functional approximation is achieved by the scaling of basis functions • The class of basis functions are to be selected as well as their ‘weights’ are to be trained so that the functional approximation error is within prescribed bounds

19. RELEVANT WORK REVIEW • O'hara (1990), Book (1998) • Concept of “Inferred Flow Feedback” • Requires a priori knowledge of the flow characteristics of the valve via offline calibration Squematic Diagram for Programmable Valve

20. RELEVANT WORK REVIEW • Garimella and Yao (2002) • Velocity observer based on cylinder cap and rod side pressures • Adaptive robust techniques • Parametric uncertainty for bulk modulus, load mass, friction, and load force • Nonlinear model based • Discontinuous projection mapping • Adaptation is used when PE conditions are satisfied

21. RELEVANT WORK REVIEW • Liu and Yao (2005) • Modeling of valve’s flow mapping • Online approach without removal from overall system • Combination of model based approach, identification, and NN approximation • Comparison among automated modeling, offline calibration, and manufacturer’s calibration

22. PRESENTATION OUTLINE • INTRODUCTION • PROBLEM STATEMENT • OBJECTIVES • REVIEW OF MOST RELEVANT WORK • PROPOSED RESEARCH • PRELIMINARY WORK • EXPECTED CONTRIBUTIONS • CONCLUSION

23. PROPOSED RESEARCH • AUTO-CALIBRATION AND CONTROL • k = 0,1,2… (discrete-time index) • 0 ≤ ui ≤ iUMAX, i = {1,2,…,m} • Set of admissible states • Set of admissible inputs

24. PROPOSED RESEARCH • AUTO-CALIBRATION AND CONTROL • k = 0,1,2… (discrete-time index) • 0 ≤ ui ≤ iUMAX, i = {1,2,…,m} The control purpose is to learn the input sequence {uk}that forces the states of the system xk to follow a desired state trajectory dxk as k→∞ PROPOSED: Adaptive approach without requiring detailed knowledge about the system’s model

25. PROPOSED RESEARCH • SQUARE NONLINEAR SYSTEM • ASSUMPTIONS • The system is strongly controllable: • The system is strongly observable: • The functions F and H are continuously differentiable

26. PROPOSED RESEARCH • SQUARE NONLINEAR SYSTEM • CONTROL DESIGN • Tracking Error: • Error Dynamics:

27. PROPOSED RESEARCH • SQUARE NONLINEAR SYSTEM • CONTROL DESIGN • Error Dynamics: • Deadbeat Control Law:

28. PROPOSED RESEARCH • SQUARE NONLINEAR SYSTEM • CONTROL DESIGN • Deadbeat Control Law: • Proposed Control Law:

29. PROPOSED RESEARCH Nominal inverse mapping Inverse Mapping Correction uk xk NLPN PLANT dxk Adaptive Proportional Feedback Jacobian Controllability Estimation

30. PROPOSED RESEARCH • ESTIMATION APPROACHES • Modified Broyden

31. PROPOSED RESEARCH • ESTIMATION APPROACHES • Recursive Least Squares

32. PROPOSED RESEARCH • APPLICATION • Kv Observer For each valve:

33. PROPOSED RESEARCH • APPLICATION • Health Monitoring • Failures: sensor fault, wear of the mating parts, contamination, break of a component, or component stiction • Assess valve’s behavior with respect to the nominal behavior. • Establish the criteria to declare faulting on the valves by studying the deviations from the nominal pattern. Kv as a Function of Input Current: Deviations from Nominal Patterns

34. THEORETICAL TASKS Work on the convergence properties of the estimated matrices Perform analysis about the closed loop stability of the overall system. Work on a nonlinear observer for the valves’ flow conductances. EXPERIMENTAL TASKS Hydraulic testbed setup Sensor integration, calibration, and filtering design Data acquisition and analysis Validation of theory Compare the performance under learning to that of fixed input/output mapping PROPOSED RESEARCH

35. PRESENTATION OUTLINE • INTRODUCTION • PROBLEM STATEMENT • OBJECTIVES • REVIEW OF MOST RELEVANT WORK • PROPOSED RESEARCH • PRELIMINARY WORK • EXPECTED CONTRIBUTIONS • CONCLUSION

36. PRELIMINARY WORK Implemented Nominal Mapping • NONLINEAR 1ST ORDER DISCRETE TIME SYSTEM Comparison: implemented and true steady state mapping

37. PRELIMINARY WORK

38. PRELIMINARY WORK Closed-loop and open-loop performance

39. PRELIMINARY WORK Estimated Jacobian and Controllability

40. PRELIMINARY WORK • Single EHPV learning control being investigated at Georgia Tech • Controller employs Neural Network in the feedforward loop with adaptive proportional feedback • Satisfactory results for single EHPV used for pressure control

41. PRELIMINARY WORK

42. PRELIMINARY WORK • Initial test response, no NLPN learning Flow Conductance Estimated Jacobian and Controllability

43. PRELIMINARY WORK • EHPV response with NLPN learning Flow Conductance Estimated Jacobian and Controllability

44. PRESENTATION OUTLINE • INTRODUCTION • PROBLEM STATEMENT • OBJECTIVES • REVIEW OF MOST RELEVANT WORK • PROPOSED RESEARCH • PRELIMINARY WORK • EXPECTED CONTRIBUTIONS • CONCLUSION

45. EXPECTED CONTRIBUTIONS • An alternative methodology for control system design of nonlinear systems with time-varying characteristics and parametric uncertainty. • A method to estimate and learn the flow conductance of the valve online. • Guidelines to experimentally use this control methodology and health monitoring efficiently in the area of electro-hydraulic control.

46. PRESENTATION OUTLINE • INTRODUCTION • PROBLEM STATEMENT • OBJECTIVES • REVIEW OF MOST RELEVANT WORK • PROPOSED RESEARCH • PRELIMINARY WORK • EXPECTED CONTRIBUTIONS • CONCLUSION

47. CONCLUSIONS • The proposed control methodology combines adaptive proportional feedback control with online corrected feedforward compensation • The input/output mapping of the system can be easily extracted via a functional approximator on the feedforward compensation • Extensive knowledge about the dynamics of the system are not needed a priori for satisfactory performance • The proposed method is to be employed in a Wheatstone bridge arrangement of novel Electro-Hydraulic Poppet Valves seeking a self-calibrated system