November 29, 2005 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.)

November 29, PRESENTATION OUTLINE  INTRODUCTION  PROBLEM STATEMENT  OBJECTIVES  REVIEW OF MOST RELEVANT WORK  PROPOSED RESEARCH  PRELIMINARY WORK  EXPECTED CONTRIBUTIONS  CONCLUSION

November 29, 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 Spool Valve Spool piece Piston Low Pressure High Pressure Piston motion Spool motion

November 29, 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 Piston motion Low Pressure High Pressure Valve motion

November 29, INTRODUCTION  ADVANTAGES  Independent control  More degrees of freedom  More efficient operation  Simple circuit  Ease in maintenance  Distributed system  No need to customize Piston motion High Pressure Valve motion Low Pressure

November 29, INTRODUCTION  METERING MODES  Standard Extend  Standard Retract  High Side Regeneration  Low Side Regeneration  DISADVANTAGES  Nonlinear system  Complex control Piston motion High Pressure Valve motion Low Pressure

November 29, INTRODUCTION  POPPET ADVANTAGES  Excellent sealing  Less faulting  High resistance to contamination  High flow to poppet displacement ratios  Low cost and low maintenance Pilot Pin Main Poppet Reverse (Nose) Flow Forward (Side) Flow Control Chamber Modulating Spring Coil Armature Bias Spring Pressure Compensating Spring Coil CapAdjustment Screw Input Current U.S. Patents (6,328,275) & (6,745,992)

November 29, INTRODUCTION  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 Pilot Pin Main Poppet Reverse (Nose) Flow Forward (Side) Flow Control Chamber Modulating Spring Coil Armature Bias Spring Pressure Compensating Spring Coil CapAdjustment Screw Input Current U.S. Patents (6,328,275) & (6,745,992)

November 29, INTRODUCTION  VALVE CHARACTERIZATION Flow Conductance K v or

November 29, INTRODUCTION  FORWARD MAPPING  REVERSE MAPPING Forward K v at different input currents [A] Reverse K v at different input currents [A] Side to nose Nose to side

November 29, INTRODUCTION  MOTIVATION  Need to control valve’s K V  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 K v.  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.

November 29, PRESENTATION OUTLINE  INTRODUCTION  PROBLEM STATEMENT  OBJECTIVES  REVIEW OF MOST RELEVANT WORK  PROPOSED RESEARCH  PRELIMINARY WORK  EXPECTED CONTRIBUTIONS  CONCLUSION

November 29, 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.

November 29, PROBLEM STATEMENT  RESEARCH QUESTIONS  How well can the system’s mappings be learned online while at the same time trying to achieve good state tracking performance?  How can the tracking error dynamics be maintained stable while applying learning and estimation on the system?  How is the learning affected by input saturation and time- varying dynamics?  In particular for the EHPV’s, how well can the forward and reverse flow mappings be learned?  How can the learned mappings be used for fault detection?

November 29, PRESENTATION OUTLINE  INTRODUCTION  PROBLEM STATEMENT  OBJECTIVES  REVIEW OF MOST RELEVANT WORK  PROPOSED RESEARCH  PRELIMINARY WORK  EXPECTED CONTRIBUTIONS  CONCLUSION

November 29, OBJECTIVES  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 K v 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

November 29, PRESENTATION OUTLINE  INTRODUCTION  PROBLEM STATEMENT  OBJECTIVES  REVIEW OF MOST RELEVANT WORK  PROPOSED RESEARCH  PRELIMINARY WORK  EXPECTED CONTRIBUTIONS  CONCLUSION

November 29, RELEVANT WORK REVIEW  CONTROL  Sadegh, N., (1995), A nodal link perceptron network with applications to control of a nonholonomic system, IEEE Transactions on Neural Network, Vol. 6, No. 6, pp  Sadegh, N., (1998), A multilayer nodal link perceptron network with least squares training algorithm, International Journal of Control, Vol. 70, No. 3, pp

November 29, RELEVANT WORK REVIEW  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. Sadegh (1995)

November 29, RELEVANT WORK REVIEW  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 Sadegh (1998)

November 29, RELEVANT WORK REVIEW  FLOW OBSERVER  O'hara, D.E., (1990), Smart valve, in Proc: Winter Annual Meeting of the American Society of Mechanical Engineers pp  Book, R., (1998), "Programmable electrohydraulic valve", Ph.D. dissertation, Agricultural Engineering, University of Illinois at Urbana-Champaign  Garimella, P. and Yao, B., (2002), Nonlinear adaptive robust observer for velocity estimation of hydraulic cylinders using pressure measurement only, in Proc: ASME International Mechanical Engineering Congress and Exposition pp

November 29, 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

November 29, 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

November 29, 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

November 29, RELEVANT WORK REVIEW  HEALTH MONITORING  Polycarpou and Vemuri (1995)  Selmic and Lewis (2000)  Linear modeling techniques  NN for nonlinear identification Multimodel Failure Detection Failure Detection and Accommodation: Monitoring off- nominal behavior

November 29, RELEVANT WORK REVIEW  HEALTH MONITORING  Polycarpou, M.M. and Vemuri, A.T., (1995), Learning methodology for failure detection and accommodation, IEEE Control Systems, Vol. No. pp  Selmic, R.R. and Lewis, F.L., (2000), Identification of nonlinear systems using rbf neural networks: Application to multimodel failure detection, in Proc: XVI International Conference on "Material flow, machines, and devices in industry"

November 29, PRESENTATION OUTLINE  INTRODUCTION  PROBLEM STATEMENT  OBJECTIVES  REVIEW OF MOST RELEVANT WORK  PROPOSED RESEARCH  PRELIMINARY WORK  EXPECTED CONTRIBUTIONS  CONCLUSION

November 29, PROPOSED RESEARCH  AUTO-CALIBRATION AND CONTROL  k = 0,1,2… (discrete-time index)  0 ≤ u i ≤ i U MAX, i = {1,2,…,m}  Set of admissible states  Set of admissible inputs

November 29, PROPOSED RESEARCH  AUTO-CALIBRATION AND CONTROL  k = 0,1,2… (discrete-time index)  0 ≤ u i ≤ i U MAX, i = {1,2,…,m} The control purpose is to learn the input sequence {u k } that forces the states of the system x k to follow a desired state trajectory d x k as k→∞ PROPOSED: Adaptive approach without requiring detailed knowledge about the system’s model

November 29, PROPOSED RESEARCH  SQUARE NONLINEAR SYSTEM  ASSUMPTIONS  The system is strongly controllable:  The system is strongly observable:  The functions F and H are continuously differentiable

November 29, PROPOSED RESEARCH  SQUARE NONLINEAR SYSTEM  DEFINITIONS  Jacobian Matrix:  Controllability Matrix:  Observability Matrix:

November 29, PROPOSED RESEARCH  SQUARE NONLINEAR SYSTEM  CONTROL DESIGN  Tracking Error:  Error Dynamics:

November 29, PROPOSED RESEARCH  SQUARE NONLINEAR SYSTEM  CONTROL DESIGN  Error Dynamics:  Deadbeat Control Law:

November 29, PROPOSED RESEARCH  SQUARE NONLINEAR SYSTEM  CONTROL DESIGN  Deadbeat Control Law:  Proposed Control Law:

November 29, PROPOSED RESEARCH  Proposed Control Law Estimation of Jacobian and controllability Feedback correction Nominal inverse mapping inverse mapping correction

November 29, PROPOSED RESEARCH Nominal inverse mapping Inverse Mapping Correction Adaptive Proportional Feedback NLPN PLANT Jacobian Controllability Estimation xkxk dxkdxk ukuk

November 29, PROPOSED RESEARCH  ESTIMATION APPROACHES  Modified Broyden

November 29, PROPOSED RESEARCH  ESTIMATION APPROACHES  Recursive Least Squares

November 29, PROPOSED RESEARCH  APPLICATION  K v Observer For each valve:

November 29, 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. K v as a Function of Input Current: Deviations from Nominal Patterns

November 29, PROPOSED RESEARCH  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

November 29, PRESENTATION OUTLINE  INTRODUCTION  PROBLEM STATEMENT  OBJECTIVES  REVIEW OF MOST RELEVANT WORK  PROPOSED RESEARCH  PRELIMINARY WORK  EXPECTED CONTRIBUTIONS  CONCLUSION

November 29, PRELIMINARY WORK  NONLINEAR 1 ST ORDER DISCRETE TIME SYSTEM Comparison: implemented and true steady state mapping Implemented Nominal Mapping

November 29, PRELIMINARY WORK

November 29, PRELIMINARY WORK Closed-loop and open-loop performance

November 29, PRELIMINARY WORK Estimated Jacobian and Controllability

November 29, PRELIMINARY WORK  MORE INFORMATION AT:  Opdenbosch, P. and Sadegh, N., (2005), Control of discrete-time systems via online learning and estimation, in Proc: IEEE/ASME International Conference on Advanced Intelligent Mechatronics pp

November 29, 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

November 29, PRELIMINARY WORK

November 29, PRELIMINARY WORK Estimated Jacobian and Controllability Flow Conductance  Initial test response, no NLPN learning

November 29, PRELIMINARY WORK Estimated Jacobian and Controllability Flow Conductance  EHPV response with NLPN learning

November 29, PRELIMINARY WORK  MORE INFORMATION AT  Opdenbosch, P. and Sadegh, N., (2005), Control of electro- hydraulic poppet valves via online learning and estimation, in Proc: ASME International Mechanical Engineering Congress and Exposition, IMECE (Accepted)

November 29, PRESENTATION OUTLINE  INTRODUCTION  PROBLEM STATEMENT  OBJECTIVES  REVIEW OF MOST RELEVANT WORK  PROPOSED RESEARCH  PRELIMINARY WORK  EXPECTED CONTRIBUTIONS  CONCLUSION

November 29, 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.

November 29, PRESENTATION OUTLINE  INTRODUCTION  PROBLEM STATEMENT  OBJECTIVES  REVIEW OF MOST RELEVANT WORK  PROPOSED RESEARCH  PRELIMINARY WORK  EXPECTED CONTRIBUTIONS  CONCLUSION

November 29, 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