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Auto-calibration & Control Applied To Electro-Hydraulic Valves A Ph.D. Dissertation Defense Presented to the Academic Faculty By PATRICK OP DEN BOSCH Committee Members: Dr. Nader Sadegh (Co-Chair, ME) Dr. Wayne Book (Co-Chair, ME) Dr. Chris Paredis (ME) Dr. Bonnie Heck Ferri (ECE) Dr. Roger Yang (HUSCO Intl.) The George W. Woodruff School of Mechanical Engineering Georgia Institute of Technology Atlanta, GA October 30, 2007 PRESENTATION OUTLINE October 30, 2007 RESEARCH MOTIVATION PROBLEM STATEMENT INVERSE MAPPING LEARNING & STATE CONTROL SIMULATION RESULTS APPLICATION TO HYDRAULICS EXPERIMENTAL VALIDATION CONCLUSION 2 RESEARCH MOTIVATION Excavator 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 Spool Valve Spool piece Spool motion Kramer (1984), Roberts (1988), Garnjost (1989), Jansson and Palmberg (1990), Aardema (1999), Tabor (2005) October 30, 2007 Low Pressure Piston Piston motion 3 RESEARCH MOTIVATION CURRENT APPROACH Backhoes 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 Kramer (1984), Roberts (1988), Garnjost (1989), Jansson and Palmberg (1990), Aardema (1999), Tabor (2005) October 30, 2007 4 RESEARCH MOTIVATION ADVANTAGES Independent control More degrees of freedom More efficient operation Simple circuit Ease in maintenance Distributed system No need to customize NASA Ames Flight Simulator DISADVANTAGES Nonlinear system Complex control Kramer (1984), Roberts (1988), Garnjost (1989), Jansson and Palmberg (1990), Aardema (1999), Tabor (2005) October 30, 2007 5 RESEARCH MOTIVATION 8000 7000 INCOVA LOGIC (VELOCITY BASED CONTROL) Flow Conductance, Kv [LPH/sqrtMPa] HUSCO’S CONTROL TOPOLOGY 6000 5000 4000 3000 2000 1000 0 0 200 400 600 800 1000 Coil Current [mA] 1200 1400 1600 1800 Steady State Mapping (Design) INVERSE MAPPING (FIXED LOOK-UP TABLE) 1800 1600 1400 EHPV Opening 1200 Coil Current [mA] OPERATOR INPUT: Commanded Velocity 1000 800 600 COIL CURRENT SERVO (PWM + dither) 400 200 0 0 1000 2000 3000 4000 5000 Flow Conductance, Kv [LPH/sqrtMPa] 6000 7000 8000 Inverse Mapping (Control) Tabor and Pfaff (2004), Tabor (2004,2005) October 30, 2007 HUSCO OPEN LOOP CONTROL FOR EHPV’s 6 RESEARCH MOTIVATION Theoretical Research Questions How well can the system’s inverse input-state mapping be learned online while trying to achieve state tracking control? How can the tracking error dynamics and mapping errors be driven arbitrarily close to zero with an auto-calibration method? Experimental Research Questions How can the performance of solenoid driven poppet valves be improved? How well can these calibration mappings be learned online? How can the learned mappings be used for fault detection? October 30, 2007 8 PRESENTATION OUTLINE October 30, 2007 RESEARCH MOTIVATION PROBLEM STATEMENT INVERSE MAPPING LEARNING & STATE CONTROL SIMULATION RESULTS APPLICATION TO HYDRAULICS EXPERIMENTAL VALIDATION CONCLUSION 11 PROBLEM STATEMENT Consider a general discrete-time nonlinear dynamic plant October 30, 2007 12 PROBLEM STATEMENT Consider a general discrete-time nonlinear dynamic plant CONTROL PROBLEM: October 30, 2007 13 PROBLEM STATEMENT Proposition: Similar Results in: Levin and Narendra (1993,1996), Sadegh(1991,2001) October 30, 2007 18 PRESENTATION OUTLINE October 30, 2007 RESEARCH MOTIVATION PROBLEM STATEMENT INVERSE MAPPING LEARNING & STATE CONTROL SIMULATION RESULTS APPLICATION TO HYDRAULICS EXPERIMENTAL VALIDATION CONCLUSION 19 INVERSE MAPPING LEARNING & CTRL Inverse Model Control Internal Model Control Recurrent hybrid NN Direct and indirect learning approach Backpropagation training Requires feedback controller Pham and Yildirim (2000, 2002) October 30, 2007 23 INVERSE MAPPING LEARNING & CTRL The plant is linearized about a desired state 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 (1991,1993,1995) October 30, 2007 24 INVERSE MAPPING LEARNING & CTRL NLPN Based Input Matching Control (INMAC) Direct learning accomplished via: Feedforward control by: October 30, 2007 25 INVERSE MAPPING LEARNING & CTRL NLPN Based Input Matching Control (INMAC) Direct learning accomplished via: Functional Approximator: Perceptron with single hidden layer Compatible with lookup tables Nodal Link Perceptron Network (NLPN) Local basis function activation 10 7 9 6.5 8 6 7 5.5 6 f(x) f(x) 5 5 4.5 4 4 3 3.5 2 3 1 0 October 30, 2007 0 0.2 0.4 0.6 0.8 1 x 1.2 1.4 1.6 1.8 2 2.5 0 0.2 0.4 0.6 0.8 1 x 1.2 1.4 1.6 1.8 27 2 INVERSE MAPPING LEARNING & CTRL Composite Input Matching Control (COMPIM) October 30, 2007 29 INVERSE MAPPING LEARNING & CTRL Composite Input Matching Control (COMPIM) October 30, 2007 30 INVERSE MAPPING LEARNING & CTRL Deadbeat Control and Non-deadbeat Control Deadbeat Control Law: Non-deadbeat Control Law: Example: Linear Time Invariant Plant Deadbeat: Non-deadbeat: October 30, 2007 31 INVERSE MAPPING LEARNING & CTRL Composite Input Matching Control (COMPIM) Stability Analysis THEOREM 1: Steepest Descent (SD) Control Law: (and non-deadbeat) Adaptation: Conditions: Meets PE condition October 30, 2007 32 INVERSE MAPPING LEARNING & CTRL Composite Input Matching Control (COMPIM) Stability Analysis THEOREM 1: Steepest Descent (SD) Control Law: (and non-deadbeat) If: Then: October 30, 2007 33 INVERSE MAPPING LEARNING & CTRL Composite Input Matching Control (COMPIM) Stability Analysis THEOREM 2: Recursive Least Squares (RLS) Control Law: (and non-deadbeat) Adaptation: Conditions: Meets PE condition October 30, 2007 34 INVERSE MAPPING LEARNING & CTRL Composite Input Matching Control (COMPIM) Stability Analysis THEOREM 2: Recursive Least Squares (RLS) Control Law: (and non-deadbeat) If: Then: October 30, 2007 35 INVERSE MAPPING LEARNING & CTRL Composite Input Matching Control (COMPIM) General Case Plant: Example: October 30, 2007 36 INVERSE MAPPING LEARNING & CTRL Composite Input Matching Control (COMPIM) General Case Plant: Feedforward: Direct Learning: October 30, 2007 37 PRESENTATION OUTLINE October 30, 2007 RESEARCH MOTIVATION PROBLEM STATEMENT INVERSE MAPPING LEARNING & STATE CONTROL SIMULATION RESULTS APPLICATION TO HYDRAULICS EXPERIMENTAL VALIDATION CONCLUSION 38 SIMULATION RESULTS FIRST ORDER LINEAR PLANT Plant: Sampling Time: Parameters: October 30, 2007 39 SIMULATION RESULTS FIRST ORDER NONLINEAR PLANT Plant: Initial Mapping: October 30, 2007 41 SIMULATION RESULTS FIRST ORDER NONLINEAR PLANT RLS: SD: October 30, 2007 42 PRESENTATION OUTLINE October 30, 2007 RESEARCH MOTIVATION PROBLEM STATEMENT INVERSE MAPPING LEARNING & STATE CONTROL SIMULATION RESULTS APPLICATION TO HYDRAULICS EXPERIMENTAL VALIDATION CONCLUSION 46 APPLICATION TO HYDRAULICS Poppet type valve Pilot driven Solenoid activated Internal pressure compensation Virtually ‘zero’ leakage Bidirectional Low hysteresis Low gain initial metering PWM current input Adjustment Screw Coil Cap Modulating Spring Input Current Coil Armature Control Chamber Pressure Compensating Spring U.S. Patents (6,328,275) & (6,745,992) ELECTRO-HYDRAULIC POPPET VALVE (EHPV) Pilot Pin Armature Bias Spring Main Poppet Forward (Side) Flow October 30, 2007 Reverse (Nose) Flow 47 APPLICATION TO HYDRAULICS EHPV Forward Flow Conductance Coefficient Measurement 100 1.5044 1.3565 1.2074 1.0584 1.4308 1.2818 1.1326 0.98395 90 SIMPLIFIED EHPV MODEL 80 Kv [LPM/sqrt(MPa)] 70 60 50 40 30 20 10 0 0 0.2 0.4 0.6 0.8 1 Pressure Differential [MPa] 1.2 1.4 1.6 1.8 Forward Kv at different input currents [A] EHPV Reverse Flow Conductance Coefficient Measurement 120 1.507 1.3587 1.2091 1.0594 1.4333 1.2838 1.134 0.9845 100 Kv [LPM/sqrt(MPa)] 80 60 40 20 0 Forward Kv October 30, 2007 0 0.2 0.4 0.6 0.8 Pressure Differential [MPa] 1 1.2 1.4 Reverse Kv at different input currents [A] 50 APPLICATION TO HYDRAULICS EHPV Forward Flow Conductance Coefficient Measurement 100 1.5044 1.3565 1.2074 1.0584 1.4308 1.2818 1.1326 0.98395 90 SIMPLIFIED EHPV MODEL 80 Kv [LPM/sqrt(MPa)] 70 60 50 40 30 20 10 0 0 0.2 0.4 0.6 0.8 1 Pressure Differential [MPa] 1.2 1.4 1.6 1.8 Forward Kv at different input currents [A] EHPV Reverse Flow Conductance Coefficient Measurement 120 1.507 1.3587 1.2091 1.0594 1.4333 1.2838 1.134 0.9845 100 Kv [LPM/sqrt(MPa)] 80 60 40 20 0 Reverse Kv October 30, 2007 0 0.2 0.4 0.6 0.8 Pressure Differential [MPa] 1 1.2 1.4 Reverse Kv at different input currents [A] 51 PRESENTATION OUTLINE October 30, 2007 RESEARCH MOTIVATION PROBLEM STATEMENT INVERSE MAPPING LEARNING & STATE CONTROL SIMULATION RESULTS APPLICATION TO HYDRAULICS EXPERIMENTAL VALIDATION CONCLUSION 52 EXPERIENTAL VALIDATION HYDRAULIC TEST-BED CAN bus interface Balluff position/velocity transducer XPC-Target (SIMULINK) Pressure Control Flow Control October 30, 2007 53 EXPERIENTAL VALIDATION SUPPLY PRESSURE CONTROL Desired Flow Conductance Kv Pump Flow Characteristics October 30, 2007 55 EXPERIENTAL VALIDATION SUPPLY PRESSURE CONTROL: Generic Initial mapping Flow Conductance Kv October 30, 2007 Supply Pressure PS 56 EXPERIENTAL VALIDATION SUPPLY PRESSURE CONTROL: Calibrated Initial mapping Flow Conductance Kv October 30, 2007 Supply Pressure PS 57 EXPERIENTAL VALIDATION SUPPLY PRESSURE CONTROL: SD COMPIM with Generic Initial mapping Flow Conductance Kv October 30, 2007 Supply Pressure PS 58 EXPERIENTAL VALIDATION SUPPLY PRESSURE CONTROL: RLS COMPIM with Generic Initial map Flow Conductance Kv October 30, 2007 Supply Pressure PS 59 EXPERIENTAL VALIDATION SUPPLY PRESSURE CONTROL SD Flow Conductance Kv October 30, 2007 RLS Flow Conductance Kv 60 EXPERIENTAL VALIDATION FLOW CONTROL Control Topology INCOVA LOGIC (VELOCITY BASED CONTROL) OPERATOR INPUT: Commanded Velocity INVERSE MAPPING (ADAPTIVE (FIXED LOOK-UP LOOKUP TABLE) TABLE) EHPV Opening COIL CURRENT SERVO (PWM + dither) October 30, 2007 62 EXPERIENTAL VALIDATION FLOW CONTROL Piston Position/Velocity October 30, 2007 Flow Conductance Kv 63 EXPERIENTAL VALIDATION FLOW CONTROL Piston Position/Velocity October 30, 2007 Flow Conductance Kv 64 EXPERIENTAL VALIDATION FLOW CONTROL Piston Position/Velocity October 30, 2007 Flow Conductance Kv 66 EXPERIENTAL VALIDATION HEALTH MONITORING Control Topology October 30, 2007 Flow Conductance Bounds 67 EXPERIENTAL VALIDATION HEALTH MONITORING October 30, 2007 70 PRESENTATION OUTLINE October 30, 2007 RESEARCH MOTIVATION PROBLEM STATEMENT INVERSE MAPPING LEARNING & STATE CONTROL SIMULATION RESULTS APPLICATION TO HYDRAULICS EXPERIMENTAL VALIDATION CONCLUSION 71 CONCLUSIONS RESEARCH CONTRIBUTIONS Deadbeat/non-deadbeat control method based on input matching with composite adaptation Rigorous closed-loop stability analyses for the above controllers using steepest descent and recursive least squares methods A procedure to handle arbitrary state and input delays A model of the EHPV Intelligent control technology for the EHPV RESEARCH IMPACT An alternative discrete-time control design based on an auto-calibration scheme for nonlinear systems Improvement of hydraulic controls using solenoid driven valves based on calibration routines Intelligent control technology for the hydraulic industry Easily extended to other engineering applications October 30, 2007 72 CONCLUSIONS FUTURE RESEARCH Extend these results for output control Consider/develop other schemes that suffers less from the curse of dimensionality Relax the PE condition Apply this scheme to other hydraulic component with higher order dynamics Apply this control method to other metering modes along with multi-function cases and mode switching THANK YOU FOR YOUR ATTENTION October 30, 2007 73