1. Learning Control Applied to EHPV®
PATRICK OPDENBOSCH
Graduate Research Assistant
Manufacturing Research Center 
Room 259
Ph. (404)
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Georgia Institute of Technology
George W. Woodruff School of Mechanical Engineering
May 18, 2005

2. AGENDA OBJECTIVES INTRODUCTION LEARNING TOOL: NLPN CONTROL
INVERSE MAPPING
FEEDBACK CONTROL
EXPERIMENTAL RESULTS
FUTURE RESEARCH
CONCLUSIONS
In your opening, establish the relevancy of the topic to the audience. Give a brief preview of the presentation and establish value for the listeners. Take into account your audience’s interest and expertise in the topic when choosing your vocabulary, examples, and illustrations. Focus on the importance of the topic to your audience, and you will have more attentive listeners.
May 18, 2005

3. OBJECTIVES
May 18, 2005

4. EHPV LOCAL LEVEL CONTROL
Develop a smarter and self-contained valve.
Investigate algorithms for off-line and on-line learning of the input-output map.
Develop robust trajectory learning controller
Improve the valve’s performance
Explore algorithms and applications via theory, simulation, and implementation on a Hardware-in-the-Loop simulator.
May 18, 2005

5. EHPV HIGHER LEVEL CONTROL
Compliance with INCOVA system performance requirements.
Fault prognostics and diagnostics.
May 18, 2005

6. INTRODUCTION
May 18, 2005

7. BACKGROUND
Hydraulic systems, in particular control valves, show nonlinear pressure-flow characteristics such as nonlinear gain, hysteresis, and saturation.
Common control approaches used include:
Linear methods: PID (modified), State Feedback (LQG)
Nonlinear tools: gain scheduling, sliding mode, backstepping
Advanced methods: Adaptive, robust control, Fuzzy, and Neural control
Some of the challenges: energy savings, tracking, multidisciplinary systems, improved bandwidth, modeling and parameter estimation
May 18, 2005

8. BACKGROUND Advanced approach: Learning control
Learning control is used to improve future performance.
Iterative and repetitive learning control action.
Can be used to obtain direct and inverse input-output system’s mapping
Tied to functional approximator: Neural network
May 18, 2005

9. HUSCO’S HIERARCHICAL CONTROL
Calculate desired speed, n
US PATENT # 6,732,512 & 6,718,759
Calculate desired flow,
Read port pressures, Ps PR PA PB
Calculate equivalent KvEQ
Determine Individual Kv
KvB
Hierarchical control: System controller, pressure controller, function controller
In your opening, establish the relevancy of the topic to the audience. Give a brief preview of the presentation and establish value for the listeners. Take into account your audience’s interest and expertise in the topic when choosing your vocabulary, examples, and illustrations. Focus on the importance of the topic to your audience, and you will have more attentive listeners.
KvA
Determine input current to EHPV isol=f(Kv,DP,T)
May 18, 2005

10. LOCAL (LOWER LEVEL) CONTROL
INPUT-OUTPUT MAP:
Currently obtained through offline calibration
Specifically tailored for each individual valve
Unable to reflect valve behavior after considerable continuous operation
Flow conductance coefficient Kv as a function of input current and pressure differential
In your opening, establish the relevancy of the topic to the audience. Give a brief preview of the presentation and establish value for the listeners. Take into account your audience’s interest and expertise in the topic when choosing your vocabulary, examples, and illustrations. Focus on the importance of the topic to your audience, and you will have more attentive listeners.
May 18, 2005

11. LOCAL (LOWER LEVEL) CONTROL
POSSIBLE SOLUTIONS:
Online learning of the input-output map through suitable training criterion.
Compatibility of adaptive look-up table with existing industrial trends
Improve mapping that more accurately reflects valve behavior after considerable continuous operation
Flow conductance coefficient Kv as a function of input current and pressure differential
In your opening, establish the relevancy of the topic to the audience. Give a brief preview of the presentation and establish value for the listeners. Take into account your audience’s interest and expertise in the topic when choosing your vocabulary, examples, and illustrations. Focus on the importance of the topic to your audience, and you will have more attentive listeners.
May 18, 2005

12. LOCAL (LOWER LEVEL) CONTROL
POSSIBLE SOLUTIONS:
Development of robust observer for the online estimation of the KV.
Flow conductance coefficient Kv as a function of input current and pressure differential
In your opening, establish the relevancy of the topic to the audience. Give a brief preview of the presentation and establish value for the listeners. Take into account your audience’s interest and expertise in the topic when choosing your vocabulary, examples, and illustrations. Focus on the importance of the topic to your audience, and you will have more attentive listeners.
May 18, 2005

13. LEARNING TOOL: NLPN
May 18, 2005

14. NODAL LINK PERCEPTRON NETWORK (NLPN)
MAIN FEATURE
Approximates nonlinear functions using a number of local adjustable functions.
The NLPN is a three-layer perceptron network whose input is related to the output by:
If you have several points, steps, or key ideas use multiple slides. Determine if your audience is to understand a new idea, learn a process, or receive greater depth to a familiar concept. Back up each point with adequate explanation. As appropriate, supplement your presentation with technical support data in hard copy or on disc, , or the Internet. Develop each point adequately to communicate with your audience.
NLPN structure
The idea is to choose wi and fi so that
May 18, 2005
More details found at: Sadegh, N. (1998) “A multilayer nodal link perceptron network with least squares training algorithm,” Int. J. Control, Vol.70, No. 3,

15. TRAINING
Once a basis function structure is chosen, train the network to learn the “weights”.
LEAST SQUARES
DELTA RULE
HOW IT WORKS (1D EX) f1 f2 f3
May 18, 2005

16. COMMON BASIS FUNCTIONS
Gaussian
Triangular
Hyperbolic
A B C
A B C
A B C
At most 2n components of F are nonzero.
For multidimensional input space:
For example,
May 18, 2005

17. COMMON APPLICATIONS Offline curve fitting Filtering
Actual Map
NLPN approximation
Approximation Error
Filtering
System identification & control
Selmic, R. R., Lewis, F. L., (2000) “Identification of Nonlinear Systems Using RBF Neural Networks: Application to Multimodel Failure Detection,” Proceedings of the IEEE Conference on Decision and Control, v 4, 2001, p
Sanner, R. M., J. E. Slotine, (1991) “Stable Adaptive Control and Recursive Identification Using Radial Gaussian Networks,” Proceedings of the IEEE Conference on Decision and Control, v 3, 1991, p
Sadegh, N., (1993), “A Perceptron Network for Functional Identification and Control of Nonlinear Systems,” IEEE trans. N. Networks, Vol. 4, No. 6,
May 18, 2005

18. CONTROL
May 18, 2005

19. INTERPOLATED AND INVERTED DATA
INVERSE MAPPING DP
isol Kv T
EXPERIMENTAL DATA Kv DP
isol T
If you have several points, steps, or key ideas use multiple slides. Determine if your audience is to understand a new idea, learn a process, or receive greater depth to a familiar concept. Back up each point with adequate explanation. As appropriate, supplement your presentation with technical support data in hard copy or on disc, , or the Internet. Develop each point adequately to communicate with your audience.
INTERPOLATED AND INVERTED DATA
May 18, 2005

20. EXPERIMENTAL ESTIMATION
Steady state data was obtained from the Hydraulic circuit employed at the Hardware-In-the-Loop (HIL) Simulator
Hardware-In-the Loop (HIL) Simulator
Hydraulic circuit employed at the HIL
EHPV mounted on the HIL. Quick connections for forward and reverse flow
May 18, 2005

21. EXPERIMENTAL MEASUREMENT OF STEADY STATE FLOW CONDUCTANCE COEFFICIENT Kv.
Forward Kv as a function of Pressure differential and input current
Reverse Kv as a function of Pressure differential and input current
Forward:
Side to nose
Reverse:
Nose to side
May 18, 2005

22. FORWARD Kv AND isol MAP LEARNING
Kv map
Kv map learning
isol map
isol map learning
May 18, 2005

23. REVERSE Kv AND isol MAP LEARNING
Kv map
Kv map learning
isol map
isol map learning
May 18, 2005

24. FEEDBACK CONTROL
If you have several points, steps, or key ideas use multiple slides. Determine if your audience is to understand a new idea, learn a process, or receive greater depth to a familiar concept. Back up each point with adequate explanation. As appropriate, supplement your presentation with technical support data in hard copy or on disc, , or the Internet. Develop each point adequately to communicate with your audience.
May 18, 2005

25. TRACKING CONTROL Let the behavior of the EHPV be expressed by:
Then linearizing about,
yields,
Assumptions:
1. The system is strongly controllable: there is a unique input so that
2. The controllability matrix Q has full rank for all inputs and states.
May 18, 2005

26. Upon substitution into the error equation,
Proposed control law:
where,
(NLPN learning)
Upon substitution into the error equation,
It can be shown that:
for a functional approximation bound and estimation bounds:
May 18, 2005

27. GRADIENT BASED METHOD: MODIFIED BROYDEN
ESTIMATION TASK
Control law requires knowledge of Jacobian Jk and controllability Qk:
Estimation Schemes:
Gradient based methods
Least squares methods
GRADIENT BASED METHOD: MODIFIED BROYDEN
Error dynamics:
Approximated Error dynamics:
General form:
Update law:
May 18, 2005

28. LEAST SQUARES METHOD: RECURSIVE LS (Cov. Reset/Forgetting Factor)
ESTIMATION TASK
Control law requires knowledge of Jacobian Jk and controllability Qk:
Estimation Schemes:
Gradient based methods
Least squares methods
LEAST SQUARES METHOD: RECURSIVE LS
(Cov. Reset/Forgetting Factor)
Error dynamics:
Approximated Error dynamics:
General form:
Update law:
May 18, 2005

29. EXPERIMENTAL RESULTS
May 18, 2005

30. EHPV HYDRAULIC TESTBED
Hydraulic circuit employed
Hydraulic robot employed
May 18, 2005

31. Close view of the EHPV mounted on stationary arm
EHPV HYDRAULIC TESTBED
ELECTRONICS:
Signal Amplifier
Power Supply
Breakout box
CONTROLLER:
Host and Target PC
SIMULINK xpctarget
AMPLIFIER
BREAKOUT BOX
EHPV
FLOWMETER
PC - HOST
PC - TARGET
May 18, 2005
Close view of the EHPV mounted on stationary arm

32. EHPV HYDRAULIC TESTBED (Experimental Data)
INITIAL RESPONSE:
Kv measured and desired
Input voltage to amplifier
INITIAL RESPONSE:
Temperature
Port to port pressure differential
May 18, 2005

33. EHPV HYDRAULIC TESTBED (Experimental Data)
INITIAL RESPONSE:
Kv measured
Kv desired
Kv approximated from estimation
INITIAL RESPONSE:
Estimated J
Estimated Q
May 18, 2005

34. EHPV HYDRAULIC TESTBED (Experimental Data)
STEADY RESPONSE:
Kv measured and desired
Input voltage to amplifier
STEADY RESPONSE:
Temperature
Port to port pressure differential
May 18, 2005

35. EHPV HYDRAULIC TESTBED (Experimental Data)
STEADY RESPONSE:
Kv measured
Kv desired
Kv approximated from estimation
STEADY RESPONSE:
Estimated J
Estimated Q
May 18, 2005

36. FUTURE WORK
If you have several points, steps, or key ideas use multiple slides. Determine if your audience is to understand a new idea, learn a process, or receive greater depth to a familiar concept. Back up each point with adequate explanation. As appropriate, supplement your presentation with technical support data in hard copy or on disc, , or the Internet. Develop each point adequately to communicate with your audience.
May 18, 2005

37. TASKS TO BE ACCOMPLISHED:
Investigation of other possible algorithms to extend parameter estimation
Investigate robustness
Development of Kv observer
Explore control performance for the different metering modes
If you have several points, steps, or key ideas use multiple slides. Determine if your audience is to understand a new idea, learn a process, or receive greater depth to a familiar concept. Back up each point with adequate explanation. As appropriate, supplement your presentation with technical support data in hard copy or on disc, , or the Internet. Develop each point adequately to communicate with your audience.
May 18, 2005

38. CONCLUSIONS
If you have several points, steps, or key ideas use multiple slides. Determine if your audience is to understand a new idea, learn a process, or receive greater depth to a familiar concept. Back up each point with adequate explanation. As appropriate, supplement your presentation with technical support data in hard copy or on disc, , or the Internet. Develop each point adequately to communicate with your audience.
May 18, 2005

39. Development of nonlinear mapping tool.
RESEARCH OBJECTIVE
Investigation and development of an advanced control methodology to control systems employing EHPV
NLPN
Development of nonlinear mapping tool.
Design with flexibility in basis functions
Approximation of f: Rn Rm
CURRENT TO Kv MAPPING
Experimental application for forward and reverse flow conditions on both direct and inverse mappings
If you have several points, steps, or key ideas use multiple slides. Determine if your audience is to understand a new idea, learn a process, or receive greater depth to a familiar concept. Back up each point with adequate explanation. As appropriate, supplement your presentation with technical support data in hard copy or on disc, , or the Internet. Develop each point adequately to communicate with your audience.
CONTROL APPROACH
Development of NLPN controller
Estimation methods
Experimental tracking results
May 18, 2005