Learning Control Applied to EHPV

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Learning Control Applied to EHPV
PATRICK OPDENBOSCH Graduate Research
Assistant Manufacturing Research Center  Room
259 Ph. [phone] gte608g_at_mail.gatech.edu
Georgia Institute of Technology
George W. Woodruff School of Mechanical
Engineering
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AGENDA

• OBJECTIVES
• INTRODUCTION
• LEARNING TOOL NLPN
• CONTROL
• INVERSE MAPPING
• FEEDBACK CONTROL
• EXPERIMENTAL RESULTS
• FUTURE RESEARCH
• CONCLUSIONS

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OBJECTIVES
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• 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 valves performance
• Explore algorithms and applications via theory,
  simulation, and implementation on a
  Hardware-in-the-Loop simulator.

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• EHPV HIGHER LEVEL CONTROL
• Compliance with INCOVA system performance
  requirements.
• Fault prognostics and diagnostics.

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INTRODUCTION
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• 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

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• 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 systems mapping
• Tied to functional approximator Neural network

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Calculate desired speed, n
HUSCOS HIERARCHICAL CONTROL
US PATENT 6,732,512 6,718,759
Read port pressures, Ps PR PA PB
Calculate equivalent KvEQ
Determine Individual Kv
KvB

• Hierarchical control System controller, pressure
  controller, function controller

KvA
Determine input current to EHPV isolf(Kv,DP,T)
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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
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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
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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
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LEARNING TOOL NLPN
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• INPUT-OUTPUT MAP PROPOSED SOLUTIONS
• Offline/online learning of the input-output map
  through suitable training criterion.
• Online correction of mapping to accurately
  reflect valve behavior while on continuous
  operation

NEED FUNCTIONAL APPROXIMATOR
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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
NLPN structure
The idea is to choose wi and fi so that
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, 385-404.
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• 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
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(No Transcript)
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COMMON BASIS FUNCTIONS
Triangular
Gaussian
Hyperbolic
A B
C
A B
C
A B
C
At most 2n components of F are nonzero.
For multidimensional input space
For example,
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COMMON APPLICATIONS

• Offline curve fitting

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
  3128-3133
• 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 2116-2123.
• Sadegh, N., (1993), A Perceptron Network for
  Functional Identification and Control of
  Nonlinear Systems, IEEE trans. N. Networks, Vol.
  4, No. 6, 982-988

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CONTROL
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INVERSE MAPPING
EXPERIMENTAL DATA
INTERPOLATED AND INVERTED DATA
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SIMULATED STEADY STATE EHPV Kv
Forward flow
At constant temperature
At constant opening
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SIMULATED INVERSE MAP ESTIMATION
Forward flow
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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
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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
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FORWARD Kv AND isol MAP LEARNING
Kv map
Kv map learning
isol map
isol map learning
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REVERSE Kv AND isol MAP LEARNING
Kv map
Kv map learning
isol map
isol map learning
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FEEDBACK CONTROL
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EHPV NONLINEAR MAP

• Nonlinearities arise from
• State constraints
• Nonlinear flow models
• Bidirectional mode
• Model switching
• Electromagnetic nonlinearities

Response is dominated by second order dynamics
PRELIMINAR STEP BLOCK-INPUT FORM
Let a system be described by
Then, it can be transformed to a system such that
Trivial example
For m2
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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.
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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
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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
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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
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EXPERIMENTAL RESULTS
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EHPV HYDRAULIC TESTBED
Hydraulic circuit employed
Hydraulic robot employed
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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
Close view of the EHPV mounted on stationary arm
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EHPV HYDRAULIC TESTBED (Experimental Data)

• INITIAL RESPONSE
• Kv measured and desired
• Input voltage to amplifier

• INITIAL RESPONSE
• Temperature
• Port to port pressure differential

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EHPV HYDRAULIC TESTBED (Experimental Data)

• INITIAL RESPONSE
• Kv measured
• Kv desired
• Kv approximated from estimation

• INITIAL RESPONSE
• Estimated J
• Estimated Q

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EHPV HYDRAULIC TESTBED (Experimental Data)

• STEADY RESPONSE
• Kv measured and desired
• Input voltage to amplifier

• STEADY RESPONSE
• Temperature
• Port to port pressure differential

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EHPV HYDRAULIC TESTBED (Experimental Data)

• STEADY RESPONSE
• Kv measured
• Kv desired
• Kv approximated from estimation

• STEADY RESPONSE
• Estimated J
• Estimated Q

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FUTURE WORK
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• 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

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CONCLUSIONS
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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

CONTROL APPROACH

• Development of NLPN controller
• Estimation methods
• Experimental tracking results