Title: Learning Control Applied to EHPV
1Learning Control Applied to EHPV
PATRICK OPDENBOSCH Graduate Research
Assistant Manufacturing Research Center Room
259 Ph. (404) 894 3256 gte608g_at_mail.gatech.edu
Georgia Institute of Technology
George W. Woodruff School of Mechanical
Engineering
2AGENDA
- OBJECTIVES
- INTRODUCTION
- LEARNING TOOL NLPN
- CONTROL
- INVERSE MAPPING
- FEEDBACK CONTROL
- EXPERIMENTAL RESULTS
- FUTURE RESEARCH
- CONCLUSIONS
3OBJECTIVES
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 valves performance
- Explore algorithms and applications via theory,
simulation, and implementation on a
Hardware-in-the-Loop simulator.
5- EHPV HIGHER LEVEL CONTROL
- Compliance with INCOVA system performance
requirements. - Fault prognostics and diagnostics.
6INTRODUCTION
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
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 systems mapping - Tied to functional approximator Neural network
9Calculate 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)
10LOCAL (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
11LOCAL (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
12LOCAL (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
13LEARNING TOOL NLPN
14- 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
15NODAL 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.
16- 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
17(No Transcript)
18COMMON 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,
19COMMON APPLICATIONS
Actual Map
NLPN approximation
Approximation Error
- 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
20CONTROL
21INVERSE MAPPING
EXPERIMENTAL DATA
INTERPOLATED AND INVERTED DATA
22SIMULATED STEADY STATE EHPV Kv
Forward flow
At constant temperature
At constant opening
23SIMULATED INVERSE MAP ESTIMATION
Forward flow
24EXPERIMENTAL 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
25EXPERIMENTAL 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
26FORWARD Kv AND isol MAP LEARNING
Kv map
Kv map learning
isol map
isol map learning
27REVERSE Kv AND isol MAP LEARNING
Kv map
Kv map learning
isol map
isol map learning
28FEEDBACK CONTROL
29EHPV 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
30TRACKING 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.
31Proposed control law
where,
(NLPN learning)
Upon substitution into the error equation,
It can be shown that
for a functional approximation bound and
estimation bounds
32ESTIMATION 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
33ESTIMATION 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
34EXPERIMENTAL RESULTS
35EHPV HYDRAULIC TESTBED
Hydraulic circuit employed
Hydraulic robot employed
36EHPV 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
37EHPV HYDRAULIC TESTBED (Experimental Data)
- INITIAL RESPONSE
- Kv measured and desired
- Input voltage to amplifier
- INITIAL RESPONSE
- Temperature
- Port to port pressure differential
38EHPV HYDRAULIC TESTBED (Experimental Data)
- INITIAL RESPONSE
- Kv measured
- Kv desired
- Kv approximated from estimation
- INITIAL RESPONSE
- Estimated J
- Estimated Q
39EHPV HYDRAULIC TESTBED (Experimental Data)
- STEADY RESPONSE
- Kv measured and desired
- Input voltage to amplifier
- STEADY RESPONSE
- Temperature
- Port to port pressure differential
40EHPV HYDRAULIC TESTBED (Experimental Data)
- STEADY RESPONSE
- Kv measured
- Kv desired
- Kv approximated from estimation
- STEADY RESPONSE
- Estimated J
- Estimated Q
41FUTURE WORK
42- 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
43CONCLUSIONS
44RESEARCH 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