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Journal of Dynamic Systems, Measurement, and Control | Volume 127 | Issue 4 | TECHNICAL PAPERS
TECHNICAL PAPERS

Power Scaling Bond Graph Approach to the Passification of Mechatronic Systems— with Application to Electrohydraulic Valves

[+] Author and Article Information
P. Y. Li

Department of Mechanical Engineering,  University of Minnesota, Minneapolis, MN 55455pli@me.umn.edu

R. F. Ngwompo

Department of Mechanical Engineering,  University of Bath, Bath, BA2 7AY, United Kingdomr.f.ngwompo@bath.ac.uk

Strictly speaking the term “dissipative” should be used instead unless s(u,y) is the pairing between a vector space and its dual. The supply rates we consider in this paper are indeed of this form.

J. Dyn. Sys., Meas., Control 127(4), 633-641 (Mar 28, 2005) (9 pages) doi:10.1115/1.2101848 History: Received June 28, 2003; Revised March 28, 2005
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In many applications that require physical interaction with humans or other physical environments, passivity is a useful property to have in order to improve safety and ease of use. Many mechatronic applications (e.g., teleoperators, robots that interact with humans) fall into this category. In this paper, we develop an approach to design passifying control laws for mechatronic components from a bond graph perspective. Two new bond graph elements with power scaling properties are first introduced and the passivity properties of bond graphs containing these elements are investigated. These elements are used to better model mechatronic systems that have embedded energy sources. A procedure for passifying mechatronic systems is then developed using the four-way directional electrohydraulic flow control valve as an example. The passified valve is a two-port system that is passive with respect to the scaled power input at the command and hydraulic ports. This is achieved by representing the control valve in a suitable augmented bond graph, and then by replacing the signal bonds with power scaling elements. The procedure generalizes a previous passifying control law resulting in improved performance. Similar procedure can be applied to other mechatronic systems.
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Copyright © 2005 by American Society of Mechanical Engineers
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References

1
Colgate, J. E., 1994, “Coupled Stability of Multiport Systems-Theory and Experiments,” ASME J. Dyn. Syst., Meas., Control, 116 (3), pp. 419–428.
2
Li, P. Y., and Horowitz, R., 1997, “Control of Smart Exercise Machines: Part 1. Problem Formulation and Non-Adaptive Control,” IEEE/ASME Trans. Mechatron.  [CrossRef], 2 (4), pp. 237–247.
3
Lee, D. J., and Li, P. Y., 2003, “Passive Feedforward Approach for Linear Dynamically Similar Bilateral Teleoperated Manipulators,” IEEE Trans. Rob. Autom., 19 (13), pp. 443–456.
4
Li, P. Y., 2000, “Towards Safe and Human Friendly Hydraulics: The Passive Valve,” ASME J. Dyn. Syst., Meas., Control  [CrossRef], 122 (3), pp. 402–409.
5
Li, P. Y., and Krishnaswamy, K., 2001, “Passive Bilateral Teleoperation of a Hydraulic Actuator Using an Electrohydraulic Passive Valve,” in "Proceedings of 2001 American Control Conference", pp. 3932–3937.
6
Li, P. Y., and Krishnaswamy, K., 2004, “Passive Bilateral Teleoperation of a Hydraulic Actuator Using an Electrohydraulic Passive Valve,” Int. J. Fluid Power, 13, pp. 43–56.
7
Seron, M. M., Hill, D. J., and Fradkov, A. L., 1994, “Adaptive Passification of Nonlinear Systems,” in "Proceedings of the 33rd Conference on Decision and Control", pp. 190–195.
8
Byrnes, C. I., Isidori, A., and Willems, J. C., 1991, “Passivity, Feedback Equivalence, and the Global Stabilization of Minimum Phase Nonlinear Systems,” IEEE Trans. Autom. Control  [CrossRef], 36 (11), 1228–1240.
9
Kelkar, A. G., and Joshi, S. M., 1997, “Robust Control of Non-Passive Systems via Passification,” in "Proceedings of 1997 American Control Conference", pp. 2657–2661.
10
Song, Y. I., Shim, H., and Seo, J. H., 1999, “Passification of Nonlinear Systems via Dynamic Feedback,” in "Proceedings of 36th Conference on Decision and Control", Vol. 5 , pp. 4877–4878.
11
Karnopp, D. C., Margolis, D. L., and Rosenberg, R. C., 2000, "System Dynamics—Modeling and Simulation of Mechatronic Systems", John Wiley and Sons Inc. New York.
12
Ngwompo, R. F., Scavada, S., and Thomasset, D., 1996, “Inversion of Linear Time Invariant Siso Systems Modelled by Bond Graph,” J. Franklin Inst., 333(B) (2), pp. 157–174.
13
Ngwompo, R. F., and Gawthrop, P. J., 1999, “Bond Graph-Based Simulation of Nonlinear Inverse Systems Using Physical Performance Specifications,” J. Franklin Inst., 336 , pp. 1225–1247.
14
Huang, S. Y., and Youcef-Toumi, K., 1999, “Zero Dynamics of Physical Systems From Bond Graph Models-Part 1: SISO System,” ASME J. Dyn. Syst., Meas., Control, 121 (1), pp. 19–26.
15
Willems, J. C., 1972, “Dissipative Dynamical Systems, Part 1: General Theory,” Arch. Ration. Mech. Anal.  [CrossRef], 45 , pp. 321–351.
16
Merritt, H. E., 1967, "Hydraulic Control Systems", John Wiley and Sons, New York.

Figures

Grahic Jump Location
+A regular bond graph with no active bonds or power scaling components
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A regular bond graph with no active bonds or power scaling components
Figure 1

A regular bond graph with no active bonds or power scaling components

Grahic Jump Location
+Causal relations of power scaling transformers∕gyrators
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Causal relations of power scaling transformers∕gyrators
Figure 2

Causal relations of power scaling transformers∕gyrators

Grahic Jump Location
+Example illustrating the proof procedure of Theorem 2. The subbond graphs are reconstituted and the storage functions, supply rates, and dissipation function as subgraphs are combined are scaled and added up.
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Example illustrating the proof procedure of Theorem 2. The subbond graphs are reconstituted and the storage functions, supply rates, and dissipation function as subgraphs are combined are scaled and added up.
Figure 3

Example illustrating the proof procedure of Theorem 2. The subbond graphs are reconstituted and the storage functions, supply rates, and dissipation function as subgraphs are combined are scaled and added up.

Grahic Jump Location
+A nonpassive bond graph with power scaling transformer that is not singly connected
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A nonpassive bond graph with power scaling transformer that is not singly connected
Figure 4

A nonpassive bond graph with power scaling transformer that is not singly connected

Grahic Jump Location
+A typical four-way directional control valve
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A typical four-way directional control valve
Figure 5

A typical four-way directional control valve

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+Bond graph of the hydraulic portion of the valve including fluid compressibility effects and interaction with load. This system is passive when the energy source is excluded from the system.
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Bond graph of the hydraulic portion of the valve including fluid compressibility effects and interaction with load. This system is passive when the energy source is excluded from the system.
Figure 6

Bond graph of the hydraulic portion of the valve including fluid compressibility effects and interaction with load. This system is passive when the energy source is excluded from the system.

Grahic Jump Location
+Simplified bond graph of the valve. We wish to develop a control law so that the system (with the energy source included) is passive as it interacts with the load and the command input.
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Simplified bond graph of the valve. We wish to develop a control law so that the system (with the energy source included) is passive as it interacts with the load and the command input.
Figure 7

Simplified bond graph of the valve. We wish to develop a control law so that the system (with the energy source included) is passive as it interacts with the load and the command input.

Grahic Jump Location
+Equivalent electrical circuit for the hydraulic valve equation 15 which is equivalent to Eq. 14
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Equivalent electrical circuit for the hydraulic valve equation 15 which is equivalent to Eq. 14
Figure 8

Equivalent electrical circuit for the hydraulic valve equation 15 which is equivalent to Eq. 14

Grahic Jump Location
+Active bond graph representation of four-way directional control valve. 1k is the unit fictitious stiffness (dimension [MT−2]) associated with the integral relationship between ẋv and xv. xv*≔(1kxv) is the effort variable at the 0 junction.
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Active bond graph representation of four-way directional control valve. 1k is the unit fictitious stiffness (dimension [MT−2]) associated with the integral relationship between ẋv and xv. xv*≔(1kxv) is the effort variable at the 0 junction.
Figure 9

Active bond graph representation of four-way directional control valve. 1k is the unit fictitious stiffness (dimension [MT−2]) associated with the integral relationship between ẋv and xv. xv*≔(1kxv) is the effort variable at the 0 junction.

Grahic Jump Location
+Dualized active bond graph representation of four-way directional control valve
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Dualized active bond graph representation of four-way directional control valve
Figure 10

Dualized active bond graph representation of four-way directional control valve

Grahic Jump Location
+Desired power scaling bond graph representation of four-way directional control valve with bonds replaced by PTF∕PGY
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Desired power scaling bond graph representation of four-way directional control valve with bonds replaced by PTF∕PGY
Figure 11

Desired power scaling bond graph representation of four-way directional control valve with bonds replaced by PTF∕PGY

Grahic Jump Location
+Bond graph of passified valve with robustness modification and estimation error
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Bond graph of passified valve with robustness modification and estimation error
Figure 12

Bond graph of passified valve with robustness modification and estimation error

Grahic Jump Location
+Alternate bond graph structures for passification
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Alternate bond graph structures for passification
Figure 13

Alternate bond graph structures for passification

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