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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

## Abstract

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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## Figures

Figure 1

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

Figure 2

Causal relations of power scaling transformers∕gyrators

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.

Figure 4

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

Figure 5

A typical four-way directional control valve

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.

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.

Figure 8

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

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.

Figure 10

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

Figure 11

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

Figure 12

Bond graph of passified valve with robustness modification and estimation error

Figure 13

Alternate bond graph structures for passification

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