1. Date of download: 6/1/2016 Copyright © ASME. All rights reserved. From: Power Scaling Bond Graph Approach to the Passification of Mechatronic Systems— with Application to Electrohydraulic Valves J. Dyn. Sys., Meas., Control. 2005;127(4):633-641. doi:10.1115/1.2101848 A regular bond graph with no active bonds or power scaling components Figure Legend:

2. Date of download: 6/1/2016 Copyright © ASME. All rights reserved. From: Power Scaling Bond Graph Approach to the Passification of Mechatronic Systems— with Application to Electrohydraulic Valves J. Dyn. Sys., Meas., Control. 2005;127(4):633-641. doi:10.1115/1.2101848 Causal relations of power scaling transformers∕gyrators Figure Legend:

3. Date of download: 6/1/2016 Copyright © ASME. All rights reserved. From: Power Scaling Bond Graph Approach to the Passification of Mechatronic Systems— with Application to Electrohydraulic Valves J. Dyn. Sys., Meas., Control. 2005;127(4):633-641. doi:10.1115/1.2101848 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 Legend:

4. Date of download: 6/1/2016 Copyright © ASME. All rights reserved. From: Power Scaling Bond Graph Approach to the Passification of Mechatronic Systems— with Application to Electrohydraulic Valves J. Dyn. Sys., Meas., Control. 2005;127(4):633-641. doi:10.1115/1.2101848 A nonpassive bond graph with power scaling transformer that is not singly connected Figure Legend:

5. Date of download: 6/1/2016 Copyright © ASME. All rights reserved. From: Power Scaling Bond Graph Approach to the Passification of Mechatronic Systems— with Application to Electrohydraulic Valves J. Dyn. Sys., Meas., Control. 2005;127(4):633-641. doi:10.1115/1.2101848 A typical four-way directional control valve Figure Legend:

6. Date of download: 6/1/2016 Copyright © ASME. All rights reserved. From: Power Scaling Bond Graph Approach to the Passification of Mechatronic Systems— with Application to Electrohydraulic Valves J. Dyn. Sys., Meas., Control. 2005;127(4):633-641. doi:10.1115/1.2101848 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 Legend:

7. Date of download: 6/1/2016 Copyright © ASME. All rights reserved. From: Power Scaling Bond Graph Approach to the Passification of Mechatronic Systems— with Application to Electrohydraulic Valves J. Dyn. Sys., Meas., Control. 2005;127(4):633-641. doi:10.1115/1.2101848 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 Legend:

8. Date of download: 6/1/2016 Copyright © ASME. All rights reserved. From: Power Scaling Bond Graph Approach to the Passification of Mechatronic Systems— with Application to Electrohydraulic Valves J. Dyn. Sys., Meas., Control. 2005;127(4):633-641. doi:10.1115/1.2101848 Equivalent electrical circuit for the hydraulic valve equation which is equivalent to Eq. Figure Legend:

9. Date of download: 6/1/2016 Copyright © ASME. All rights reserved. From: Power Scaling Bond Graph Approach to the Passification of Mechatronic Systems— with Application to Electrohydraulic Valves J. Dyn. Sys., Meas., Control. 2005;127(4):633-641. doi:10.1115/1.2101848 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 x ̇ v and xv. xv* ≔ (1kxv) is the effort variable at the 0 junction. Figure Legend:

10. Date of download: 6/1/2016 Copyright © ASME. All rights reserved. From: Power Scaling Bond Graph Approach to the Passification of Mechatronic Systems— with Application to Electrohydraulic Valves J. Dyn. Sys., Meas., Control. 2005;127(4):633-641. doi:10.1115/1.2101848 Dualized active bond graph representation of four-way directional control valve Figure Legend:

11. Date of download: 6/1/2016 Copyright © ASME. All rights reserved. From: Power Scaling Bond Graph Approach to the Passification of Mechatronic Systems— with Application to Electrohydraulic Valves J. Dyn. Sys., Meas., Control. 2005;127(4):633-641. doi:10.1115/1.2101848 Desired power scaling bond graph representation of four-way directional control valve with bonds replaced by PTF∕PGY Figure Legend:

12. Date of download: 6/1/2016 Copyright © ASME. All rights reserved. From: Power Scaling Bond Graph Approach to the Passification of Mechatronic Systems— with Application to Electrohydraulic Valves J. Dyn. Sys., Meas., Control. 2005;127(4):633-641. doi:10.1115/1.2101848 Bond graph of passified valve with robustness modification and estimation error Figure Legend:

13. Date of download: 6/1/2016 Copyright © ASME. All rights reserved. From: Power Scaling Bond Graph Approach to the Passification of Mechatronic Systems— with Application to Electrohydraulic Valves J. Dyn. Sys., Meas., Control. 2005;127(4):633-641. doi:10.1115/1.2101848 Alternate bond graph structures for passification Figure Legend: