Control system design method
View Patent ↗A control system design method and concomitant control system comprising representing a physical apparatus to be controlled as a Hamiltonian system, determining elements of the Hamiltonian system representation which are power generators, power dissipators, and power storage devices, analyzing stability and performance of the Hamiltonian system based on the results of the determining step and determining necessary and sufficient conditions for stability of the Hamiltonian system, creating a stable control system based on the results of the analyzing step, and employing the resulting control system to control the physical apparatus.
1. A control system design method comprising the steps of:
representing a physical apparatus to be controlled as a Hamiltonian system, wherein the Hamiltonian system comprises a mass-spring-damper dynamic system;
determining elements of the Hamiltonian system representation which are power generators, power dissipators, and power storage devices;
analyzing stability and performance of the Hamiltonian system based on the results of the determining step and determining necessary and sufficient conditions for stability of the Hamiltonian system;
creating a stable control system based on the results of the analyzing step; and
employing the resulting control system to control the physical apparatus.
2. The method of claim 1 wherein the control system is nonlinear.
3. The method of claim 1 wherein in the analyzing step stability is determined in terms of power flow.
4. The method of claim 3 wherein in the analyzing step stability is determined in terms of whether the Hamiltonian system is moving toward or away from its minimum energy and maximum entropy state.
5. The method of claim 3 wherein in the analyzing step stability is determined via a Lyapunov derivative function.
6. The method of claim 5 where in the analyzing step stability is determined via a Lyapunov derivative function that is a decomposition and sum of exergy dissipation rate and exergy generation rate.
7. The method of claim 1 wherein the Hamiltonian system comprises a forced harmonic oscillator.
8. The method of claim 1 wherein the physical apparatus is selected from the group consisting of manufacturing devices, electronic devices, communications devices, transportation apparatuses, computer devices, computer networks, military apparatus, electrical power grids, Supervisory Control And Data Acquisition apparatus, and pipeline apparatus.
9. A control system for a physical apparatus, said control system comprising a stable control system based on results of analyzing stability and performance of the physical apparatus represented as a Hamiltonian system and based on the results of determining elements of the Hamiltonian system representation which are power generators, power dissipators, and power storage devices, and on the results of determining necessary and sufficient conditions for stability of the Hamiltonian system, wherein the Hamiltonian system comprises a mass-spring-damper dynamic system or a Duffing oscillator with Coulomb friction nonlinear damper system.
10. The control system of claim 9 wherein said control system is nonlinear.
11. The control system of claim 9 wherein stability is determined in terms of power flow.
12. The control system of claim 11 wherein stability is determined in terms of whether the Hamiltonian system is moving toward or away from its minimum energy and maximum entropy state.
13. The control system of claim 11 wherein stability is determined via a Lyapunov derivative function.
14. The control system of claim 13 where stability is determined via a Lyapunov derivative function that is a decomposition and sum of exergy dissipation rate and exergy generation rate.
15. The control system of claim 9 wherein the Hamiltonian system comprises a forced harmonic oscillator.
16. The control system of claim 9 wherein the physical apparatus is selected from the group consisting of manufacturing devices, electronic devices, communications devices, transportation apparatuses, computer devices, computer networks, military apparatus, electrical power grids, Supervisory Control And Data Acquisition apparatus, and pipeline apparatus.
17. A control system design method comprising the steps of:
representing a physical apparatus to be controlled as a Hamiltonian system, wherein the Hamiltonian system comprises a Duffing oscillator with Coulomb friction nonlinear damper system;
determining elements of the Hamiltonian system representation which are power generators, power dissipators, and power storage devices;
analyzing stability and performance of the Hamiltonian system based on the results of the determining step and determining necessary and sufficient conditions for stability of the Hamiltonian system;
creating a stable control system based on the results of the analyzing step; and
employing the resulting control system to control the physical apparatus.