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The thermodynamics of port-Hamiltonian systems
Published on Oct 16, 20123580 Views
We show how the connect the tools of linear control theory - dissipativity, Kalman filtering, time-scale separation, etc. – with the main results of thermodynamics - First and Second Laws, Carnot's th
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Chapter list
V. Arnold00:00
The thermodynamics of port-Hamiltonian systems00:41
Goal01:11
Example : Time-Varying Capacitor02:20
Example: Willems’s dissipativity theory (1)05:04
Example: Willems’s dissipativity theory (2)09:31
Example: Willems’s dissipativity theory (3)11:57
Example: Haddad et al’s compartment model12:51
Example: port-Hamiltonian systems14:17
Goal and plan17:17
Time-varying port-Hamiltonian system: lossless case18:38
Time-varying port-Hamiltonian system: dissipative case22:57
First Law of Thermodynamics25:08
Second Law of Thermodynamics26:18
The linear case (1)28:05
The linear case (2)28:44
Example: time-varying capacitor (1)31:24
Example: time-varying capacitor (2)32:53
Time-varying RC circuit33:36
How to extract work from a heat source (1)34:12
How to extract work from a heat source (2)35:28
How to extract work from a heat source (3)36:44
How to extract work from a heat source (4)37:22
How to extract from a heat source (1)38:55
How to extract from a heat source (2)39:28
How to extract work from a heat source (5)39:34
How to extract work from two heat sources (1)40:19
How to extract work from two heat sources (2)43:55
Additivity of entropy, paradox of heat transfer and Fourier’s law44:43
Conclusions49:57