Lyapunov Control Method Based Optimal Control of Alpha-Type Stirling Motor

Abstract

Nowadays, the optimally developed system design has been important with the improvement of the technology. The mathematical model approach with the proper controller design provides a more efficient system with its outputs, as well. One of the complex structures is the alpha type Stirling motor in which it is used to control two independent pistons for gaining more power and but makes controlling its dynamics difficult due to its complex structure dynamics in terms of heat and mechanics interactions. In addition to these difficulties, it must be required to design optimal control via system dynamics perspectives because of the characteristics of four different phases. Due to these reasons, in this study, nonlinear Lyapunov-based optimal control for alpha type stirling engine was performed by combining ideal thermodynamic and mechanic equations. The suggested controller was tested under the different reference motor velocities by calculating optimal heat energy consumption via the control rule. After designing two cascade controllers, both mechanical and heat system controls were achieved to optimize heat energy consumption for different motor velocities. It was proved that the proposed method attained high performance for reference tracking of alpha Stirling motor velocities by interacting heat-mechanical system dynamics modeling via Lyapunov control theory.