From Beale Number to Pole Placement Design of a Free Piston Stirling Engine

Abstract In this paper, pole placement-based design and analysis of a free piston Stirling engine (FPSE) is presented and compared to the well-defined Beale number design technique. First, dynamic and thermodynamic equations governing the engine system are extracted. Then, linear dynamics of the free piston Stirling engine are studied using dynamic systems theory tools such as root locus. Accordingly, the effects of variations of design parameters such as mass of pistons, stiffness of springs, and frictional damping on the locations of dominant closed-loop poles are investigated. The design procedure is thus conducted to place the dominant poles of the dynamic system at desired locations on the s-plane so that the unstable dynamics, which is the required criterion for energy generation, is achieved. Next, the closed-loop poles are selected based on a desired frequency so that a periodical system is found. Consequently, the design parameters, including mass and spring stiffness for both power and displacer pistons, are obtained. Finally, the engine power is calculated through the proposed control-based analysis and the result is compared to those of the experimental work and the Beale number approach. The outcomes of this work clearly reveal the effectiveness of the control-based design technique of FPSEs compared to the well-known approaches such as Beale number.

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Optimisation of a Quasi-Steady Model of a Free-Piston Stirling Engine

Energies ◽

10.3390/en12010072 ◽

2018 ◽

Vol 12 (1) ◽

pp. 72 ◽

Cited By ~ 6

Author(s):

Ayodeji Sowale ◽

Edward Anthony ◽

Athanasios Kolios

Keyword(s):

Power Systems ◽

Thermal Efficiency ◽

Waste Heat ◽

Stirling Engine ◽

Design Parameters ◽

Free Piston ◽

Output Performance ◽

Free Piston Stirling Engine ◽

External Combustion ◽

Work Done

Energy from waste heat recovery is receiving considerable attention due to the demand for power systems that are less polluting. This has led to the investigation of external combustion engines such as the free-piston Stirling engine (FPSE) due to its ability to generate power from any source of heat and, especially, waste heat. However, there are still some limitations in the modelling, design and practical utilisation of this type of engine. Modelling of the FPSE has proved to be a difficult task due to the lack of mechanical linkages in its configuration, which poses problems for achieving stability. Also, a number of studies have been reported that attempt to optimise the output performance considering the characteristics of the engine configuration. In this study the optimisation of the second-order quasi-steady model of the gamma-type FPSE is carried out using the genetic algorithm (GA) to maximise the performance in terms of power output, and considering the design parameters of components such as piston and displacer damper, geometry of heat exchangers, and regenerator porosity. This present study shows that the GA optimisation of the RE-1000 FPSE design parameters improved its performance from work done and output power of 33.2 J and 996 W, respectively, with thermal efficiency of 23%, to 44.2 J and 1326 W with thermal efficiency of 27%.

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Simultaneous Structural and Control Design Using Constraint Functions

Journal of Mechanisms Transmissions and Automation in Design ◽

10.1115/1.3258908 ◽

1988 ◽

Vol 110 (1) ◽

pp. 65-72 ◽

Cited By ~ 5

Author(s):

J. M. Starkey ◽

P. M. Kelecy

Keyword(s):

Control System ◽

System Dynamics ◽

Structural Design ◽

Closed Loop ◽

Control Design ◽

Pole Placement ◽

Design Parameters ◽

Weighted Sum ◽

Design Technique ◽

And Control

A design technique is presented which modifies system dynamics by simultaneously considering control system gains and structural design parameters. Constraint functions are devised that become smaller as (1) structural design parameters and feedback gains become smaller, and (2) closed-loop eigenvalues migrate toward more desirable regions. By minimizing a weighted sum of these functions, the interaction between design performance and design parameters can be explored. Examples are given that show the effects of the weighting parameters, and the potential advantages of this technique over traditional pole placement techniques.

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Numerical Analysis of the Adiabatic and Quasi Steady Model of Free Piston Stirling Engine

MATEC Web of Conferences ◽

10.1051/matecconf/201819804005 ◽

2018 ◽

Vol 198 ◽

pp. 04005

Author(s):

Ayodeji Sowale ◽

Athanasios J. Kolios

Keyword(s):

Output Power ◽

Stirling Engine ◽

Operating Conditions ◽

Design Parameters ◽

Stable Operation ◽

Free Piston ◽

Temperature Efficiency ◽

Mathematical Equations ◽

Free Piston Stirling Engine ◽

Good Agreement

This study presents the numerical simulation of the adiabatic and Quasi steady models of the free piston Stirling engine, the mathematical equations are presented, and design parameters are determined and used as input for the simulation. The simulations are computed under adiabatic and Quasi operating conditions, and their output results are compared. The similarities and differences in the model predictions in terms of the pressure to volume diagram, the amplitudes of the pistons and displacer, temperature, efficiency, power output and stable operation are observed and investigated. The models are validated against the experimental output and the results show a good agreement with the experiment. The adiabatic model predicted an output power of 862 W, while Quasi steady model predicted more accurate output power of 997W at frequency of 30 Hz in relation to the 1000 W of the experimental output. The effects of the variation of engine’s parameters on the output power are also observed and presented.

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Modeling of a 1kW free piston Stirling engine: Opportunity for sustainable electricity production

Ingeniería Investigación y Tecnología ◽

10.22201/fi.25940732e.2020.21.4.035 ◽

2020 ◽

Vol 21 (4) ◽

pp. 1-13

Author(s):

José Rodrigo Ávila Pérez ◽

Geydy Luz Gutiérrez Urueta ◽

Fidencio Tapia Rodríguez ◽

Joseph Ademar Araoz

Keyword(s):

Combustion Engine ◽

Stability Study ◽

Stirling Engine ◽

Electricity Production ◽

Design Parameters ◽

Storage Device ◽

Free Piston ◽

Order Analysis ◽

First Order ◽

Free Piston Stirling Engine

As part of the many alternatives for the development of new methods for sustainable energy transformation, the Stirling engine is distinguished due to the characteristics of an external combustion engine, with many advantages. These engines can be activated with heat, representing an additional option for the use of renewable energy. The Free Piston Stirling Engine (FPSE) is special due to the elimination of all wearing mechanisms of a typical kinematic Stirling engine. A linear mechanical storage device replaces the crank device of the kinematic one, making possible long operating life, higher efficiency and zero maintenance. This document presents a theoretical model of a Free Piston Stirling Engine (FPSE) based on a dynamical and thermal analysis. As the core of the study, the “first order analysis” of the thermal machine is implemented by taking some ideal assumptions. A technique of evolutionary computation is presented as a feasible solution for finding functional correct design parameters. For the dynamical part, the mathematical model is obtained through energy balances, and then a stability study is implemented to assure the oscillations of the machine. Results include several cases, which offers parameters such as cylinder and rod area, cooler temperature, heater temperature, piston and displacer mass, piston and displacer stiffness, phase angle, frequency and power. It is critical to consider the sensibility of the system, and therefore, it is essential to apply a stability analysis in order to fully understand the behavior of the thermal machine. Results are compared are compared in terms of a calculated error considering first order analysis and the stability study developed with the Schmidt analysis.

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Modeling and Validation of Free-Piston Stirling Engines Using Impedance Controlled Hardware-in-the-Loop

ASME 2011 Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control, Volume 1 ◽

10.1115/dscc2011-6105 ◽

2011 ◽

Cited By ~ 7

Author(s):

Mark E. Hofacker ◽

John M. Tucker ◽

Eric J. Barth

Keyword(s):

Closed Loop ◽

Linear Models ◽

Stirling Engine ◽

Imaginary Component ◽

Sustained Oscillation ◽

Operating Characteristics ◽

Real Component ◽

Free Piston ◽

Experimental Apparatus ◽

Free Piston Stirling Engine

This paper describes a method of energetically modeling a free-piston Stirling engine. This model is compared to a lower order Schmidt model, and both models are linearized from nonlinear continuous form and cast into closed-loop state space models. To validate the linear models, an experimental apparatus to simulate the performance of different engines was constructed using linear actuators, sensors, and a free-piston Stirling engine. The behavior of the experimental apparatus was compared to the behavior predicted by the linear models. The operating characteristics of the experimental apparatus are compared to the dominant poles of the closed loop models. Relations are described between the imaginary component of the dominant poles and the operating frequency of the engine and between the real component and the ability of the engine to enter sustained oscillation.

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