# Linear Mathematical Model for State-Space Representation of Small Scale Turbojet Engine with Variable Exhaust Nozzle

• Károly Beneda Department of Aeronautics, Naval Architecture and Railway Vehicles, Faculty of Transport Engineering, Budapest University of Technology and Economics, Hungary
• Rudolf Andoga Department of Aviation Engineering, Faculty of Aeronautics, Technical University of Košice, Hungary
• Ladislav Főző Department of Aviation Engineering, Faculty of Aeronautics, Technical University of Košice, Hungary

### Abstract

The goal of this article is to develop a linear mathematical model for a small scale turbojet engine with variable convergent nozzle, and validate it on existing laboratory hardware owned by the authors’ Departments.
Control of gas turbine engines plays an essential role in the safety of aviation. Although its role is constantly expanding, ranging from pilot workload reduction to detailed diagnostics, the basic competence is to regulate the thrust output of the power plant with maximum available accuracy, rapidity, stability, and robustness. The linear quadratic control is one possible solution for the above mentioned criteria.
Although civil aircraft engines include fixed exhaust nozzle geometry, in military applications the exhaust nozzle geometry is also adjustable to reach optimum efficiency due to better matching of individual engine components, etc.
In the present article the authors deduce the members of state space governing equations to acquire the basis of the LQ control.
The established model is based on the physical laws describing the operational behavior of the engine as well as its complexity should be reduced to an acceptable level where still enough details remain to reflect the nature of the controlled object.

Keywords: turbojet engine, optimal control, LQR, state-space model, MATLAB Simulink, variable convergent exhaust nozzle, MIMO control
Published online
2017-03-16
How to Cite
Beneda, K., Andoga, R. and Főző, L. (2018) “Linear Mathematical Model for State-Space Representation of Small Scale Turbojet Engine with Variable Exhaust Nozzle”, Periodica Polytechnica Transportation Engineering, 46(1), pp. 1-10. doi: https://doi.org/10.3311/PPtr.10605.
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