Abstract
Min-max selector structure is traditionally used as the industrial control architecture of commercial turbofan engines. However, recent studies indicate that this structure with linear compensators suffers from lack of safety guarantee in fast demands. On the other hand, model predictive control (MPC) technique, which incorporates input/output constraints in its optimization process, has the potential to fulfill the control requirements of an aircraft engine. In this paper, a practical approach is performed for design and optimization of the turbofan engine controller through a comparative study where all control modes and requirements have been taken into account simultaneously. For this purpose, a thermodynamic nonlinear model is firstly developed for the turbofan engine. The linear regulators of minmax structure are then optimized via genetic algorithm (GA). The MPC technique is formulated based on the proper discrete-time linearized state-space models at desired operating points with real-time optimization, in which the MPC tuning horizons are obtained through GA optimization procedure. The both controllers are implemented on appropriate hardware taking the real-time aspects into account. Finally, a hardware in the loop (HIL) platform is developed for the turbofan engine electronic control unit (ECU) testing. The software and HIL simulation results confirm that MPC improves the response time of the system in comparison with min-max algorithm and guarantees the engine limit protection. This study demonstrates competitive advantages of MPC in terms of limit protection assurance and fast response, despite more computational burden.
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Abbreviations
- A, B, C, D :
-
Matrices of the linear state-space model
- b i :
-
The value of the ith limit
- e :
-
The white-noise disturbance
- F, Φ :
-
Matrices of the predicted outputs equation
- f 1 :
-
The look-up table of the compressor map
- f 3 :
-
The look-up table of the turbine map
- f 2, f 4, g :
-
The tables of the thermodynamic characteristics
- h :
-
Enthalpy
- H :
-
Fuel heating value
- HPC:
-
High pressure compressor
- HPC-SM:
-
High pressure compressor stall margin
- HPS:
-
High pressure spool
- HPT:
-
High pressure turbine
- I :
-
Identity matrix
- J :
-
Objective function
- J LP, J HP :
-
Moment of inertia of low pressure and high pressure shafts
- k :
-
Time step
- K i :
-
Min-max compensators
- LPC:
-
Low pressure compressor
- LPS:
-
Low pressure spool
- LPT:
-
Low pressure turbine
- M :
-
Mach number
- M, N, Q :
-
Matrices of the augmented model of MPC
- m :
-
The number of limits
- N LP, N HP :
-
Speed of low pressure and high pressure shafts
- Ṅ LP, Ṅ HP :
-
Angular acceleration of low pressure and high pressure shafts
- n u, n y :
-
Control and prediction horizons
- P :
-
Pressure
- PF :
-
Penalty factor
- PLA:
-
Power lever angle
- PR :
-
Pressure ratio
- Ps3 :
-
High pressure compressor discharge static pressure
- PW :
-
Power
- r :
-
Reference trajectory
- t :
-
Time
- T :
-
Temperature
- T45 :
-
High pressure turbine exit total temperature
- u :
-
Velocity
- u :
-
Vector of control variables
- û :
-
Vector of predicted inputs
- U min, U max :
-
Vector of lower and upper bounds of the inputs
- W f :
-
Fuel flow rate
- W f/Ps3, RU:
-
Ratio unit limiter
- w i :
-
Weighting values
- x :
-
Vector of state variables
- y :
-
Vector of output variables
- ŷ :
-
Vector of predicted outputs
- Y min, Y max :
-
Vector of lower and upper bounds of the outputs
- η :
-
Efficiency
- λ :
-
Scalar weighting factor
- a :
-
Augmented matrix
- acc :
-
Acceleration
- amb :
-
Ambient
- b :
-
Burner
- c :
-
Corrected
- con:
-
Controlled
- d:
-
Discrete time
- dec :
-
Deceleration
- e :
-
Exit
- f :
-
Fuel
- _g :
-
Gas
- HP:
-
High pressure
- in :
-
Intlet
- LP:
-
Low pressure
- out :
-
Outlet
- s :
-
Static
- std :
-
Standard atmospheric condition
- t :
-
Total
- T :
-
Transpose
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Recommended by Associate Editor Hanho Song
Morteza Montazeri-Gh is a Professor of Mechanical Engineering at Iran University of Science and Technology (IUST), in Tehran, Iran. He is also Director of the Systems Simulation and Control Laboratory at IUST since 1996. His current research is directed towards simulation, control and diagnosis of gas turbine engine as well as HIL test for performance evaluation of Engine ECU and FCU.
Ali Rasti is a Ph.D candidate in Mechanical Engineering Department of Iran University of Science and Technology (IUST), in Tehran, Iran. His research interests include model predictive control, HIL tests and gas turbine engine control system and fault diagnosis.
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Montazeri-Gh, M., Rasti, A. Comparison of model predictive controller and optimized min-max algorithm for turbofan engine fuel control. J Mech Sci Technol 33, 5483–5498 (2019). https://doi.org/10.1007/s12206-019-0847-3
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DOI: https://doi.org/10.1007/s12206-019-0847-3