A Decentralized LQR Output Feedback Control for Aero-Engines
Abstract
:1. Introduction
- With the improvement of aero-engine performance, the function and complexity of control tasks have greatly increased, which has increased the workload of controller. The control system needs to use high-performance, multi-core processors as its controller, which in turn puts relatively high demands on the thermal management system of the aero-engine.
- The amount of software code in aero-engine control systems is increasing rapidly, which significantly impacts the software reliability.
- The core control tasks of the aero-engine, such as control-law calculation, are executed in the central controller. The central controller determines the performance of the entire aero-engine control system, and its failure or damage has significant impact on the aero-engine or even the aircraft.
2. Aero-Engine Model
2.1. Nonlinear Modeling
- (1)
- Intake
- (2)
- Fan
- (3)
- Compressor
- (4)
- Combustion chamber
- (5)
- High-pressure turbine
- (6)
- Low-pressure turbine
- (7)
- Bypass duct
- (8)
- Mixer
- (9)
- Nozzle
- (1)
- High-pressure rotor power balance
- (2)
- Low-pressure rotor power balance
- (3)
- Fan air flow balance
- (4)
- High-pressure turbine gas flow balance
- (5)
- Low-pressure turbine gas flow balance
- (6)
- Nozzle gas flow balance
2.2. Linear State Space Model
3. Output Feedback of Decentralized Control System
4. Q-Learning Based LQR Output Feedback Control
4.1. General LQR Problem Solving
4.2. Construction of the Output Feedback Control
4.3. Acquisition of the VCTs
5. Parameter Tuning Based on the Primal-Dual Method
- If is the optimal point of the primal problem, is the optimal point of the dual problem of the primal problem, then satisfies the KKT condition of :
- Define , then, if , , and is a symmetric positive semi-definite cone. A matrix norm makes a contractive map**. There is a unique symmetric matrix that makes , that is, has a unique fixed point .
- The in the following algorithm converges to the optimal solution of the dual problem, that is, the optimal solution of the matrix required in Equation (58).
- Initialization of , , and .
- Calculate .
- Solve from .
- Repeat.
- .
- Dual update: .
- Primal update: .
- .
- Until .
6. Simulation Analyses
7. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
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Steps | ||||
---|---|---|---|---|
0.1 | 3 | 0.0659 | 0.0274 | |
0.01 | 4 | 6.0304 × 10−4 | 0.0140 | |
0.001 | 4 | 6.0304 × 10−4 | 0.0140 | |
0.0007 | 4 | 6.0304 × 10−4 | 0.0140 | |
0.0006 | 8 | 3.5857 × 10−5 | 4.6999 × 10−5 |
Steps | ||||
---|---|---|---|---|
0.1 | 1 | 0.0041 | 0.0041 | |
0.01 | 1 | 0.0041 | 0.0042 | |
0.001 | 2 | 4.8053 × 10−9 | 6.9260 × 10−8 | |
0.0001 | 2 | 4.8053 × 10−9 | 4.1779 × 10−5 | |
4.0 × 10−9 | 5 | 3.8062 × 10−9 | 5.6807 × 10−8 |
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Ji, X.; Li, J.; Ren, J.; Wu, Y. A Decentralized LQR Output Feedback Control for Aero-Engines. Actuators 2023, 12, 164. https://doi.org/10.3390/act12040164
Ji X, Li J, Ren J, Wu Y. A Decentralized LQR Output Feedback Control for Aero-Engines. Actuators. 2023; 12(4):164. https://doi.org/10.3390/act12040164
Chicago/Turabian StyleJi, **aoxiang, Jianghong Li, Jiao Ren, and Yafeng Wu. 2023. "A Decentralized LQR Output Feedback Control for Aero-Engines" Actuators 12, no. 4: 164. https://doi.org/10.3390/act12040164