A Gain Scheduling Design Method of the Aero-Engine Fuel Servo Constant Pressure Valve with High Accuracy and Fast Response Ability
Abstract
:1. Introduction
- Firstly, the design theory of the system is revealed successfully by using the linear incremental analysis method. Evidently, the controlled object and the stabilization controller are the two fundamental units of the closed-loop system, as demonstrated by the study results.
- Secondly, the accurate loop transfer function models of the system are calculated. In addition, the precise influences of the design parameters on the dynamic performance and stability are analyzed by using the bode frequency domain analysis methods, and some useful guidance measures are offered.
- Finally, a gain scheduling design method for the stabilization control gain is proposed, and the proposed method is demonstrated to exactly solve the design work based on the nonlinear simulation.
2. Design Analysis and Dynamic Equations
2.1. Design Analysis
- is the dynamic matrix of the controlled object.
- is the dynamic matrix of the motion valve, is the generalized stabilization control gain, and they construct the stabilization controller.
2.2. Dynamic Equations
2.2.1. Controlled Object
2.2.2. Stabilization Controller
3. Linear Models
3.1. Open-Loop Transfer Function
3.2. Disturbance Input Transfer Functions
3.3. Control Output Transfer Functions
- The closed-loop disturbance transfer function from to is
- 2.
- The closed-loop disturbance transfer function from to is
4. Bode Frequency Domain Characteristic Analysis
4.1. Calculation of the Corner Frequencies
- If , the second-order section is an underdamped oscillation link, and its poles are
- 2.
- If , the second-order section is an overdamped non-oscillation link, and its poles are
- The stabilization control gain mainly influences and the open-loop gain ;
- The spring stiffness mainly influences , , and the open-loop gain ;
- The volume of the controlled chamber mainly influences ;
- The pressure-bearing area mainly influences and the open-loop gain ;
- The mass mainly influences and .
4.2. Analysis of the Frequency Domain Characteristic
- Reducing the stabilization control gain ;
- Reducing the mass of the motion valve ;
- Increasing the viscous friction coefficient .
- Increasing the stabilization control gain ;
- Reducing the spring stiffness ;
- Reducing the pressure-bearing area of the motion valve.
4.3. Influence of the Stabilization Control Gain on the Frequency Domain Characteristic
- According to Equations (20) and (22), the steady-state gain and decrease, thus the steady error caused by the disturbance inputs is reduced, resulting in better disturbance rejection performance;
- The crossover frequency increases and the regulating time is reduced, resulting in faster response performance;
- The phase margin decreases, resulting in worse robustness performance.
4.4. Stability Analysis
5. Gain Scheduling Design Method
- Steady-state performance: The designed controlled pressure is , and the working range is .
- Dynamic performance: The regulation time is not greater than .
5.1. Dynamic Design
5.1.1. Calculation of the Stabilization Control Gain
5.1.2. Constraint Condition
5.2. Calculation processes
6. Design and Simulation
- The working range of the variable outlet flow area is [0, 3.1416] × 10−6 m2.
- The designed controlled pressure is 1.5 ± 0.01 MPa;
- The designed regulating time is not more than 0.006 s.
- Designing the stabilization control law as .
6.1. Design
- Since the designed pressure is 1.5 MPa, according to Equation (43), the steady-state spring compression is 13.404129 mm;
- Since the design range of is [1.49, 1.51] MPa, according to Equation (44), the variation of the spring compression is 0.22340214 mm.
6.2. Simulation
7. Conclusions
- The linear incremental analysis method vividly displays the design theory of the constant pressure valve when compared to the conventional direct transfer function transformation analysis method. In addition, the key design parameter, the stabilization control gain, is clarified, as well as the system’s input-output characteristics, which were not covered in earlier studies.
- The analysis results of the bode frequency domain characteristics explain quantitatively how the design parameters affect the system performance and give correct guidance to design the performance parameters, preventing trial and error in the research process.
- Evidently, when using the gain scheduling design method, both the steady-state and dynamic performance of the designed system satisfies the design requirements. The predesign and analysis of other components of the fuel metering system, including the position control system, can be realized using the proposed design methods.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Parameter/Unit | Value | Parameter/Unit | Value |
---|---|---|---|
/Kg | 0.0115 | /m3 | 10−5 |
/(N·m/s) | 10 | /(Kg/m3) | 800 |
/m | 0.008 | /bar | 17,000 |
/MPa | 1.5 | /m | 0.001 |
/MPa | 0.3 | 0.7 |
/MPa | /mm | /mm2 | |||
---|---|---|---|---|---|
2 | 2 | 6.08366800 | 0.139094570 | [0.002, 0.007] | 0.0068 |
1 | 2.43346720 | 0.041787194 | [0.002, 0.015] | 0.0048 | |
0 | 1.21673360 | 0.019299005 | [0.002, 0.009] | 0.0028 | |
3 | 2 | 3.51240740 | 0.034057185 | [0.001, 0.006] | 0.0058 |
1 | 1.40496290 | 0.011826533 | [0.001, 0.0055] | 0.0028 | |
0 | 0.70248147 | 0.006026016 | [0.001, 0.0025] | 0.0018 | |
4 | 2 | 2.72069900 | 0.020693472 | [0.0010, 0.005] | 0.0048 |
1 | 1.08827960 | 0.007491835 | [0.0005, 0.003] | 0.0028 | |
0 | 0.54413981 | 0.003934234 | [0.0005, 0.001] | 0.0008 | |
5 | 2 | 2.29941040 | 0.015556697 | [0.0008, 0.0045] | 0.0043 |
1 | 0.91976415 | 0.005747635 | [0.0007, 0.0027] | 0.0025 | |
0 | 0.45988207 | 0.003064452 | [0.0005, 0.0009] | 0.0007 | |
6 | 2 | 2.02788930 | 0.012802030 | [0.0005, 0.004] | 0.0038 |
1 | 0.81115574 | 0.004787408 | [0.0005, 0.002] | 0.0018 | |
0 | 0.40557787 | 0.002576085 | [0.0005, 0.001] | 0.0008 | |
7 | 2 | 1.83429490 | 0.011061443 | [0.0005, 0.0035] | 0.0033 |
1 | 0.73371797 | 0.004169889 | [0.0005, 0.0020] | 0.0018 | |
0 | 0.36685898 | 0.002257730 | [0.00055, 0.00065] | 0.0004 | |
8 | 2 | 1.68730590 | 0.009849004 | [0.0005, 0.0030] | 0.0028 |
1 | 0.67492237 | 0.003734197 | [0.0005, 0.0017] | 0.0015 | |
0 | 0.33746118 | 0.002030850 | [0.0004, 0.0005] | 0.0003 |
mm2 | mm | |
---|---|---|
0.33746118 | 0.0003 | 0 |
0.36685898 | 0.0004 | 0.097992667 |
0.40557787 | 0.0008 | 0.19478989 |
0.45988207 | 0.0007 | 0.26267014 |
0.54413981 | 0.0008 | 0.38303834 |
0.67492237 | 0.0015 | 0.54651654 |
0.70248147 | 0.0018 | 0.56488927 |
0.73371797 | 0.0018 | 0.58224289 |
0.81115574 | 0.0018 | 0.62526387 |
0.91976415 | 0.0025 | 0.68560187 |
1.0882796 | 0.0028 | 0.75300805 |
1.2167336 | 0.0028 | 0.79888448 |
1.4049629 | 0.0028 | 0.86610923 |
1.6873059 | 0.0028 | 0.96694602 |
1.8342949 | 0.0033 | 1.01944210 |
2.0278893 | 0.0038 | 1.07810710 |
2.2994104 | 0.0043 | 1.14956000 |
2.4334672 | 0.0048 | 1.18073600 |
2.7206990 | 0.0048 | 1.24057590 |
3.5124074 | 0.0058 | 1.40551520 |
6.0836680 | 0.0068 | 1.84883600 |
mm2 | mm | |
---|---|---|
0.33746118 | 0.0006 | 0 |
0.36685898 | 0.0007 | 0.045227385 |
0.40557787 | 0.0008 | 0.096852571 |
0.45988207 | 0.0008 | 0.16473282 |
0.54413981 | 0.0015 | 0.23800042 |
0.67492237 | 0.0017 | 0.31973952 |
0.70248147 | 0.0027 | 0.33226638 |
0.73371797 | 0.0018 | 0.34614927 |
0.81115574 | 0.0025 | 0.38216684 |
0.91976415 | 0.0027 | 0.42393931 |
1.0882796 | 0.0039 | 0.47500459 |
1.2167336 | 0.0100 | 0.49348718 |
1.4049629 | 0.0049 | 0.51875286 |
1.6873059 | 0.0040 | 0.58220073 |
1.8342949 | 0.0038 | 0.61989021 |
2.0278893 | 0.0055 | 0.66152342 |
2.2994104 | 0.0049 | 0.71373902 |
2.4334672 | 0.0160 | 0.72656742 |
2.7206990 | 0.0080 | 0.75050340 |
3.5124074 | 0.0075 | 0.85265932 |
6.0836680 | 0.0060 | 1.23358680 |
mm | mm2 |
---|---|
0 | 0 |
0.2 | 0.33746118 |
0.24522738 | 0.36685898 |
0.29685257 | 0.40557787 |
0.36473282 | 0.45988207 |
0.43800042 | 0.54413981 |
0.51973952 | 0.67492237 |
0.53226638 | 0.70248147 |
0.54614927 | 0.73371797 |
0.58216684 | 0.81115574 |
0.62393931 | 0.91976415 |
0.67500459 | 1.0882796 |
0.69348718 | 1.2167336 |
0.71875286 | 1.4049629 |
0.78220073 | 1.6873059 |
0.81989021 | 1.8342949 |
0.86152342 | 2.0278893 |
0.91373902 | 2.2994104 |
0.92656742 | 2.4334672 |
0.95050340 | 2.7206990 |
1.05265930 | 3.5124074 |
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Zhao, W.; Wang, X.; Jiang, Z.; Long, Y. A Gain Scheduling Design Method of the Aero-Engine Fuel Servo Constant Pressure Valve with High Accuracy and Fast Response Ability. Symmetry 2023, 15, 45. https://doi.org/10.3390/sym15010045
Zhao W, Wang X, Jiang Z, Long Y. A Gain Scheduling Design Method of the Aero-Engine Fuel Servo Constant Pressure Valve with High Accuracy and Fast Response Ability. Symmetry. 2023; 15(1):45. https://doi.org/10.3390/sym15010045
Chicago/Turabian StyleZhao, Wenshuai, Xi Wang, Zhen Jiang, and Yifu Long. 2023. "A Gain Scheduling Design Method of the Aero-Engine Fuel Servo Constant Pressure Valve with High Accuracy and Fast Response Ability" Symmetry 15, no. 1: 45. https://doi.org/10.3390/sym15010045
APA StyleZhao, W., Wang, X., Jiang, Z., & Long, Y. (2023). A Gain Scheduling Design Method of the Aero-Engine Fuel Servo Constant Pressure Valve with High Accuracy and Fast Response Ability. Symmetry, 15(1), 45. https://doi.org/10.3390/sym15010045