Fixed-Time Active Disturbance Rejection Temperature–Pressure Decoupling Control for a High-Flow Air Intake System
Abstract
1. Introduction
- We introduce a static decoupling method to remove the IESS’s static coupling. By defining virtual control inputs, the system is split into pressure and temperature loops, each equipped with a dedicated fixed-time sliding-mode controller (FT-SMC) and super-twisting fixed-time ESO (ST-FT-ESO) to achieve high-quality decoupling under high airflow.
- We employ ST-FT-ESO for rapid and precise estimation of dynamic coupling and other disturbances and FT-SMC as the core controller to reject the total disturbance. Lyapunov analysis shows that the ST-FT-ESO converges in a fixed time and, together with the FT-SMC law, guarantees fixed-time stability of the entire closed-loop system.
- We implement FT-ADRCDC on a hardware-in-the-loop (HIL) simulation platform for the IESS and compare it with LADRC, demonstrating faster response and superior stability in rapid transient tests.
2. Intake Environment Simulation System
2.1. Front-Chamber Cavity Model
2.2. Motion and Flow Characteristics of the Control Valve
2.3. Airflow Model of the Aeroengine
3. Pressure and Temperature Decoupling Design of the IESS
3.1. Decoupling Design
3.1.1. Affine Model of the IESS
3.1.2. Decoupling Design of Valve Control Quantity and System Output
3.2. Static Coupling Matrix Reversibility Analysis
4. Design of Fixed-Time Active Disturbance Rejection Decoupling Controller
4.1. Pressure and Temperature Decoupling Control Structure
4.2. Design of ST-FT-ESO
- Super-twisting correcting law:
- Error feedback functions:
- The FT-ST-ESO dynamics (pressure loop) are as follows:
4.3. Design of the FT-SMC
5. System Stability Analysis
5.1. Stability of the ST-FT-ESO
- (1)
- Homogeneity property
- (2)
- Fixed-time convergence of the ESO
5.2. Stability of the Closed-Loop IESS
- (1)
- Sliding-surface reachability
- (2)
- Vanishing of the position error
- (3)
- Closed-loop fixed-time stability
6. Experimental Simulation and Validation Analysis
6.1. Simulation Verification Platform Setup
- Task 1:
- Constant-altitude ascent/descent and level-flight acceleration.
- Task 2:
- Simultaneous variation in Mach number and altitude.
- Task 3:
- Thrust transient: sudden engine flow change under constant altitude and Mach number.
6.2. Real-Time Implementation of Control Algorithm
6.3. Experimental Task Setup
- Task 1:
- This test evaluates the control system’s simulation performance under level-flight acceleration and constant-Mach-number ascent/descent conditions.
- 0–30 s (level-flight acceleration) at fixed altitude of 8 km:
- –
- 0–5 s: Mach number, 0.5; throttle, 20°.
- –
- 5–15 s: uniform acceleration to Mach number of 0.75 (hold to 20 s) and throttle of 22°.
- –
- 20–28 s: uniform acceleration to Mach number of 0.9 (hold to 30 s) and throttle of 24°.
- 30–75 s (constant-Mach-number ascent/descent) at Mach number of 0.9 and throttle of 24°:
- –
- 30–38 s: climb from 8 km to 10 km (hold to 43 s).
- –
- 43–53 s: climb from 10 km to 12 km (hold to 58 s).
- –
- 58–63 s: descend from 12 km to 11 km.
- Task 2:
- This test evaluates performance under simultaneous variation in Mach number and altitude (75–110 s):
- Altitude: 11 km → 5 km (uniform descent).
- Mach number: 0.9 → 0.5 (uniform deceleration).
- Throttle: 24° → 10° (uniform decrease).
- Task 3:
- This test evaluates the control system’s response to a thrust transient (110–180 s):
- Altitude: hold at 5 km; Mach number: hold at 0.5.
- 110–130 s: hold throttle at 10°.
- 130–135 s: increase throttle to 48°; hold to 155 s.
- 155–160 s: decrease throttle back to 10°; hold to 180 s.
6.4. Simulation Conditions and Control Parameters
6.5. Results Analysis
- Comparison of Collaborative Decoupling Control Performance for Dual-Variable Temperature–Pressure Tracking
- 2.
- Comparison of anti-disturbance abilities under changing flow rates of aeroengine
- 3.
- Comparison of convergence rates of FT-ADRDC and LADRDC.
- 4.
- Discussion on algorithmic differences and open issues.
- (i)
- Convergence mechanism: FT-ADRDC adopts a fixed-time sliding-mode law whose settling time is upper-bounded and independent of the initial error, whereas the linear feedback in LADRDC converges proportionally to both the initial error and the ESO bandwidth.
- (ii)
- Observer bandwidth: The super-twisting fixed-time ESO (ST-FT-ESO) in FT-ADRDC permits a higher effective bandwidth without noise, enabling disturbance estimation roughly one sampling period earlier and thereby suppressing the temperature spike at t = 48–53 s in Figure 11.
- (i)
- The fixed-time gains , , and are tuned for flows below ; robustness at higher rates remains to be verified. Adaptive scheduling or data-driven tuning merits investigation.
- (ii)
- Actuator saturation and dead-zone effects are currently only handled implicitly, which may degrade performance under extreme throttle commands. A structured anti-windup design could mitigate this issue.
- (iii)
- The current model neglects distributed duct losses and measurement uncertainty; these factors become important in larger, more complex piping networks.
7. Conclusions
- The algorithm achieves fixed-time convergence by introducing virtual control variables that decouple the intake environment simulation system (IESS) into two single-input, single-output loops. This decoupling mitigates the static coupling between pressure and temperature. The ST-FT-ESO provides rapid, noise-free estimation of the system states and total disturbances. These disturbances are then compensated for in real time by the FT-SMC, enhancing control robustness.
- Compared with the linear ADRDC (LADRDC) baseline, the proposed FT-ADRCDC achieves significantly better performance across the full simulation window (–180 s). Specifically, the absolute integral error (AIE) for pressure tracking is reduced by 71.9%, and for temperature tracking, it is reduced by 77.9%. The corresponding reductions in the mean-squared error (MSE) are 46.0% and 41.3%, respectively. Moreover, the FT-ADRCDC maintains settling times within 1–2 s, compared to 5 s or more under LADRDC. These results validate the fixed-time design and demonstrate improved anti-disturbance capability and tracking accuracy.
- The proposed controller structure is compact, requires moderate parameter tuning, and is compatible with real-time industrial PLC deployment. These properties make FT-ADRCDC a promising solution for high-speed, high-accuracy intake environment control in high-altitude test facilities. Future work will investigate its scalability to more complex multivariable test systems and its robustness under actuator constraints and sensor noise.
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Conflicts of Interest
Appendix A. Eight-Coefficient Polynomials for Dry Air
0.992313 | 0.236688 | 6.083152 | 7.097112 | 0.794571 |
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Method | Core Controller | ESO |
---|---|---|
FT-ADRCDC | ||
LADRDC |
Category | Metric | FT-ADRCDC | LADRDC | Unit |
---|---|---|---|---|
Pressure tracking | MAR | 0.899 | 1.271 | kPa |
MSE | 0.0821 | 0.1521 | kPa2 | |
AIE | 5.122 | 18.206 | kPa·s | |
Temperature tracking | MAR | 1.137 | 1.655 | °C |
MSE | 0.267 | 0.456 | °C2 | |
AIE | 5.013 | 22.689 | °C·s |
Category | Metric | FT-ADRCDC | LADRDC | Unit |
---|---|---|---|---|
Pressure tracking | MAR | 0.899 | 1.271 | kPa |
MSE | 0.109 | 0.213 | kPa2 | |
AIE | 2.965 | 10.015 | kPa·s | |
Temperature tracking | MAR | 1.137 | 1.655 | °C |
MSE | 0.497 | 0.666 | °C2 | |
AIE | 3.851 | 13.332 | °C·s |
Category | Metric | FT-ADRCDC | LADRDC | Unit |
---|---|---|---|---|
Pressure tracking | MAR | 0.372 | 0.843 | kPa |
MSE | 0.005 | 0.051 | kPa2 | |
AIE | 2.019 | 6.381 | kPa·s | |
Temperature tracking | MAR | 0.489 | 1.203 | °C |
MSE | 0.009 | 0.101 | °C2 | |
AIE | 2.625 | 8.435 | °C·s |
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Zhang, L.; Zhang, H.; Shi, D.; Dan, Z.; Wang, X.; Zhai, C.; Xiao, G.; Xu, Z. Fixed-Time Active Disturbance Rejection Temperature–Pressure Decoupling Control for a High-Flow Air Intake System. Entropy 2025, 27, 880. https://doi.org/10.3390/e27080880
Zhang L, Zhang H, Shi D, Dan Z, Wang X, Zhai C, Xiao G, Xu Z. Fixed-Time Active Disturbance Rejection Temperature–Pressure Decoupling Control for a High-Flow Air Intake System. Entropy. 2025; 27(8):880. https://doi.org/10.3390/e27080880
Chicago/Turabian StyleZhang, Louyue, Hehong Zhang, Duoqi Shi, Zhihong Dan, Xi Wang, Chao Zhai, Gaoxi Xiao, and Zhouzhe Xu. 2025. "Fixed-Time Active Disturbance Rejection Temperature–Pressure Decoupling Control for a High-Flow Air Intake System" Entropy 27, no. 8: 880. https://doi.org/10.3390/e27080880
APA StyleZhang, L., Zhang, H., Shi, D., Dan, Z., Wang, X., Zhai, C., Xiao, G., & Xu, Z. (2025). Fixed-Time Active Disturbance Rejection Temperature–Pressure Decoupling Control for a High-Flow Air Intake System. Entropy, 27(8), 880. https://doi.org/10.3390/e27080880