A Hybrid Linear Quadratic Regulator Controller for Unmanned Free-Swimming Submersible
Abstract
:1. Introduction
1.1. Related Work
1.2. Research Gap
1.3. Contributions
- We have proposed a novel and robust design of a hybrid controller, termed as HLQR, for the UFSS system. It is achieved by using two LQR controllers to efficiently tackle the hydrodynamic disturbances (see Section 5);
- The proposed HLQR controller is integrated in the UFSS system to analyze the response in terms of settling time, rise time, overshoot, and steady-state error;
- The robustness of the proposed HLQR controller is evaluated in the presence of noisy sensor data and a disturbed environment;
- The performance comparison of the proposed controller is provided with PID and lead-compensator controllers (shown in Section 6).
2. Preliminaries
2.1. UFSS
2.2. LQR
3. Mathematical Structure of UFSS
3.1. Dynamical Modeling of Pitch
3.2. Dynamical Modeling of Head
4. Stability Criterion of UFSS
5. Proposed HLQR Controller Design
Adaptive Structure for Error Elimination Based on HLQR
6. Experimental Results
6.1. Results
6.2. Hydrodynamic Disturbances and Noisy Environmental Effect
6.3. Comparison and Discussion
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Symbol | Meaning |
---|---|
pitch angle of the vehicle | |
commanded pitch angle | |
commanded elevator deflection | |
pitch command | |
transfer function of pitch/head | |
pitch angle through the vehicle | |
commanded rudder deflection | |
heading command | |
heading of vehicle |
1 | |||
0 | |||
0 | |||
0 | 0 | ||
0 | 0 |
1 | |||
0 | |||
0 | |||
0 | 0 | ||
0 | 0 |
K | Overshoot | Settling Time | Rise Time | Peak Amplitude |
---|---|---|---|---|
1 | 8.82% | 22.8 s | 6.65 s | 0.787 |
15 | 71.1% | 28.6 s | 1.05 s | 1.67 |
27 | undefined | undefined | undefined | increasing |
K | Overshoot | Settling Time | Rise Time | Peak Amplitude |
---|---|---|---|---|
1 | 6.06% | 27.7 s | 8.88 s | 1.06 |
15 | 70.6% | 26.6 s | 1.07 s | 1.71 |
27 | undefined | undefined | undefined | increasing |
Controllers | Overshoot | Settling Time | Rise Time | Steady-State Error |
---|---|---|---|---|
PID | 20.1% | 10.1 s | 1.22 s | 0% |
Lead | 19.8% | 10.1 s | 1.25 s | 0.12% |
HLQR | 20.2% | 9.83 s | 0.94 s | 0% |
Controllers | Overshoot | Settling Time | Rise Time | Steady-State Error |
---|---|---|---|---|
PID | 20.2% | 10 s | 1.07 s | 0% |
Lead | 19.8% | 10.3 s | 1.31 s | 0% |
HLQR | 19.9% | 9.8 s | 0.792 s | 0% |
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Tariq, H.; Rashid, M.; Hafeez, M.A.; Alotaibi, S.S.; Sinky, M.H. A Hybrid Linear Quadratic Regulator Controller for Unmanned Free-Swimming Submersible. Appl. Sci. 2021, 11, 9131. https://doi.org/10.3390/app11199131
Tariq H, Rashid M, Hafeez MA, Alotaibi SS, Sinky MH. A Hybrid Linear Quadratic Regulator Controller for Unmanned Free-Swimming Submersible. Applied Sciences. 2021; 11(19):9131. https://doi.org/10.3390/app11199131
Chicago/Turabian StyleTariq, Hassan, Muhammad Rashid, Muhammad Asfand Hafeez, Saud S. Alotaibi, and Mohammed H. Sinky. 2021. "A Hybrid Linear Quadratic Regulator Controller for Unmanned Free-Swimming Submersible" Applied Sciences 11, no. 19: 9131. https://doi.org/10.3390/app11199131
APA StyleTariq, H., Rashid, M., Hafeez, M. A., Alotaibi, S. S., & Sinky, M. H. (2021). A Hybrid Linear Quadratic Regulator Controller for Unmanned Free-Swimming Submersible. Applied Sciences, 11(19), 9131. https://doi.org/10.3390/app11199131