Improved PVTOL Test Bench for the Study of Over-Actuated Tilt-Rotor Propulsion Systems
Abstract
:1. Introduction
- There is a high degree of heterogeneity in the propulsion system configurations, including number, distribution, and operating conditions.
- There is an increasing use of distributed tilting rotors (or similar thrust vectoring elements).
- The multiplicity of propulsors and control surfaces results in a high number of control inputs, introducing an over-actuation problem, which is normally denoted as the control allocation problem in the literature (although under-actuation problems have also been treated as allocation problems by some authors).
- The control allocation problem is commonly dealt with by separating the vehicle into two parts: (1) a rigid body, which is driven by virtual control inputs (i.e., force and moment vectors), and (2) the propulsion subsystem, which is driven in such a way that the desired force and moment vectors are obtained. In practice, it is difficult to pair specific physical inputs to a particular force or moment component without introducing cross-coupling in the rigid body control loop.
- Although many control approaches have been proposed, linear Proportional Integral Derivative (PID) controllers are still used in many practical setups due to their simplicity and low computational overhead.
- There is a high level of heterogeneity in the propulsion configuration of recent VTOL vehicles with a movement towards a higher number of actuators.
- The resulting control allocation problems are highly dependent on the propulsion configuration. Therefore, the study of this issue can yield vehicle-specific results.
- The use of simplified test benches (such as the PVTOL) can aid in the study of prospective control strategies while preserving many of the dynamic and experimental complexities, allowing a more rapid development of novel/better solutions.
- The typical PVTOL test bench configuration is unable to represent many of the difficulties found in recent VTOL vehicles.
- Although non-linear control and allocation approaches can deliver improved performance for wider operating ranges, in many Unmanned Aerial Vehicle (UAV) applications, linear controllers and allocation approaches are still being used and researched due to their simplicity and efficiency.
- A novel PVTOL test bench configuration containing an arbitrary number of co-linear tilting rotors is proposed as a progression of the traditional PVTOL test bench configuration. This configuration can reproduce several of the interesting issues found in novel VTOL vehicles, mainly the control allocation and cross-coupling problems. In addition, this configuration can be easily extended to include an arbitrary number of co-planar tilting propulsors, so that a wider range of vehicles can be mimicked.
- A general method for obtaining a closed form of the linearization of the propulsion model for the modified PVTOL configuration is presented. This can be useful because, as mentioned before, many control allocation strategies depend on it.
- A simple test bench, based on the modified PVTOL configuration, is implemented experimentally. This simple test bench allows testing control allocation and cross-coupling problems.
- A simple decoupling control allocation scheme for the test bench, based on a linear approximation derived through Singular Value Decomposition (SVD), is presented. This approach allows defining an optimal solution for the allocation problem of the modified PVTOL configuration. The resulting optimization can solve the over-actuation problem by introducing a wide range of considerations. In this case, low-error and practical physical considerations are used.
- The proposed SVD control allocation approach is compared with a more traditional input mixer algorithm, derived from physical insight, both through simulations and using the experimental test bench. The results show that the proposed control allocation scheme allows decreasing the cross-coupling with a simple static decoupling matrix.
2. Materials and Methods
2.1. A PVTOL with an Arbitrary Number of Co-Linear Tilting Rotors
- Matrix A contains information regarding the physical position and rotation direction of each propeller. Since these properties are normally constant, updating matrix A is not necessary when calculating a linear approximation on a different operating point. However, analyzing its structure could be useful to determine which particular propulsive configuration is better for particular applications.
- Matrix B contains information regarding the tilt angle of each of the propellers. Depending on the operating range and behavior of the propulsion system, this matrix could be the most sensible for operating point modifications, and should be updated accordingly in scheduling approaches.
- Matrix C contains information regarding the thrust force of each propeller. This matrix could also require regular updates in a scheduling approach depending on the operating behavior of the vehicle.
2.2. Experimental Test Bench
- Two 2304 Racestar brushless motors (81 W max power).
- Two Gemfan 51466 three-blade propellers, one CW and one CCW.
- Two MG995 servo-motors.
- One BNO055 absolute orientation sensor.
- Input variables:
- –
- Right motor thrust ;
- –
- Left motor thrust ;
- –
- Tilt angle of right motor ;
- –
- Tilt angle of left motor .
- Output variables:
- –
- Pitch rate ;
- –
- Yaw rate ;
- –
- Pitch angle ;
- –
- Yaw angle .
2.3. Control Allocation Problem
2.3.1. Physical Intuition-Based Decentralized Control Allocation
- A decentralized control approach for the pitch and yaw angles is sufficient to stabilize the test bench. This implies that pitch and yaw moments are derived separately without considering their interaction. This normally implies, for instance, that when calculating the pitch angle input mixer (directly related to ), it is assumed that . In addition, if the pitch angle mixer also affects the yawing moment N, then these effects are neglected, or at best considered as input perturbations for the yaw angle controller. That is, any residual cross-coupling is neglected.
- A small range of operation for the tilt-rotors is enough to stabilize the test bench. This assumption allows maintaining the focus of this study on the linear elements of the control allocation problem, which is the basis of most scheduling approaches. Later, it will be confirmed experimentally that indeed only small tilt angles are required for the stabilization of this PVTOL configuration. Nonetheless, extension of these results for wider operating ranges will be forthcoming in future studies.
2.3.2. Singular Value Decomposition Control Allocation
2.3.3. SVD-Based Control Allocation Configuration
2.3.4. Final Mixer Algorithm Comparison
3. Results
3.1. Simulation Results
- Pitch-Varying Case: The pitch reference changes in steps, while the yaw reference remains constant at zero.
- Yaw-Varying Case: The yaw reference changes in steps, while the pitch reference remains constant at zero.
3.1.1. Pitch-Varying Case
3.1.2. Yaw-Varying Case
3.1.3. Discussion
3.2. Experimental Results
3.2.1. Pitch-Varying Case
3.2.2. Yaw-Varying Case
3.3. Quantitative Analysis
4. Discussion and Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
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Variable | Value |
---|---|
0° | |
0° | |
Requirement | Pitch | Yaw |
---|---|---|
Overshoot | <35% | <25% |
Settling Time | <11 s | <15 s |
Constant | Pitch | Yaw |
---|---|---|
Proportional | 2 | 1.5 |
Integral | 0.1 | 0.1 |
Derivative | 1.5 | 1 |
Constant | Pitch | Yaw |
---|---|---|
Proportional | 1.5 | 1.5 |
Integral | 1 | 0.5 |
Derivative | 0.5 | 1 |
Experiment | DoF | Decentralized | Decoupling | % |
---|---|---|---|---|
Pitch | Pitch | 37.4525 | 38.2600 | 2.1560 |
Variation | Yaw | 4.1196 | 3.2768 | −20.4583 |
Yaw | Pitch | 2.3904 | 0.7042 | −70.5405 |
Variation | Yaw | 118.6156 | 120.5088 | 1.5960 |
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Amezquita-Brooks, L.; Maciel-Martínez, E.; Hernandez-Alcantara, D. Improved PVTOL Test Bench for the Study of Over-Actuated Tilt-Rotor Propulsion Systems. Machines 2024, 12, 46. https://doi.org/10.3390/machines12010046
Amezquita-Brooks L, Maciel-Martínez E, Hernandez-Alcantara D. Improved PVTOL Test Bench for the Study of Over-Actuated Tilt-Rotor Propulsion Systems. Machines. 2024; 12(1):46. https://doi.org/10.3390/machines12010046
Chicago/Turabian StyleAmezquita-Brooks, Luis, Eber Maciel-Martínez, and Diana Hernandez-Alcantara. 2024. "Improved PVTOL Test Bench for the Study of Over-Actuated Tilt-Rotor Propulsion Systems" Machines 12, no. 1: 46. https://doi.org/10.3390/machines12010046
APA StyleAmezquita-Brooks, L., Maciel-Martínez, E., & Hernandez-Alcantara, D. (2024). Improved PVTOL Test Bench for the Study of Over-Actuated Tilt-Rotor Propulsion Systems. Machines, 12(1), 46. https://doi.org/10.3390/machines12010046