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Автор: Grafiati

Опубліковано: 8 червня 2024

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1

Rigatos, Gerasimos G. "Differential flatness theory-based control and filtering for a mobile manipulator." Cybernetics and Physics, Volume 9, 2020, Number 1 (June 30, 2020): 57–68. http://dx.doi.org/10.35470/2226-4116-2020-9-1-57-68.

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The article proposes a differential flatness theory based control and filtering method for the model of a mobile manipulator. This is a difficult control and robotics problem due to the system’s strong nonlinearities and due to its underactuation. Using the Euler-Lagrange approach, the dynamic model of the mobile manipulator is obtained. This is proven to be a differentially flat one, thus confirming that it can be transformed into an input-output linearized form. Through a change of state and control inputs variables the dynamic model of the manipulator is finally written into the linear canonical (Brunovsky) form. For the latter representation of the system’s dynamics the solution of both the control and filtering problems becomes possible. The global asymptotic stability properties of the control loop are proven. Moreover, a differential flatness theory-based state estimator, under the name of Derivative-free nonlinear Kalman Filter, is developed. This comprises (i) the standard Kalman Filter recursion on the linearized equivalent model of the mobile manipulator and (ii) an inverse transformation, relying on the differential flatness properties of the system which allows for estimating the state variables of the initial nonlinear model. Finally, by redesigning the aforementioned Kalman Filter as a disturbance observer one can achieve estimation and compensation of the disturbance inputs that affect the model of the mobile manipulator.

2

Hagenmeyer, Veit, and Emmanuel Delaleau. "Exact feedforward linearization based on differential flatness." International Journal of Control 76, no. 6 (January 2003): 537–56. http://dx.doi.org/10.1080/0020717031000089570.

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3

Lu, Wen-Chi, Lili Duan, Fei-Bin Hsiao, and Félix Mora-Camino. "Neural Guidance Control for Aircraft Based on Differential Flatness." Journal of Guidance, Control, and Dynamics 31, no. 4 (July 2008): 892–98. http://dx.doi.org/10.2514/1.33276.

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4

Liang, Dingkun, Ning Sun, Yiming Wu, and Yongchun Fang. "Differential Flatness-Based Robust Control of Self-balanced Robots." IFAC-PapersOnLine 51, no. 31 (2018): 949–54. http://dx.doi.org/10.1016/j.ifacol.2018.10.058.

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5

An, Ningbo, Qishao Wang, Xiaochuan Zhao, and Qingyun Wang. "Differential flatness-based distributed control of underactuated robot swarms." Applied Mathematics and Mechanics 44, no. 10 (September 30, 2023): 1777–90. http://dx.doi.org/10.1007/s10483-023-3040-8.

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6

Elango, P., and R. Mohan. "Trajectory optimisation of six degree of freedom aircraft using differential flatness." Aeronautical Journal 122, no. 1257 (November 2018): 1788–810. http://dx.doi.org/10.1017/aer.2018.99.

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ABSTRACTThe flatness of a six-degree-of-freedom (6DoF) aircraft model with conventional control surfaces – aileron, flap, rudder and elevator, along with thrust vectoring ability is established in this work. Trajectory optimisation of an aircraft can be cast as an inverse problem where the solution for control inputs that yield desired trajectories for certain states is sought. The solution to the inverse problems for certain systems is made tractable when they exhibit differential flatness. Flatness-based trajectory optimisation has a significant advantage over an equivalent collocation-based method in terms of computational efficiency and viability for real-time implementation. An application for the flatness of 6DoF aircraft is shown in the trajectory optimisation for dynamic soaring, and its connection with an equivalent 3DoF flatness-based implementation is also brought out. The results are compared with that from a collocation-based approach.

7

Silva-Ortigoza, Ramón, Magdalena Marciano-Melchor, Rogelio Ernesto García-Chávez, Alfredo Roldán-Caballero, Victor Manuel Hernández-Guzmán, Eduardo Hernández-Márquez, José Rafael García-Sánchez, Rocío García-Cortés, and Gilberto Silva-Ortigoza. "Robust Flatness-Based Tracking Control for a “Full-Bridge Buck Inverter–DC Motor” System." Mathematics 10, no. 21 (November 4, 2022): 4110. http://dx.doi.org/10.3390/math10214110.

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By developing a robust control strategy based on the differential flatness concept, this paper presents a solution for the bidirectional trajectory tracking task in the “full-bridge Buck inverter–DC motor” system. The robustness of the proposed control is achieved by taking advantage of the differential flatness property related to the mathematical model of the system. The performance of the control, designed via the flatness concept, is verified in two ways. The first is by implementing experimentally the flatness control and proposing different shapes for the desired angular velocity profiles. For this aim, a built prototype of the “full-bridge Buck inverter–DC motor” system, along with Matlab–Simulink and a DS1104 board from dSPACE are used. The second is via simulation results, i.e., by programming the system in closed-loop with the proposed control algorithm through Matlab–Simulink. The experimental and the simulation results are similar, thus demonstrating the effectiveness of the designed robust control even when abrupt electrical variations are considered in the system.

8

Mounier, Hugues, Silviu-Iulian Niculescu, Arben Cela, and Marcel Stefan Geamanu. "Flatness-based longitudinal vehicle control with embedded torque constraint." IMA Journal of Mathematical Control and Information 36, no. 3 (September 6, 2018): 729–44. http://dx.doi.org/10.1093/imamci/dny005.

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Abstract This paper aims at establishing a simple yet efficient solution to the problem of trajectory tracking with input constraint of a non-linear longitudinal vehicle model. We make use of differential flatness by embedding the constraint into the reference trajectory design.

9

Mahadevan, Radhakrishnan, Sunil K. Agrawal, and Francis J. Doyle III. "Differential flatness based nonlinear predictive control of fed-batch bioreactors." Control Engineering Practice 9, no. 8 (August 2001): 889–99. http://dx.doi.org/10.1016/s0967-0661(01)00054-5.

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10

Rauniyar, Shyam, Sameer Bhalla, Daegyun Choi, and Donghoon Kim. "EKF-SLAM for Quadcopter Using Differential Flatness-Based LQR Control." Electronics 12, no. 5 (February 24, 2023): 1113. http://dx.doi.org/10.3390/electronics12051113.

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SLAM (Simultaneous Localization And Mapping) in unmanned aerial vehicles can be an advantageous proposition during dangerous missions where aggressive maneuvers are paramount. This paper proposes to achieve it for a quadcopter using a differential flatness-based linear quadratic regulator while utilizing sensor measurements of an inertial measurement unit and light detection and ranging considering sensors’ constraints, such as a limited sensing range and field of view. Additionally, a strategy to reduce the computational effort of Extended Kalman Filter-based SLAM (EKF-SLAM) is proposed. To validate the performance of the proposed approach, this work considers a quadcopter traversing an 8-shape trajectory for two scenarios of known and unknown landmarks. The estimation errors for the quadcopter states are comparable for both cases. The accuracy of the proposed method is evident from the Root-Mean-Square Errors (RMSE) of 0.04 m, 0.04 m/s, and 0.34 deg for the position, velocity, and attitude estimation of the quadcopter, respectively, including the RMSE of 0.03 m for the landmark position estimation. Lastly, the averaged computational time for each step of EKF-SLAM with respect to the number of landmarks can help to strategically choose the respective number of landmarks for each step to maximize the use of sensor data and improve performance.

11

Wang, Yuxiao, Tao Chao, Songyan Wang, and Ming Yang. "Trajectory tracking control of hypersonic vehicle considering modeling uncertainty." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 233, no. 13 (February 20, 2019): 4779–87. http://dx.doi.org/10.1177/0954410019830811.

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The tightly coupled, highly nonlinear, and notoriously uncertain nature of hypersonic vehicle dynamics brings a great challenge to the control system design. In this paper, an integrated controller based on Differential flatness theory and L1 adaptive theory is designed, and a nonlinear disturbance observer is added to solve the problem of model uncertainty. Differential flatness is applied to the outer loop to linearize the nonlinear model, and L1 adaptive control is applied to the inner loop to stabilize the attitude. The combination realizes the complementarity of their shortcomings. It can not only retain the advantages of L1 adaptive controller, but also avoid wide range of state changes and makes it easy to design parameters satisfying global convergence. The computational order of differential flatness is also reduced and the design of nonlinear disturbance observer becomes feasible. Simulation results for the hypersonic vehicle are presented to demonstrate the effectiveness and robustness of the proposed control scheme.

12

Gil-Antonio, Leopoldo, Belem Saldivar, Otniel Portillo-Rodríguez, Juan Carlos Ávila-Vilchis, Pánfilo Raymundo Martínez-Rodríguez, and Rigoberto Martínez-Méndez. "Flatness-Based Control for the Maximum Power Point Tracking in a Photovoltaic System." Energies 12, no. 10 (May 15, 2019): 1843. http://dx.doi.org/10.3390/en12101843.

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Solar energy harvesting using Photovoltaic (PV) systems is one of the most popular sources of renewable energy, however the main drawback of PV systems is their low conversion efficiency. An optimal system operation requires an efficient tracking of the Maximum Power Point (MPP), which represents the maximum energy that can be extracted from the PV panel. This paper presents a novel control approach for the Maximum Power Point Tracking (MPPT) based on the differential flatness property of the Boost converter, which is one of the most used converters in PV systems. The underlying idea of the proposed control approach is to use the classical flatness-based trajectory tracking control where a reference voltage will be defined in terms of the maximum power provided by the PV panel. The effectiveness of the proposed controller is assessed through numerical simulations and experimental tests. The results show that the controller based on differential flatness is capable of converging in less than 0.15 s and, compared with other MPPT techniques, such as Incremental Conductance and Perturb and Observe, it improves the response against sudden changes in load or weather conditions, reducing the ringing in the output of the system. Based on the results, it can be inferred that the new flatness-based controller represents an alternative to improve the MPPT in PV systems, especially when they are subject to sudden load or weather changes.

13

AGUILAR-IBÁÑEZ, CARLOS, MIGUEL SUÁREZ-CASTAÑÓN, and HEBERTT SIRA-RAMÍREZ. "CONTROL OF THE CHUA'S SYSTEM BASED ON A DIFFERENTIAL FLATNESS APPROACH." International Journal of Bifurcation and Chaos 14, no. 03 (March 2004): 1059–69. http://dx.doi.org/10.1142/s0218127404009594.

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In this paper, we present a flatness based control approach for the stabilization and tracking problem, for the well-known Chua chaotic circuit, that includes an additional input. We introduce two feedback controller design options for the set-point stabilization and the trajectory tracking problem: a direct pole placement approach, and Generalized Proportional Integral (GPI) approach based only on measured inputs and outputs.

14

Rigatos, G., P. Siano, P. Wira, and V. Loia. "A PEM Fuel Cells Control Approach Based on Differential Flatness Theory." Intelligent Industrial Systems 2, no. 2 (May 20, 2016): 107–17. http://dx.doi.org/10.1007/s40903-016-0044-y.

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15

Rigatos, G., and P. Siano. "Differential Flatness Theory-Based Adaptive Fuzzy Control of Underactuated Nonlinear Systems." Intelligent Industrial Systems 2, no. 3 (June 3, 2016): 217–31. http://dx.doi.org/10.1007/s40903-016-0045-x.

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16

Lu, Hao, Cunjia Liu, Lei Guo, and Wen-Hua Chen. "Constrained anti-disturbance control for a quadrotor based on differential flatness." International Journal of Systems Science 48, no. 6 (October 20, 2016): 1182–93. http://dx.doi.org/10.1080/00207721.2016.1244307.

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17

Mauledoux, Mauricio, Edilberto Mejia-Ruda, Oscar Aviles Sanchez, Max Suell Dutra, and Alejandra Rojas Arias. "Design of Sliding Mode Based Differential Flatness Control of Leg-Wheel Hybrid Robot." Applied Mechanics and Materials 835 (May 2016): 681–86. http://dx.doi.org/10.4028/www.scientific.net/amm.835.681.

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The sliding mode based differential flatness control is used to stabilize the error dynamics in view of unmodeled dynamics employing position, velocity and acceleration as reference values but feeding back to system only the position and velocity measurements. This controller is able to plan trajectories of control gains within the proposed scheme of the controller. By above this paper describes a sliding mode based differential flatness control to a leg-wheel hybrid robot, in order to design a robotic prototype with the ability to move an uneven ground. To prove the controller working a simulation in Matlab-Simulink using Simmechanics is made. The result of this work shows a controller that is able to follow the reference trajectories without overshoots and small chattering.

18

Yao, Xinya, He Chen, and Zhenyue Fan. "Active Disturbance Rejection Control Approach for Double Pendulum Cranes with Variable Rope Lengths." Journal of Intelligent Systems and Control 1, no. 1 (October 30, 2022): 46–59. http://dx.doi.org/10.56578/jisc010105.

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The overhead crane is a typical underactuated system with complicated dynamics and strong couplings. It is widely employed to transport heavy cargoes in many industrial fields. Due to the complexity of working environments, however, cranes often encounter various unfavorable factors, which may degrade the transportation efficiency. To enhance control performance and anti-disturbance ability, this paper proposes an active disturbance rejection control approach based on differential flatness for double pendulum cranes with variable rope lengths. The proposed approach can position the trolley accurately, regulate rope length, and suppress the swing angles of the payload and the hook simultaneously. During the controller design, flat outputs were constructed based on differential flatness technique to deal with system couplings, and the results prove that double pendulum crane system is differentially flat. After that, model uncertainties and external disturbances were estimated by the designed extended state observer. On this basis, a controller was developed based on the feedback control technique. Finally, a series of simulations were carried out to show that the control scheme is effective and robust.

19

Eikyu, Wataru, Kazuma Sekiguchi, and Kenichiro Nonaka. "Differential Flatness-Based Parameter Estimation for Suspended Load Drones." Journal of Robotics and Mechatronics 35, no. 2 (April 20, 2023): 408–16. http://dx.doi.org/10.20965/jrm.2023.p0408.

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The transportation of goods by drones using cable towing has recently attracted considerable attention. When flying a suspended load drone, any discrepancy between the mathematical model and the actual drone deteriorates control performance. However, because some physical parameters are difficult to measure, creating an accurate mathematical model is extremely difficult. Therefore, we propose a parameter estimation method using differential flatness that can be extended for application to suspended load drones. This method overcomes the problem of dealing with higher-order derivatives of flat outputs and enables the estimation of physical parameters. In this study, we experimentally show that the proposed method improves trajectory tracking performance.

20

Alshahir, Ahmed, Mohammed Albekairi, Kamel Berriri, Hassen Mekki, Khaled Kaaniche, Shahr Alshahr, Bassam A. Alshammari, and Anis Sahbani. "Quadrotor UAV Dynamic Visual Servoing Based on Differential Flatness Theory." Applied Sciences 13, no. 12 (June 10, 2023): 7005. http://dx.doi.org/10.3390/app13127005.

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In this paper, we propose 2D dynamic visual servoing (Dynamic IBVS), where a quadrotor UAV tries to track a moving target using a single facing-down perspective camera. As an application, we propose the tracking of a car-type vehicle. In this case, data related to the altitude and the lateral angles have no importance for the visual system. Indeed, to perform the tracking, we only need to know the longitudinal displacements (along the x and y axes) and the orientation along the z-axis. However, those data are necessary for the quadrotor’s guidance problem. Thanks to the concept of differential flatness, we demonstrate that if we manage to extract the displacements according to the three axes and the orientation according to the yaw angle (the vertical axis) of the quadrotor, we can control all the other variables of the system. For this, we consider a camera equipped with a vertical stabilizer that keeps it in a vertical position during its movement (a gimbaled camera). Other specialized sensors measure information regarding altitude and lateral angles. In the case of classic 2D visual servoing, the elaboration of the kinematic torsor of the quadrotor in no way guarantees the physical realization of instructions, given that the quadrotor is an under-actuated system. Indeed, the setpoint has a dimension equal to six, while the quadrotor is controlled only by four inputs. In addition, the dynamics of a quadrotor are generally very fast, which requires a high-frequency control law. Furthermore, the complexity of the image processing stage can cause delays in motion control, which can lead to target loss. A new dynamic 2D visual servoing method (Dynamic IBVS) is proposed. This method makes it possible to generate in real time the necessary movements for the quadrotor in order to carry out the tracking of the target (vehicle) using a single point of this target as visual information. This point can represent the center of gravity of the target or any other part of it. A control by flatness has been proposed, which guarantees the controllability of the system and ensures the asymptotic convergence of the generated trajectory in the image plane. Numerical simulations are presented to show the effectiveness of the proposed control strategy.

21

García-Sánchez, José Rafael, Ramón Silva-Ortigoza, Salvador Tavera-Mosqueda, Celso Márquez-Sánchez, Victor Manuel Hernández-Guzmán, Mayra Antonio-Cruz, Gilberto Silva-Ortigoza, and Hind Taud. "Tracking Control for Mobile Robots Considering the Dynamics of All Their Subsystems: Experimental Implementation." Complexity 2017 (2017): 1–18. http://dx.doi.org/10.1155/2017/5318504.

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The trajectory tracking task in a wheeled mobile robot (WMR) is solved by proposing a three-level hierarchical controller that considers the mathematical model of the mechanical structure (differential drive WMR), actuators (DC motors), and power stage (DC/DC Buck power converters). The highest hierarchical level is a kinematic control for the mechanical structure; the medium level includes two controllers based on differential flatness for the actuators; and the lowest hierarchical level consists of two average controllers also based on differential flatness for the power stage. In order to experimentally validate the feasibility of the proposed control scheme, the hierarchical controller is implemented via a Σ–Δ-modulator in a differential drive WMR prototype that we have built. Such an implementation is achieved by using MATLAB-Simulink and the real-time interface ControlDesk together with a DS1104 board. The experimental results show the effectiveness and robustness of the proposed control scheme.

22

Rigatos, Gerasimos G., and Guilherme V. Raffo. "Input–Output Linearizing Control of the Underactuated Hovercraft Using the Derivative-Free Nonlinear Kalman Filter." Unmanned Systems 03, no. 02 (April 2015): 127–42. http://dx.doi.org/10.1142/s2301385015500089.

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The paper proposes a nonlinear control approach for the underactuated hovercraft model based on differential flatness theory and uses a new nonlinear state vector and disturbances estimation method under the name of derivative-free nonlinear Kalman filter. It is proven that the nonlinear model of the hovercraft is a differentially flat one. It is shown that this model cannot be subjected to static feedback linearization, however it admits dynamic feedback linearization which means that the system's state vector is extended by including as additional state variables the control inputs and their derivatives. Next, using the differential flatness properties it is also proven that this model can be subjected to input–output linearization and can be transformed to an equivalent canonical (Brunovsky) form. Based on this latter description the design of a state feedback controller is carried out enabling accurate maneuvering and trajectory tracking. Additional problems that are solved in the design of this feedback control scheme are the estimation of the nonmeasurable state variables in the hovercraft's model and the compensation of modeling uncertainties and external perturbations affecting the vessel. To this end, the application of the derivative-free nonlinear Kalman filter is proposed. This nonlinear filter consists of the Kalman Filter's recursion on the linearized equivalent model of the vessel and of an inverse nonlinear transformation based on the differential flatness features of the system which enables to compute estimates for the state variables of the initial nonlinear model. The redesign of the filter as a disturbance observer makes possible the estimation and compensation of additive perturbation terms affecting the hovercraft's model. The efficiency of the proposed nonlinear control and state estimation scheme is confirmed through simulation experiments.

23

Thounthong, P., S. Pierfederici, J. P. Martin, M. Hinaje, and B. Davat. "Modeling and Control of Fuel Cell/Supercapacitor Hybrid Source Based on Differential Flatness Control." IEEE Transactions on Vehicular Technology 59, no. 6 (July 2010): 2700–2710. http://dx.doi.org/10.1109/tvt.2010.2046759.

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24

Hagenmeyer, Veit, and Emmanuel Delaleau. "Robustness analysis of exact feedforward linearization based on differential flatness." Automatica 39, no. 11 (November 2003): 1941–46. http://dx.doi.org/10.1016/s0005-1098(03)00215-2.

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25

Gu, Xue Qiang, Yu Zhang, Jing Chen, and Lin Cheng Shen. "Real-Time Cooperative Trajectory Planning Using Differential Flatness Approach and B-Splines." Applied Mechanics and Materials 333-335 (July 2013): 1338–43. http://dx.doi.org/10.4028/www.scientific.net/amm.333-335.1338.

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This paper proposed a cooperative receding horizon optimal control framework, based on differential flatness and B-splines, which was used to solve the real-time cooperative trajectory planning for multi-UCAV performing cooperative air-to-ground target attack missions. The planning problem was formulated as a cooperative receding horizon optimal control problem (CRHC-OCP), and then the differential flatness and B-splines were introduced to lower the dimension of the planning space and parameterize the spatial trajectories. Moreover, for the dynamic and uncertainty of the battlefield environment, the cooperative receding horizon control was introduced. Finally, the proposed approach is demonstrated, and the results show that this approach is feasible and effective.

26

Greeff, Melissa, and Angela P. Schoellig. "Exploiting Differential Flatness for Robust Learning-Based Tracking Control Using Gaussian Processes." IEEE Control Systems Letters 5, no. 4 (October 2021): 1121–26. http://dx.doi.org/10.1109/lcsys.2020.3009177.

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27

Mehrasa, Majid, Edris Pouresmaeil, Shamsodin Taheri, Ionel Vechiu, and Joao P. S. Catalao. "Novel Control Strategy for Modular Multilevel Converters Based on Differential Flatness Theory." IEEE Journal of Emerging and Selected Topics in Power Electronics 6, no. 2 (June 2018): 888–97. http://dx.doi.org/10.1109/jestpe.2017.2766047.

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28

Poultney, Alexander, Christopher Kennedy, Garrett Clayton, and Hashem Ashrafiuon. "Robust Tracking Control of Quadrotors Based on Differential Flatness: Simulations and Experiments." IEEE/ASME Transactions on Mechatronics 23, no. 3 (June 2018): 1126–37. http://dx.doi.org/10.1109/tmech.2018.2820426.

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29

Zhang, Zhongcai, Yuqiang Wu, and Jinming Huang. "Differential-flatness-based finite-time anti-swing control of underactuated crane systems." Nonlinear Dynamics 87, no. 3 (October 25, 2016): 1749–61. http://dx.doi.org/10.1007/s11071-016-3149-7.

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30

Linares-Flores, Jesús, Bogdan García Rivera, Arturo Hernández-Méndez, José Juárez-Abad, and Antonio Orantes Molina. "Synchronization and Consensus of a Group of Direct Current Servo Motors Using the Differential Flatness Control Approach." Memorias del Congreso Nacional de Control Automático 6, no. 1 (October 27, 2023): 485–90. http://dx.doi.org/10.58571/cnca.amca.2023.065.

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This article deals with a differential flatness control leader-follower for a group of DC servo motors. Graph theory uses to design the form of connection and communication between servo motors. Each servo motor includes an integral action in its local control. In contrast, the input control law of the leader incorporates the speed desired reference trajectory, which will track each servo motor connected to the leader. The speed desired reference trajectory build employing a high-order Bezier polynomial-the experimental setup using the dSPACE equipment DS1104 model. The experimental results show the effectiveness and robustness of the synchronization and consensus of the control based on the differential flatness property for the group of DC servomotors.

31

Noda, Yoshiyuki, and Yuta Sueki. "Implementation and Experimental Verification of Flow Rate Control Based on Differential Flatness in a Tilting-Ladle-Type Automatic Pouring Machine." Applied Sciences 9, no. 10 (May 14, 2019): 1978. http://dx.doi.org/10.3390/app9101978.

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In this paper, we study an advanced pouring control system using a tilting-ladle-type automatic pouring machine. In such a machine, it is difficult to precisely pour the molten metal into the pouring basin of the mold, as the outflow from the ladle can be indirectly controlled by controlling its tilt. Therefore, model-based pouring control systems have been developed as a part of conventional studies to solve this problem. In the results of a recent study, the efficacy of a pouring flow rate control system based on differential flatness has been verified, by performing a simulation. In this study, we apply the flow rate control system based on differential flatness to a tilting-ladle-type automatic pouring machine, using experiments to verify the efficacy of the flow rate control system in suppressing any disturbances. In these experiments, the tracking performance using the developed flow rate control system was better than the performance obtained using a conventional feed-forward-type flow rate control system.

32

Wu, Dongli, Hao Zhang, Yunping Liu, Weihua Fang, and Yan Wang. "Real-Time Trajectory Planning and Control for Constrained UAV Based on Differential Flatness." International Journal of Aerospace Engineering 2022 (June 20, 2022): 1–17. http://dx.doi.org/10.1155/2022/8004478.

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The trajectory planning of UAV with nonholonomic constraints is usually taken as differential algebraic equation to solve the optimal control problem of functional extremum under the condition of inequality constraints. However, it can be challenging to meet the requirements of real-time for the high complexity. A differential flat theory based on B-spline trajectory planning can replace the optimal control problem with nonlinear programming and be a good means to achieve the efficient trajectory planning of an UAV under multiple dynamic constraints. This research verifies the feasibility of this theory with actual flight experiments.

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Yodwong, Burin, Phatiphat Thounthong, Damien Guilbert, and Nicu Bizon. "Differential Flatness-Based Cascade Energy/Current Control of Battery/Supercapacitor Hybrid Source for Modern e–Vehicle Applications." Mathematics 8, no. 5 (May 2, 2020): 704. http://dx.doi.org/10.3390/math8050704.

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This article proposes a new control law for an embedded DC distributed network supplied by a supercapacitor module (as a supplementary source) and a battery module (as the main generator) for transportation applications. A novel control algorithm based on the nonlinear differential flatness approach is studied and implemented in the laboratory. Using the differential flatness theory, straightforward solutions to nonlinear system stability problems and energy management have been developed. To evaluate the performance of the studied control technique, a hardware power electronics system is designed and implemented with a fully digital calculation (real-time system) realized with a MicroLabBox dSPACE platform (dual-core processor and FPGA). Obtained test bench results with a small scale prototype platform (a supercapacitor module of 160 V, 6 F and a battery module of 120 V, 40 Ah) corroborate the excellent control structure during drive cycles: steady-state and dynamics.

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Ryu, Ji-Chul, and Sunil K. Agrawal. "Differential flatness-based robust control of mobile robots in the presence of slip." International Journal of Robotics Research 30, no. 4 (December 7, 2010): 463–75. http://dx.doi.org/10.1177/0278364910385586.

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35

Rigatos, G. G. "Adaptive fuzzy control for non-linear dynamical systems based on differential flatness theory." IET Control Theory & Applications 6, no. 17 (November 15, 2012): 2644–56. http://dx.doi.org/10.1049/iet-cta.2011.0464.

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36

Thounthong, Phatiphat, Serge Pierfederici, and Bernard Davat. "Analysis of Differential Flatness-Based Control for a Fuel Cell Hybrid Power Source." IEEE Transactions on Energy Conversion 25, no. 3 (September 2010): 909–20. http://dx.doi.org/10.1109/tec.2010.2053037.

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37

Gil-Antonio, Leopoldo, Belem Saldivar, Otniel Portillo-Rodriguez, Gerardo Vazquez-Guzman, and Saul Montes De Oca-Armeaga. "Trajectory Tracking Control for a Boost Converter Based on the Differential Flatness Property." IEEE Access 7 (2019): 63437–46. http://dx.doi.org/10.1109/access.2019.2916472.

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38

RIGATOS, GERASIMOS, and EFTHYMIA RIGATOU. "SYNCHRONIZATION OF CIRCADIAN OSCILLATORS AND PROTEIN SYNTHESIS CONTROL USING THE DERIVATIVE-FREE NONLINEAR KALMAN FILTER." Journal of Biological Systems 22, no. 04 (November 11, 2014): 631–57. http://dx.doi.org/10.1142/s0218339014500259.

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The paper proposes a new method for synchronization of coupled circadian cells and for nonlinear control of the associated protein synthesis process using differential flatness theory and the derivative-free nonlinear Kalman filter. By proving that the dynamic model of the FRQ protein synthesis is a differentially flat one, its transformation to the linear canonical (Brunovsky) form becomes possible. For the transformed model, one can find a state feedback control input that makes the oscillatory characteristics in the concentration of the FRQ protein vary according to desirable setpoints. To estimate nonmeasurable elements of the state vector, the derivative-free nonlinear Kalman filter is used. The derivative-free nonlinear Kalman filter consists of the standard Kalman filter recursion on the linearized equivalent model of the coupled circadian cells and on computation of state and disturbance estimates using the diffeomorphism (relations about state variables transformation) provided by differential flatness theory. Moreover, to cope with parametric uncertainties in the model of the FRQ protein synthesis and with stochastic disturbances in measurements, the derivative-free nonlinear Kalman filter is redesigned in the form of a disturbance observer. The efficiency of the proposed Kalman filter-based control scheme is tested through simulation experiments.

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Schulze, Moritz, and René Schenkendorf. "Robust Model Selection: Flatness-Based Optimal Experimental Design for a Biocatalytic Reaction." Processes 8, no. 2 (February 5, 2020): 190. http://dx.doi.org/10.3390/pr8020190.

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Considering the competitive and strongly regulated pharmaceutical industry, mathematical modeling and process systems engineering might be useful tools for implementing quality by design (QbD) and quality by control (QbC) strategies for low-cost but high-quality drugs. However, a crucial task in modeling (bio)pharmaceutical manufacturing processes is the reliable identification of model candidates from a set of various model hypotheses. To identify the best experimental design suitable for a reliable model selection and system identification is challenging for nonlinear (bio)pharmaceutical process models in general. This paper is the first to exploit differential flatness for model selection problems under uncertainty, and thus translates the model selection problem to advanced concepts of systems theory and controllability aspects, respectively. Here, the optimal controls for improved model selection trajectories are expressed analytically with low computational costs. We further demonstrate the impact of parameter uncertainties on the differential flatness-based method and provide an effective robustification strategy with the point estimate method for uncertainty quantification. In a simulation study, we consider a biocatalytic reaction step simulating the carboligation of aldehydes, where we successfully derive optimal controls for improved model selection trajectories under uncertainty.

40

Li, Zongyang, Yiheng Wei, Xi Zhou, Jiachang Wang, Jianli Wang, and Yong Wang. "Differential flatness‐based ADRC scheme for underactuated fractional‐order systems." International Journal of Robust and Nonlinear Control 30, no. 7 (February 17, 2020): 2832–49. http://dx.doi.org/10.1002/rnc.4905.

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41

Tapia-Olvera, Ruben, Francisco Beltran-Carbajal, and Antonio Valderrabano-Gonzalez. "Adaptive Neural Trajectory Tracking Control for Synchronous Generators in Interconnected Power Systems." Applied Sciences 13, no. 1 (December 31, 2022): 561. http://dx.doi.org/10.3390/app13010561.

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The synchronous generator is one of the most important active components in current electric power systems. New control methods should be designed to guarantee an efficient dynamic performance of the synchronous generator in strongly interconnected nonlinear power systems over a wide range of variable operating conditions. In this context, active suppression capability for different uncertainties and external disturbances represents a current trend in the development of new control design methodologies. In this paper, a new adaptive neural control scheme based on differential flatness with a modified structure including B-spline Neural Networks for transient stabilization and tracking of power-angle reference profiles for synchronous generators in interconnected electric power systems is introduced. These features are attained due to the advantages extracted of these two approaches: (a) a control design stage based on a power system model by differential flatness and (b) an adaptive performance using a correct design of B-spline Neural Networks, minimizing parameter dependency. The effectiveness of the proposed algorithm is demonstrated by simulation results in two test systems: single machine infinite bus and an interconnected power system. Transient stability and robust power-angle reference profile tracking are both verified.

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Stumper, Jean-Francois, Veit Hagenmeyer, Sascha Kuehl, and Ralph Kennel. "Deadbeat Control for Electrical Drives: A Robust and Performant Design Based on Differential Flatness." IEEE Transactions on Power Electronics 30, no. 8 (August 2015): 4585–96. http://dx.doi.org/10.1109/tpel.2014.2359971.

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43

Tang, Chin Pei, Patrick T. Miller, Venkat N. Krovi, Ji-Chul Ryu, and Sunil K. Agrawal. "Differential-Flatness-Based Planning and Control of a Wheeled Mobile Manipulator—Theory and Experiment." IEEE/ASME Transactions on Mechatronics 16, no. 4 (August 2011): 768–73. http://dx.doi.org/10.1109/tmech.2010.2066282.

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44

Xia, Yuanqing, Fan Pu, Shengfei Li, and Yuan Gao. "Lateral Path Tracking Control of Autonomous Land Vehicle Based on ADRC and Differential Flatness." IEEE Transactions on Industrial Electronics 63, no. 5 (May 2016): 3091–99. http://dx.doi.org/10.1109/tie.2016.2531021.

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45

Sanchez, L. V., A. B. Oertega, and C. D. G. Beltran. "Trajectory Tracking Of An IMC Control Based On Differential Flatness For An Electric Machine." IEEE Latin America Transactions 16, no. 3 (March 2018): 785–91. http://dx.doi.org/10.1109/tla.2018.8358656.

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46

Li, Guang. "Nonlinear model predictive control of a wave energy converter based on differential flatness parameterisation." International Journal of Control 90, no. 1 (September 30, 2015): 68–77. http://dx.doi.org/10.1080/00207179.2015.1088173.

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47

Silva-Ortigoza, R., C. Márquez-Sánchez, F. Carrizosa-Corral, M. Antonio-Cruz, J. M. Alba-Martínez, and G. Saldaña-González. "Hierarchical Velocity Control Based on Differential Flatness for a DC/DC Buck Converter-DC Motor System." Mathematical Problems in Engineering 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/912815.

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This paper presents a hierarchical controller that carries out the angular velocity trajectory tracking task for a DC motor driven by a DC/DC Buck converter. The high level control is related to the DC motor and the low level control is dedicated to the DC/DC Buck converter; both controls are designed via differential flatness. The high level control provides a desired voltage profile for the DC motor to achieve the tracking of a desired angular velocity trajectory. Then, a low level control is designed to ensure that the output voltage of the DC/DC Buck converter tracks the voltage profile imposed by the high level control. In order to experimentally verify the hierarchical controller performance, a DS1104 electronic board from dSPACE and Matlab-Simulink are used. The switched implementation of the hierarchical average controller is accomplished by means of pulse width modulation. Experimental results of the hierarchical controller for the velocity trajectory tracking task show good performance and robustness against the uncertainties associated with different system parameters.

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Saied, M., T. Mahairy, C. Francis, H. Shraim, H. Mazeh, and M. El Rafei. "Differential Flatness-Based Approach for Sensors and Actuators Fault Diagnosis of a Multirotor UAV." IFAC-PapersOnLine 52, no. 16 (2019): 831–36. http://dx.doi.org/10.1016/j.ifacol.2019.12.066.

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49

AOKI, Nobuaki, and Tomoaki KOBAYASHI. "Differential flatness based control design for input and state constrained nonlinear systems via control Lyapunov barrier functions." Proceedings of Conference of Kansai Branch 2018.93 (2018): 721. http://dx.doi.org/10.1299/jsmekansai.2018.93.721.

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50

Sriprang, Songklod, Nitchamon Poonnoy, Damien Guilbert, Babak Nahid-Mobarakeh, Noureddine Takorabet, Nicu Bizon, and Phatiphat Thounthong. "Design, Modeling, and Differential Flatness Based Control of Permanent Magnet-Assisted Synchronous Reluctance Motor for e-Vehicle Applications." Sustainability 13, no. 17 (August 24, 2021): 9502. http://dx.doi.org/10.3390/su13179502.

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This paper presents the utilization of differential flatness techniques from nonlinear control theory to permanent magnet assisted (PMa) synchronous reluctance motor (SynRM). The significant advantage of the proposed control approach is the potentiality to establish the behavior of the state variable system during the steady-state and transients operations as well. The mathematical models of PMa-SynRM are initially proved by the nonlinear case to show the flatness property. Then, the intelligent proportional-integral (iPI) is utilized as a control law to deal with some inevitable modeling errors and uncertainties for the torque and speed of the motor. Finally, a MicroLab Box dSPACE has been employed to implement the proposed control scheme. A small-scale test bench 1-KW relying on the PMa-SynRM has been designed and developed in the laboratory to approve the proposed control algorithm. The experimental results reflect that the proposed control effectively performs high performance during dynamic operating conditions for the inner torque loop control and outer speed loop control of the motor drive compared to the traditional PI control.