Model-Free Control of an Unmanned Aircraft Quadcopter Type System

A model-free control algorithm based on the sliding mode control method for unmanned aircraft systems is proposed. The mathematical model of the dynamic system is not required to derive the sliding mode control law for this proposed method. The knowledge of the system’s order, state measurements and control input gain matrix shape and bounds are assumed to derive the control law to track the required trajectories. Lyapunov’s Stability criteria is used to ensure closed-loop asymptotic stability and the error estimate between previous control inputs is used to stabilize the system. A smoothing boundary layer is introduced into the system to eliminate the high frequency chattering of the control input and the higher order states. The [B] matrix used in the model-free algorithm based on the sliding mode control is derived for a quadcopter system. A simulation of a quadcopter is built in Simulink and the model-free control algorithm based on sliding mode control is implemented and a PID control law is used to compare the performance of the model-free control algorithm based off of the RMS (Root-Mean-Square) of the difference between the actual state and the desired state as well as average power usage. The model-free algorithm outperformed the PID controller in all simulations with the quadcopter’s original parameters, double the mass, double the moments of inertia, and double both the mass and the moments of inertia while keep both controllers exactly the same for each simulation

A Model-Free Control Algorithm Based on the Sliding Mode Control Method with Applications to Unmanned Aircraft Systems

Control methods require the use of a system model for the design and tuning of the controllers in meeting and/or exceeding the control system performance objectives. However, system models contain errors and uncertainties that also may be complex to develop and to generalize for a large class of systems such as those for unmanned aircraft systems. In particular, the sliding control method is a superior robust nonlinear control approach due to the direct handling of nonlinearities and uncertainties that can be used in tracking problems for unmanned aircraft system. However, the derivation of the sliding mode control law is tedious since a unique and distinct control law needs to be derived for every individual system and cannot be applied to general systems that may encompass all classifications of unmanned aircraft systems. In this work, a model-free control algorithm based on the sliding mode control method is developed and generalized for all classes of unmanned aircraft systems used in robust tracking control applications. The model-free control algorithm is derived with knowledge of the system’s order, state measurements, and control input gain matrix shape and bounds and is not dependent on a mathematical system model. The derived control law is tested using a high-fidelity simulation of a quadrotor-type unmanned aircraft system and the results are compared to a traditional linear controller for tracking performance and power consumption. Realistic type hardware inputs from joysticks and inertial measurement units were simulated for the analysis. Finally, the model-free control algorithm was implemented on a quadrotor-type unmanned aircraft system testbed used in real flight experimental testing. The experimental tracking performance and power consumption was analyzed and compared to a traditional linear-type controller. Results showed that the model-free approach is superior in tracking performance and power consumption compared to traditional linear-type control strategies

A Model-Free Control System Based on the Sliding Mode Control Method with Applications to Multi-Input-Multi-Output Systems

In this work, a model-free sliding mode control technique for linear and nonlinear uncertain multi-input multi-output systems is proposed. The developed method does not require a mathematical model of the dynamic system. Instead, knowledge of the system’s order, state measurements, and control input gain matrix shape and bounds are assumed to develop the control law and drive the system’s states to track a desired trajectory. The control system relies on estimating the error between previous and current control inputs to stabilize the system. Lyapunov’s stability criterion is used in the derivation process to ensure closed-loop asymptotic stability. High frequency chattering of the control input and higher-order states, often observed with the sliding mode control method, is eliminated using a smoothing boundary layer. Simulations are performed on a variety of linear and nonlinear systems, including a quadrotor model, to test the performance of the control law. Finally, the model-free sliding mode control system is modified to account for the effects of actuator time-delays

A Model-Free Control Algorithm Derived Using the Sliding Model Control Method

In this work, a model-free sliding mode control scheme is derived and applied to linear and nonlinear systems that is solely based on observable measurements and therefore does not require a theoretical system model in developing the controller form. The general sliding mode controller form is derived for an nth-order system and is strictly limited to a single-input unit input influence gain case for this work. The controller form is based solely on system measurements assuming the order of the system is known. The switching gain form is developed so that stability of the closed-loop sliding mode controller system is guaranteed using Lyapunov’s Direct Method. The controller form is reformulated using a smoothing moving boundary layer to eliminate chattering of the control effort. A simulation study is presented for a single-input unit input influence gain case applied to both a linear and nonlinear system with and without a smoothing boundary layer. The measurement based controller form is shown to be identical regardless of the system’s kinematics to be controlled assuming the order is known. Results of the simulation efforts show good state tracking performance is achieved with stable convergence for the tracking performance regardless of the system to be controlled

A New Model-Free Sliding Mode Control Method with Estimation of Control Input Error

A new type of sliding mode controller scheme, which requires no knowledge of system model, is derived in this work. The controller is solely based on previous control inputs and state measurements to generate the updated control input effort. The only knowledge required to derive the controller is the system order and the bounds of the control input gain, if one exists. The switching gain, which is required to drive the system states onto the sliding surface in the presence of disturbances and uncertainties, is derived using Lyapunov’s stability theorem, ensuring closed-loop asymptotic stability. The chattering effect, which is excited by the switching gain due to high activity of the control input, is reduced by using a smoothing boundary layer into the control law form. Simulations are performed, using first and second-order, linear and nonlinear systems, to test the performance of the new control law. In the last part of this work, the problem with state measurement noise is addressed. Results of the simulations validates the feasibility of the proposed control scheme

A Model-Free Control System Based on the Sliding Mode Control with Automatic Tuning Using as On-Line Parameter Estimation Approach

The sliding mode control algorithm and Lyapunov-based methods, have received much attention recently due to their ability to directly handle nonlinear systems while guaranteeing closed-loop tracking stability. In this work, a unique model-free sliding mode control technique has developed solely based on previous control inputs. The new method requires only knowledge of the system order and state measurements and does not require a theoretical model of the dynamic system. Lyapunov’s stability theorem is used in the controller formulation process to ensure closed-loop asymptotic stability. High frequency chattering of the control effort is reduced by using a smoothing boundary layer into the control law. Parameters variation during control operating and noise effect cannot be handled by the model-free controller if the controller tuning parameters are chosen arbitrarily since tracking performance becomes unacceptable. In addition, in previous work, the bounds of the input influence gain parameters were assumed to be known to derive the model-free controller. Therefore, in this work, a new approach is proposed for estimating the increment to the switching gain in real-time to ensure the sliding condition (which guarantees closed-loop tracking stability) is satisfied using a control law form that assumes a strictly unitary input influence gain. In formulation of estimation law, an exponential forgetting factor is combined with the least-squares estimator to ensure the updated data are used and past data are excluded. An automatic bounded forgetting tuning technique is developed to maintain the benefits of data forgetting while avoiding the possibility of gain unboundedness in absence of persistent excitation. The tuning estimator is assured that the resulting gain matrix is upper bounded regardless of the persistent excitation by suspending the data forgetting if the gain matrix reaches the specified upper bound. Simulations are performed on a series of linear and nonlinear SISO and MIMO systems with and without including actuator time-delay effects. Finally, a model is developed to simulate a quadcopter as a real-world application case. In all cases, the controller achieved perfect or near-perfect tracking performance using updated controller and on-line estimator tuning process

Model Free Control Based on Integral Sliding Modes for Underactuated Underwater Robots.

[EN] A combination of a model-free control law at the dynamic level and a guidance law at the kinematic level is proposed for the tracking of an underactuated underwater robot vehicle. The closed-loop system gives rise to chattering-free integral sliding modes for local exponential tracking of actuated coordinates, while ensuring a global stable internal dynamics under certain conditions easy to meet in practice. The design methodology relies on a careful manipulation of the quasi-lagrangian model of the underwater vehicle with a control law that is independent of dynamic model and its parameters assuming full access to the state. Comparative simulations versus a PID show the feasibility and robust behavior under parametric and model uncertainties.[ES] Se propone la combinación de una ley de control libre de modelo dinámico, en conjunto con una ley de guiado cinemático, para el seguimiento de trayectorias actuadas de un vehículo robo‘tico submarino subactuado. El sistema en lazo cerrado da lugar a modos deslizantes integrales, libres de castañeo, que garantizan la estabilidad exponencial local del seguimiento de las coordenadas actuadas con dinámica interna estable, bajo condiciones fáciles de encontrar en la práctica. La metodología del diseño se basa en una manipulación cuidadosa del modelo cuasilagrangiano de vehículos submarinos y de una ley de control que es independiente del modelo y sus parámetros, asumiendo acceso total del estado. Simulaciones comparativas considerando el PID convencional ilustran la factibilidad del control en las condiciones establecidas ante incertidumbres paramétricas y del modelo.Proyecto realizado parcialmente con financiamiento de los contratos #133346, #174597 y #21969 de CONACyT de MéxicoRaygosa Barahona, R.; Olguín Díaz, E.; Parra Vega, V.; Muñoz Ubando, L. (2015). Control Libre de Modelo basado en Modos Deslizantes Integrales para Robots Submarinos Subactuados. Revista Iberoamericana de Automática e Informática industrial. 12(3):313-324. https://doi.org/10.1016/j.riai.2015.04.004OJS313324123Antoneilli, G., 2006. Underwater Robots. Springer.Blanke, M., Lindegaard, K.P., Fossen, T.I., 2000. Dynamic model for thrust generation of marine propellers. presented at the Proc. IFAC Conf. Manoeuvreing of Marine Craft. Aalborg Denamark, Aug. 2000, pp. 23-25.Breivik, M., Fossen, T., 2009. Guidance laws for autonomous underwater vehicles. In: In Intelligent Underwater Vehicles. I-Tech Education and Publishing (A. V. Inzartsev, Ed.), Vienna.Brogliato, B., Lozano, R., Maschke, B., Egeland, O., 2007. Dissipative systems analysis and control: theory and applications, 2nd Edition.Byrnes, C., Isidori, A., October 1991. Asymptotic stabilization of minimum phase nonlinear systems. IEEE Tansactions on Automatic Control 36 (10).Chin, C., Lau, M., Low, E., Set, G., 2006. Software for modelling and simulation of a remotely-operated vehicle. Int. J. Simul. Model 5 (3), 114-125.Chun Nan, Tong Ge, 2012. Model-free high order sliding controller for under-water vehicle with transient process. Advanced Materials Research 591-593.Fossen, T., 2011. Handbook of marine craft hydrodynamics and motion control. John Wiley and Sons LTD, Institut for teknisk kybernetikk NTNU.Healey, A., Leanard, D., July 1993. Multivariable sliding mode control for autonomous diving and steering of unmanned underwater vehicles. IEEE Journal of Oceanic Engineering, Vol. 18, No. 3, July 18 (3).Krstic, M., Kanellakopoulos, I., Kokotovich, P., 1995. Nonlinear and Adaptive Control Design. John Wiley and Sons.Leonard, N., 1997. Stability of a bottom-heavy underwater vehicle. Automatica 33 (3), 331-346.Meirovich, L., 2003. Methods of Analytical Dynamics. Dover Publications, New York.Olfati-Saber, R., February 2000. Nonlinear control of underactuated mechanical systems with applications to robotics and aerospace vehicles. Ph.D. thesis, M.I.T., Massachusetts.Olguín-Díaz, E., Arechavaleta, G., Jarquin, G., Parra-Vega, V., December 2013. A passivity-based model-free force–motion control of underwater vehicle-manipulator systems. IEEE Transactions on Robotics 29 (6), 1469-1484.Olguín-Díaz, E., Parra-Vega, V., 2007. On the force/posture control of a constrained submarine robot. In: 4th International Conference on Informatics in Control, Robotics and Automation, Conference Prodeedings.Parra-Vega, V., Arimoto, S., Li, Y.-H., Hirzinger, G., Akella, P., December 2003. Dynamic sliding pid control for tracking of robot manipulators. IEEE Transactions on Robotic and Automation 19 (6), 967-976.Perrier, M., Canudas de Wit, C., 1996. Experimental comparison of pid vs. pid plus nonlinear controller for subsea robots. In: Autonomous Robots. pp. 195-212.Raygosa-Barahona, R., Parra-Vega, V., Olguín-Díaz, E., Munoz-Ubando, A., October 2011. A model-free backstepping with integral sliding mode control for underactuated rovs. In: Electrical Engineering Computing Science and Automatic Control (CCE), 8th International Conference on. pp. 1-7.Sagatun, S., Fossen, T., 1991. Lagrangian formulation of underwater vehicles dynamics. In: Proceedings on International Conference on Systems, Man, and Cybernetics, IEEE. Noruega.Smallwood, D.A., Whitcomb, L.L., 2001. Preliminary experiments in the adaptive identification of dynamically positioned underwater robotic vehicles. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems. pp. 1803-1810.Smallwood, D.A., Whitcomb, L.L., 2004. Model-based dynamic positioning of underwater robotic vehicles: Theory and experiment. IEEE Journal of Oceanic Engineering 29, 1.Spong, M., 1994. Partial feedback linearization of underactuated mechanical systems. In: Intelligent Robots and Systems’94’Advanced Robotic Systems and the Real World’, IROS’94. Vol. 1. pp. 314-321 vol.1.Tedrake, R., March 2010. Underactuated Robotics. MIT Press.García-Valdovinos, L.G., Salgado, T., Torres, H., 2009. Model-free high order sliding mode control for rov: Station-keeping approach. In: Proceedings of the MTS/IEEE Oceans, pp. 1-7.Whitcomb, L., Stephen, M., 2013. Preliminary experiments in fully actuated model based control with six degree-of-freedom coupled dynamic plant models for underwater vehicles. In: Proceedings of the IEEE International Conference on Robotics and Automation.Yoerger, D., Slotine, J., 1991. Adaptive sliding control of an experimental underwater vehicle. In: Proceedings of the IEEE International Conference on Robotics and Automation