A Combined Path-Following and Model Predictive Control Scheme for kite trajectory control in Airborne Wind Energy Systems

In crosswind Airborne Wind Energy Systems (AWES) the kite must portray an optimized periodical motion. Such behavior can be achieved by a previous specification of a geometric path which is then to be followed by means of a path following controller (dividing the optimization problem of a power maximizing kite controller into two problems: path planning and path following). This work will address the path following issue. We will part from a modification of a well known nonlinear guidance logic, which computes the kite reference heading angle based on the required centripetal acceleration for the kite to join the path in a given reference point [1][2]. This guidance logic has been proven to be asymptotically stable in the whole state space, although it does not provide an optimal control input. To achieve a high performance controller and thus maximize the system power production, optimization based tools, such as Model Predictive Control (MPC), should be used. MPC strategies are known for their ability to deal adequately with input and state constraints. However, their real time application in fast paced nonlinear systems can be difficult. Joining a (traditional) path following controller and a MPC term in a combined architecture can help to surpass some of these difficulties. In this manner, the MPC term serves as a performance booster of an already functioning and stabilizing basis controller (while guaranteeing compliance with input and state constraints) and the basis controller serves as an initial guess for the optimization process (thus increasing its efficiency) as well as a backup plan in case the optimization procedure fails to deliver a solution in due time. Besides, a proper choice of MPC design parameters has been shown to assure the stability of this MPC component, therefore, this term can be designed in a way that does not jeopardize the stability of the already stable basis controller [3]. This work will comprehend a combined controller, joining a path following controller based on a nonlinear guidance logic, entitled “L0 controller” [1], and a MPC term, whose cost functions are based on a Lyapunov function pair, contrasting with a conventional quadratic error design. -References: [1] M.C.R.M. Fernandes, S. Vinha, L.T. Paiva, and F.A.C.C. Fontes, “L0 and L1 Guidance and Path-Following Control for Airborne Wind Energy Systems,” Energies, vol. 15, no. 4, pp. 1390, Feb. 2022. [2] G.B. Silva, L.T. Paiva, and F. A. Fontes, “A Path-following Guidance Method for Airborne Wind Energy Systems with Large Domain of Attraction,” in 2019 American Control Conference (ACC), pp. 2771–2776, Jul. 2019. [3] F.A.C.C. Fontes, “A general framework to design stabilizing nonlinear model predictive controllers,” Systems and Control Letters, vol. 42, no. 2, pp. 127–143, 2001.Also funded by FCT Grant 2021.07346.B