Prof. Dr. Diego Eckhard

Quadcopter is a type of Unmanned Aerial Vehicle which is lifted and propelled by four rotors. The vehicle has a complex non-linear dynamic which makes the tuning of the roll and pitch controllers difficult. Usually the control design is based on a mathematical model which is strongly related to physical components of vehicle: mass, moment of inertia and aerodynamic. When a tool is attached to the vehicle, a new model must be computed to redesign the controllers. In this article we will adjust the controllers of a real experimental quadcopter using the Cascade Iterative Feedback Tuning method. The method is data-driven, so it does not uses a model for the vehicle; all it uses is input-output data collect from the closed-loop system. The method minimizes the \{H2\} error between the desired response and the actual response of the vehicle angle using the Newton-Raphson algorithm. The method achieves the desired performance without the need of the vehicle model, with low cost and low complexity.

Data-based control design methods consist of adjusting the parameters of the controller directly from batches of input-output data of the process; no process model is used. The adjustment is done by solving an optimization problem, which searches the argument that minimizes a specific cost function. Iterative algorithms based on the gradient are applied to solve the optimization problem, like the steepest descent algorithm, Newton algorithm and some variations. The only information utilized for the steepest descent algorithm is the gradient of the cost function, while the others need more information like the hessian. Longer and more complex experiments are used to obtain more informations, that turns the application more complicated. For this reason, the steepest descent method was chosen to be studied in this work. The convergence of the steepest descent algorithm to the global minimum is not fully studied in the literature. This convergence depends on the initial conditions of the algorithm and on the step size. The initial conditions must be inside a specific domain of attraction, and how to enlarge this domain is treated by the methodology Cost Function Shaping. The main contribution of this work is a method to compute efficiently the step size, to ensure convergence to the global minimum. Some informations about the process are utilized, and this work presents how to estimate these informations. Simulations and experiments demonstrate how the methods work.