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.

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