The performance of Multivariable Step-Wise Safe Switching Iterative Feedback Tuning is studied for a constant turning force system under varying cutting conditions. The tuning technique does not use a plant's model, neither nonlinear or approximate linearized, and is based on specific experiments performed on the closed-loop plant. Controller parameter tuning aims to achieve minimization of a quadratic performance criterion, that limits cutting force deviations from a desired value, as cutting depth varies with time. A state feedback PI controller is combined with a state observer estimating the acceleration of the servomechanism feeding the cutting machine. The proposed tuning algorithm is shown through simulation results to improve the performance of "common" controllers initially tuned through a metaheuristic search algorithm.