Uncertainty Modelling of Mechanical Systems with Derivative Behaviour for Robust Control Synthesis

This paper proposes a comparative study of uncertainty modelling approaches for inverted-pendulum type mechanical systems with input-output derivative behaviour to be directly used for robust controller synthesis. Besides three approaches from the literature to obtain the mathematical model of the parametric uncertainties, we propose an additional nonlinear optimization-based approach, which manages to maintain the reduced-order structure of the convex optimization fit, but with better performance and robustness attainable through less conservativeness of the obtained model. A numerical case study is presented for a set of parameter values and tolerances with a closed-loop shaping design procedure.