A new approach for quasi-LPV modeling and state-feedback control of nonlinear systems with application on a 5-DOF pendulum

This paper presents a new approach for quasi linear parameter-varying (LPV) modeling and state-feedback control of a class of nonlinear systems. In terms of modeling, it is proposed as contribution a Taylor series expansion of arbitrary degree, giving rise to a polynomial quasi-LPV model capable to represent nonlinear systems around an operating point with more accuracy than the standard linear time-invariant (LTI) model. In addition, an H2 gain-scheduled state-feedback synthesis condition is proposed to deal with the polynomial quasi-LPV models generated by the proposed technique. To illustrate the approach, a case study based on a 5-DOF pendulum is investigated in details. Two numerical experiments are performed. The first one performs an open-loop test, comparing the proposed polynomial quasi-LPV model, the standard LTI model and the nonlinear model. The second test relies on a closed-loop simulation to demonstrate the performance of gain-scheduled controller designed with the proposed synthesis conditions.