Linear parameter-varying control of complex mechanical systems

In standard linear fractional representation (LFR)-based linear parameter-varying (LPV) modeling the size of the (diagonal) scheduling block depends on the number of scheduling parameters and their repetitions, which in turn influences both the complexity of synthesis conditions and the computational load during online implementation of LPV controllers. A modeling framework motivated by, but not limited to, mechanical systems is proposed, where the size of the scheduling block depends on the system's physical degrees-of-freedom. The scheduling block then turns out block-diagonal and can be parameterized in an affine or rational manner. This parameterization yields less complex LFRs when considering the example of a three degrees-of-freedom robotic manipulator, for which then full-block multipliers are tractable and also necessary in synthesis. Synthesis and both simulation and experimental implementation results indicate that the novel rational LPV controller provides improved performance at both reduced implementation and synthesis complexity as compared to an affine LPV controller.