On the Discretization of Linear Fractional Representations of LPV Systems


Commonly, controllers for linear parameter-varying (LPV) systems are designed in continuous time employing a linear fractional representation (LFR) of the plant. But, the resulting controllers are implemented on digital hardware. Furthermore, discrete-time LPV synthesis approaches need a discrete-time model of the plant that is usually derived from endless-time initial-principle model. Existing discretization approaches for LFRs describing LPV systems suffer from disadvantages like the possibility of significant approximation errors, issues of complexity, etc. To explore the disadvantages, existing discretization ways are reviewed and novel approaches are derived to beat them. The proposed and existing ways are compared and analyzed in terms of approximation error, considering ideal zero-order hold actuation and sampling. Criteria to choose acceptable sampling times with respect to the investigated ways also are presented. The proposed discretization ways are tested and compared both on a simulation example and on the electronic throttle management problem of a race motorcycle.

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