Design of robust optimal Linear Parameter Varying (LPV) controller for DC servo system

Abstract

This paper presents the design of a robust optimal control system satisfying some system performance constraints The design problem is a problem of dynamic feedback, mixed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> robust optimal control systems with multi constraints and parametric uncertainties. The main purpose of the robust optimal Linear Parameter Varying (LPV) control is to parametrize a controller via a linear convex combination of all controllers minimizing mixed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> norm of the closed loop transfer function matrix under parametric uncertainties and some constraints. In this paper, mixed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance index is minimized under the constraints of H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> performance, H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance, control input constraints and the regional pole placement. The LPV control synthesis with multi constraints is formulated as a convex optimization problem involving Linear Matrix Inequalities(LMIs). A linear parameter varying (LPV) controller design example for the control of a DC servo motor system is presented.