State feedback control for stabilization of PMSM-based servo-drive with parametric uncertainty using interval analysis

Abstract

For a class of multivariable uncertain dynamic systems, the parametric uncertainties are belonging to a closed interval with lower and upper boundaries a priori known. Thereby, these systems can be analyzed based on interval structures and interval matrices. In this article, a fully interval analysis–based method is developed and applied to the state feedback control of permanent magnet synchronous motor (PMSM) in order to design a stabilized servo-drive. Indeed, the parametric uncertainties are investigated in state space representation, which represents a simplified and effective way to analyze the robust stability for the interval system. Firstly, a robust state feedback control technique, dedicated to an uncertain system is introduced. For that, the robust controllability test is performed for the interval system by using the linear independency condition of column interval vectors. It is proven that there is a direct correlation between the controllability test and the existence of a robust modal P-regulator for the correction of the uncertain system. It is also shown that it invariably relies on each input's controllability indices and thus their effect on the uncertain system's state variables. In order to ensure stability in a closed loop, the modal P-regulator is designed with possibility of incorporation of an integral action. The modified modal PI regulator has the ability to reject disturbance and guarantee zero-steady-state error for step inputs. In fact, the stability is achieved by placing all coefficients of the system characteristic polynomial within assigned intervals based on Kharitonov's Theorem. The technique provides a matrix gain with interval coefficients for the stabilizing regulator. Finally, the developed approach is applied to position control of linearized model of the PMSM-based servo-drive, presenting parametrical uncertainties. To demonstrate the efficiency of the proposed method, a numerical and graphical comparison of conventional LQR and pole placement, state feedback controllers for the PMSM servo-drive with the robust interval controller is provided. In order to verify the feasibility of the whole proposed technique, calculations and simulations are performed by using Matlab/Intlab toolbox. Real-time simulation is also investigated using Lab-View Compact-RIO