Optimum Design of Decentralized Magnetic Bearings for Rotor Systems

Magnetic bearings are currently being explored as viable alternatives to existing hydrodynamic or rolling element support devices for high speed rotating machinery in various applications. Incorporation of active magnetic bearings into rotor systems can lead to enhanced stability characteristics by proper choice of the feedback control law. Traditionally low-order PD type controllers or high-order LQR/LQG based controllers have been used for such bearings. In this paper, a method of designing low—order decentralized magnetic bearing controllers for high-order plants is proposed. The controller is represented by a minimum set of design parameters (numerator and denominator coefficients of the transfer functions of the controller), and the optimum controller parameters are obtained by means of a numerical search in the parameter space. The various design specifications for such a design could be insurance of stability, boundedness of design parameters within upper and lower limits, placement of closed-loop eigenvalues within an acceptable region in the complex plane, and avoidance of closed—loop eigenfrequendes from an envelope around the rotor operating speed. Satisfaction of the multiple specifications is attempted by solving the problem as a sequence of constrained minimization problems, with more and more constraints being introduced in each subsequent stage. The design requirements specified in terms of the closed—loop characteristics of the system are achieved through a step by step process. The algorithm utilizes the method of feasible directions to solve the nonlinear constrained minimization problem at each stage. This methodology emphasizes the designer's interaction with the algorithm to generate acceptable controller designs by changing various specifications and altering the initial guesses interactively. A graphical interface has been developed to facilitate design interaction by the user.