Partial Pole Placement in LMI Region

Abstract

A new approach for pole placement of single-input system is proposed in this paper. Noncritical closed loop poles can be placed arbitrarily in a specified convex region when dominant poles are fixed in anticipant locations. The convex region is expressed in the form of linear matrix inequality (LMI), with which the partial pole placement problem can be solved via convex optimization tools. The validity and applicability of this approach are illustrated by two examples.

Pole Assignment for Active Vibration Control of Linear Vibrating Systems through Linear Matrix Inequalities

“…The assignment of the dynamic response of vibrating mechanical systems, such as structures, mechanisms, or multibody systems, is often performed by properly assigning the poles of the controlled systems. Both active feedback control [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] and passive approaches (i.e., parameter modifications, see e.g., [19][20][21]) or are exploited to accomplish this important task. Indeed, the system poles, which are often denoted as the eigenvalues, define the system stability as well as the properties of the transient response such as the damping ratio, the rise time, and the settling time.…”

“…In practice, it is a "non-strict" assignment of some poles. Some solutions have been proposed for some simple electronic power systems or chemistry plants in [11][12][13][14]; however, such methods employ mathematical methods that are not numerically reliable (e.g., the characteristic polynomial, the controllability matrix). Therefore, these approaches are not appropriate for vibrating systems modelled through medium or large dimensional and ill-conditioned matrices.…”