On the Problem of Robust Assignment of Dynamic System Poles

Abstract

For a linear time-invariant single-input system with a linear inertia-free state feedback, a problem of such assignment of poles, in which bounded parametric perturbations do not bring these poles outside a certain region is considered. A generalization of the well-known solution to this problem, based on Rouche's theorem and assuming that the structure of system and the input matrices meet the consistency conditions, to linear control systems with matrices of an arbitrary form is proposed. A special parameter is introduced, on the value of which the fulfilment of the conditions of Rouche's theorem, the shape of the pole scatter region, its "volume" and the minimum attainable root measures of the dynamics performance depend. The relationship between the width of parametric uncertainty intervals and the minimum required value of the geometric mean root of the characteristic polynomial of a system with a modal controller is revealed. An example of application of the proposed technique and a computer program developed on its basis in the MATLAB language for the synthesis of a modal controller for an electromechanical system is given.