The greatest degree of the stability of a two-mass system for regulators of the lowered order

Authors: Koryukin A. N., Voevoda A. A.

Annotation: This work continues a research of the greatest (optimum, limiting, maximum) degrees of stability of any singlechannel two mass systems. The management is carried out by a PID-control and its generalization, the numerator of transfer function is a degree polynom no more than 2, and a denominator – a polynom of degree 1. The operating force is attached to the mass closest to the motionless basis. The exit is a deviation of the same mass. The friction is small. The research was carried out for any object from all class of operated objects listed above. For generalized PID-controls by search of the greatest stability it is possible to be limited to controls, for which on the right vertical of the characteristic polynom there is a quadruple root; for PID-controls with double complex pair on the right vertical. It is given an example calculations of the greatest degree of stability, roots of a characteristic polynom, the polynom, the control providing the greatest stability. This work can form a sample and a basis of a methodology of research and calculation of the greatest degree of stability and the controls of the lowered order providing this stability, and for other classes of operated single-channel systems of the lowered order.

Keywords: modal synthesis, regulators of the lowered order, stability according to gurvits, the greatest degree of stability, maximum degree of stability, limiting degree of stability