多输入的二阶广义分布参数系统的控制综合问题

Abstract

Singular distributed parameter system is widely applicable, for example, to the studies of the temperature distribution of composites, signal propagation in electrical cables, voltage distribution of electromagnetically coupled superconductive circuits, and aerocraft attitude control. Pole assignment and feedback stability are two important research aspects of the system. This paper, first of all, defines the pole assignment and feedback stability for the second order singular distributed parameter system with multiple inputs in Hilbert space, the subnegative definite operator, and the generalized inverse of the bounded linear operators, and presents some relevant properties; and then, it systemizes the second order singular distributed parameter system with multiple inputs into the first order singular distributed parameter system with multiple inputs by using the suitable transformation, which makes the two systems be of the same generalized eigenvalues, and discusses the pole assignment and feedback stability problems of the first order singular distributed parameter system with multiple inputs via functional analysis, operator theory and subnegative definite operator. Based on it, some sufficient conditions of the pole assagnment and stability of the second order singular distributed parameter system with multiple inputs in Hilbert space are obtained. It establishes the constructive expressions of the feedback control laws by using complex analysis, complex series and the generalized inverse of the bounded linear operators. The research results are not only of practical significance, but of important theoretical values for studying the control synthesis problem of the singular distributed parameter system.