Recovery of Characteristics of Non-Stationary Dynamic Systems from Three Test Signals

Abstract

Non-stationary continuous and discrete dynamical systems are modeled, respectively, by Volterra integral equations of the first kind and their discrete analogues. Algorithms for the exact restoration of the impulse response (in analytical form) for continuous systems and the transient characteristic for discrete systems are constructed. We study an algorithm for the exact restoration of the impulse response of a non-stationary continuous dynamic system from three interconnected input signals. It is shown that the first signal can be arbitrary, and the second and third signals are connected by a first integral operator. The dynamic characteristic is chosen to be the exact Laplace transform formula of the impulse response, represented by an algebraic expression from the Laplace transform of the system output signals. A model example illustrating the performance of the presented algorithm is given. The practical application of the presented algorithm is discussed. An algorithm is also constructed for the exact restoration of the transient response of a non-stationary discrete dynamic system from three input signals that are interconnected. It is shown that the first signal can be arbitrary, and the second and third signals are associated with the first summation operator. We present the exact formula for the Z-transform of the transient response, which is represented by an algebraic expression from the Z-transform of the system output signals. A model example is given. The dynamic systems to which the proposed algorithms can be extended are described.