Method for recovery of the input signal in dynamic systems based on a discrete model with the exclusion of correcting feedbacks

The problem of processing data obtained during dynamic measurements is one of the central problems in measuring technology. Purpose of the study. The article is devoted to the model of the measuring system and the method of processing the results of dynamic measurements. Therefore, an urgent task is to develop algorithms for processing the results of dynamic measurements. Materials and methods. This article proposes a model of a measuring system without feedback and a method for processing data obtained from dynamic measurements based on a finite difference approach. The main prerequisites of the mathematical model of the problem of dynamic measurements associated with the processes of restoration of the input signal under conditions of incomplete and noisy initial data are as follows. Initially, the function of the noisy output signal is known. Restoration of the input signal is carried out using the transfer function of the sensor. The transfer function of the sensor is presented as a differential equation. This equation describes the state of a dynamic system in real time. The proposed computational scheme of the method is based on the finite-difference analogues of derivatives and the self-regularizing approach was built a numerical model of the sensor. The problem of the stability of the method for solving high-order differential equations is also one of the central problems of data processing in automatic control systems. Based on the approach of generalized quasi-optimal choice of the regularization parameter, the required level of accuracy was achieved. Results. The main goal of the computational experiment was to construct a numerical solution of the problem under consideration. Standard test functions were considered as input signals. As an input signal, a test signal was applied, simulating a physical process. The function of the output signal was found using the proposed numerical method, the found function was noisy with an additive noise of 5%. Conclusion. The input signal was restored from the noisy signal. The deviation of the reconstructed signal from the original in all experiments was no more than 0.05, which indicates the stability of this method with respect to noisy data and the possibility of using this approach in dynamic measurements.