Synthesis of the state observers of linear objects with elastic properties

Аннотация

The article deals with the synthesis of state observers of the first and second order for linear objects with elastic properties. The problem of synthesizing a state observer is to obtain current information about the state vector of dynamical systems in terms of the measured variables and is solved on the basis of the theory of asymptotic state observers. In real cases, there is usually no reliable information about elastic vibrations a priori. A state observer is proposed to restore this information. A comparative analysis of the observers of the first and second order was carried out, which showed the advantages of computing the model of observers of the second order. Computational efficiency is provided due to the symmetry and sparseness of the observer's matrix, which makes it possible to compensate for the elasticity of movements by changing the damping coefficient and rigidity of the original structure of the second-order observer. The prospects of using a second-order state observer for control of linear objects have been substantiated. For the synthesis of the state observer, it is proposed to use the Kalman filter, which allows to provide an optimal balance of high convergence of the observation error to zero and suppression of additive and multiplicative noise and interference, the proposed state observer makes it possible to obtain sufficiently accurate information about deformations and elastic movements according to the readings of the measuring instruments of sensors.