Synthesis of an Observer Providing a Finite-Time State Estimation Based on the Output

The paper proposes a new method for synthesizing a full-order state vector observer for a certain class of linear stationary systems with unknown input signal. Two approaches that ensure the convergence of the estimation error (i.e., the error between the state vector estimate and the true state vector) to zero in a finite time are considered. The convergence time is set by the designer in the process of observer construction. The system parameters are assumed to be known and stationary, but the relative degree (from the measured output and the unknown input) is equal to one. The synthesis process using the first approach consists of two stages. In the first stage two auxiliary observers are used to estimate the initial conditions of the object in finite time. In the second stage, a third observer is introduced into the loop to perform online estimation of the system state vector. All the above three observers have the same structure that provides their insensitivity to the input signal, but different parameters. The second approach uses aggregation of auxiliary observers and introduce a delay operator to estimate the state vector. This method provides convergence of the observation error to zero after a delay time. The paper contains a rigorous mathematical proofs of the performance of the obtained solutions. To demonstrate the effectiveness and operability of the proposed approach computer simulation was carried out in the MATLAB Simulink software environment. A two-channel fourth-order mechanical system is considered as an plant. The simulation results illustrate the convergence of the state vector estimation error to zero in a finite time specified by the developer.

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