## 5 Conclusions
the advantageous fact that the electromechanical parameters of the motor are reflected in the parameters of the amplifier model, which is realized as a linear electronic circuit with an operational amplifier. Therefore, the fault detection algorithms could be based solely on parameter estimation of the discrete or continuous model of the amplifier, which is a unique approach to the problem. Diagnosing faults caused by abrupt parameter changes is particularly demanding. Classical parameter estimation techniques yield unsatisfactory results because a sudden change in one system parameter initiates a transient process during which the effect of the change spreads to other parameters as well. To address this, more advanced estimation techniques were employed for detecting multiplicative faults induced by sudden parameter changes in the amplifier or motor. These included: the SWA for estimating parameters of the discrete model and the SIA for estimating parameters of the continuous model. An additional requirement for the application of these techniques is the necessity of a sufficiently informative input signal (i.e., persistent excitation) of adequate order to enable parameter identification. To satisfy this, a PRBS (Pseudo-Random Binary Sequence) signal was used in the experiments. This paper implements a modified version of the SIA, which introduces a constraint on the data length in the least squares algorithm, within which the sliding integral is applied. This modification aims to reduce the impact of transients on parameter estimation. To compare the two approaches to multiplicative fault detection and to assess estimation quality, as well as the influence of Coulomb friction disturbances on system behavior under fault conditions, the responses of the respective models were compared with the measured system response. It was concluded that although the continuous parameter estimation method is more demanding to implement (particularly in real-time applications), it proved equally effective in detecting multiplicative faults in the specific case studied. Furthermore, the influence of Coulomb friction as a disturbance was most pronounced in cases involving a fault in resistance \(R_{1}\), where both the SWA and SIA algorithms yielded the best results. To support fault isolation in case of SIA, a new decision algorithm was developed to enable accurate fault localization. In the case of continuous parameter estimation, fault identification--defined as the determination of both the faulty physical parameter and the magnitude of its change--is straightforward. The faulty parameter can be directly identified using the analytical relationships that define the amplifier model. An alternative approach, applicable when fault detection is performed using the SWA method, involves indirect estimation of changes in physical parameters. This technique is based on evaluating the partial derivatives (i.e., sensitivity coefficients) of the model parameters with respect to the physical parameters at the nominal operating point. The method yields accurate results when the relationship between estimated model parameters and physical parameters is linear. However, in the more common case of nonlinear dependencies, the estimation becomes an approximation, valid primarily for small deviations around the nominal point. Consequently, its accuracy diminishes as the magnitude of the physical fault increases. It was observed that better estimation results are obtained by selecting specific columns of the Jacobian matrix (i.e., the matrix of partial derivatives), rather than using the full matrix, as suggested in the literature. This approach proved especially effective in cases of nonlinear dependencies, even when the multiplicative faults are large and significantly deviate from the nominal operating point--representing one of the key contributions of this paper. For the considered multiplicative faults, LabVIEW codes with partial real-time implementation were developed, using the Flat Sequence Frame structure.