# Parameter Observer Useable for the Condition Monitoring of a Capacitor
## 1 Introduction
Observers are widely used in technology as tools for extracting information from a dynamic system. They are continuous-time or discrete-time dynamic systems, which contain, as appropriate, models of the observed system and/or models of external signals incident to the observed system. The observers approximate, depending on the situation, the signals from the observed system or incident signals, or combinations thereof [21; 22]. Generally, in a technical solution, observers are implemented as a software function of the electronic control unit, contributing to various operations such as measurement, protection, condition monitoring, etc. A unified characterization of the state and disturbance observers can be found in [23]. The area of use of the observers mainly includes control and measurement applications in many fields, including DC-DC converters, e.g., [24], but also fault diagnosis via observer-based detection filters [25], or attack detection on sensor areas in cyber-physical systems [26]. [PERSON] and [PERSON] in [3], [PERSON] et al. in [27] and [PERSON] et al. in [28] adopt a different approach, which falls into the category of estimating the parameters of electrical circuits. In [3], three continuous-time observers are used, one for the fault diagnosis of a buck converter and two, depending on the fault's localization, for the inductance estimation of the converter and for the capacitance estimation of the output capacitor of the converter. Ref. [27] develops an improved robust adaptive parameter identifier for DC-DC power electronic converters that use a continuous-time observer with amplifications designed using the Ho-type performance criterion. The use is aimed at both the capacitor and inductance of the output stage of a DC-DC boost converter. Paper [28] proposes for the output capacitor of a boost converter two parameter observers, one for ESR and one for C. Both use the R-C model of the capacitor in structures that have as inputs, in addition to the capacitor's voltage, at least one more current signal. A 100 Hz signal is injected to trigger the estimation process in the diagram. In this paper, we present a new type of observer, called parameter observer (PO), designed for first-order systems, in a free regime. The new idea is to transform the parameter into a state variable. We associate the main purpose with the illustration of the possibility of using the PO to calculate the values of the equivalent parameters of the final filter electrolytic capacitor of a DC-DC buck source. The PO monitors the so-called time constant of the capacitor discharging circuit through a resistor using only the voltage at the capacitor terminals. The method for determining the equivalent parameters of the capacitor is by dividing the discharging process of the capacitor into two stages. In [6] the dividing is carried out in three stages. From the viewpoint of the structure, the proposed observer falls into the category of open-loop observers [29], and from the viewpoint of treating the observation errors in the category of proportional integral observers [23]. Section 2 of the article describes the operating principle of the proposed parameter observer in both the continuous-time version and the discrete-time version, respectively, the method by which the equivalent parameters of an electrolytic capacitor are determined with its help. The results calculated with the PO from offline-processed experimental data are shown in Section 3. The discussion in Section 4 is intended to assess the applicability of the parameter observer. The last section summarizes the contributions of this paper. All experimental data processing and simulations were performed using the MATLAB-SIMULINK environment.