# DC-DC Buck Converters with Quasi-Online Estimation of Filter Capacitor Equivalent Parameters
## 1 Introduction  
DC-DC converters are electronic subassemblies used in a huge amount of equipment in numerous fields of activity. The online knowledge of the behavior of the circuits or components and the knowledge of their state-of-health serve in operation as a prerequisite both for the adjustment and adaptation of the control of the converters and for predictive maintenance [1, 2]. In the design and operation of DC-DC converters, it is important to model them, completely or partially, i.e., only some of the main components, mostly the output filter capacitor [3]. It can be found both at buck [4] and boost converter [5]. The filter capacitor behavior is described by models with schemes of varying complexity, depending on the details of the physical phenomena with impact on the system functioning [6, 7, 8, 9]. The most used model is the R-C series one [10, 11, 12]. The R-C series simplified model is suitable for capacitor functions in a low-band frequency [3]. Regarding the monitoring of a capacitor, the equivalent series resistance (ESR) and the equivalent capacitance are frequently used as diagnostic parameters [13]. Always, in applications, the ESR and capacitance vary over a frequency range determined by the spectrum of the current corresponding to the operating regime [13]. In this context, the \"equivalent\" attribute underlines, in addition to the \"effective\" attribute used, for example, in [14], the fact that the estimated values of the two parameters characterize the behavior of the capacitor across an entire operating regime [15]. Condition monitoring of capacitors basically includes two phases: the estimation of the equivalent parameters, followed by the use of the estimated values to assess the capacitor condition [2; 16; 17]. The classifications of estimation techniques and evaluation methods are also addressed in papers [3; 18]. In [19], attention is paid to the classification of condition monitoring techniques for aluminum electrolytic capacitors (AEC) in offline, online, and quasi-online techniques. In control systems engineering and system analysis, mathematical models called observers are frequently used to estimate individual or hybrid variables (combinations of states and input signals) from real systems, called master systems. The inputs of an observer are the measurable inputs and outputs of the master system [20]. Observers are essentially subsystems tracking one or more measurable outputs of the master system. Numerous studies on DC-DC converters and their components imply observers for estimation, performance control, and fault detection [1; 21; 22; 23; 24; 25; 26]. In [21], specific observers are used in a buck converter for the fault diagnosis, inductance, and capacitance estimations. In reference [22], the observer serves to control a switching-mode DC-DC converter. The study [25] proposes distinct observers for the ESR and for the capacitance C of the output capacitor of a boost converter. In [1], a state observer is proposed to counterbalance the errors with an ideal model of a boost converter. The paper [23] introduces a piecewise linear observer designed for fault-sensitive detection filters for power electronics systems and exemplified for a dual-redundant buck converter. The study in [24] focuses on the design, analysis, and experimental integration of an enhanced robust adaptive parameter identifier for DC-DC converter applications, based on a closed-loop linear switched state observer. This identifier is designed considering for the capacitor a simple C-model. An observer for estimating the load resistance of a DC-DC buck converter is presented in [26]. In [15] is proposed a new type of observer, distinct from those typically employed in control systems, in particular from those used in DC-DC converters, designed to estimate the time constant of a first-order system.