Stable inversion of Abel equations: Application to tracking control in DC–DC nonminimum phase boost converters

Global tracking passivity-based PI control of bilinear systems: Application to the interleaved boost and modular multilevel converters

“…As shown in the examples below this may prove to be a very complicated task and some approximations may be needed to derive them. Indeed, it is shown in Olm et al (2011) that even for the simple boost converter this task involves the search of a stable solution of an Abel ordinary differential equation, which is known to be highly sensitive to initial conditions.…”

“…The tracking problem of bilinear systems has been addressed within the context of switched power converters. In Olm, Ros-Oton, and Shtessel (2011) a methodology to track periodic signals for non-minimum phase boost converters based on a stable inversion of the internal dynamics taking the normal form of an Abel ordinary differential equation was presented-see also Fossas and Olm (2009). There are also schemes involving sliding mode control, for example Fossas and Olm (1994), Biel, Guinjoan, Fossas, and Chavarria (2004), and references therein.…”

Robust DC-Link Control in EVs With Multiple Energy Storage Systems

“…It is important to note that the change of variable (2) has been adopted in previous studies (see, e.g., [28]- [31]), and is exploited in the present article to represent the parallel boost converters in a dimensionless form. Compared with the original model, this dimensionless representation features the following main advantages: i) the number of parameters is reduced from four (L 1 , L 2 , R, C) to only two (θ 1 , θ 2 ), and ii) the number of exogenous inputs is decreased from three (v 1 , v 2 , i L ) to two (w 1 , the ratio of input voltages, and ∆ 1 , the normalized load current).…”

“…However, by following the tracking setting, it becomes necessary to find a stable inversion of the system [32], which is hampered by the nonlinearities and nonminimum phase nature of the boost converter. As a matter of fact, the stable inverse of the boost model requires the inversion of the internal dynamics -in our case the battery current -producing an Abel differential equation, difficult to solve analytically (see [31] and references therein). To overcome these hurdles, and under the assumption of slowly time-varying references (x * 2 , x * 3 ), we will simplify the control problem, replacing the output-tracking setting by a regulation one.…”

“…Nonetheless, the design described here can be easily extended to deal with variable x * 3 , e.g., by adding a second gain-scheduling variable (x * 3 ) to the controller. From a practical point of view, implementing the control law (31), in particular the integral action, requires certain care on a number of details. First, it should be noted that the controller was formulated in normalized time (τ ), while its implementation will be done in normal time (t); therefore, it is imperative to introduce a correction factor when integrating the regulation error:…”