Robust back-stepping sliding mode control for LCL-type grid-connected inverters in weak grids

Ding, Xin; Liang, Junyang; Lu, Shangping; Kong, Fannie; Chen, Yanming

doi:10.1007/s43236-022-00577-w

Cited by 2 publications

(2 citation statements)

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“…Under (22), for any value of the actuated coordinates θ a , there is a unique equilibrium of those unactuated, i.e., the system equilibria are uniquely determined by θ a . Instead, (21) guarantees internal stability of the closed-loop system. Note that the above controllers admit more general structures, see [10] and [26].…”

Section: Control Of Collocated Underactuated Mechanical Systemsmentioning

confidence: 99%

“…It can be shown that, in case of underactuation, the necessary and sufficient condition is the involutivity of the distribution spanned by the columns of the actuation matrix [17]. Unfortunately, involutivity is not easy to check, especially for high dimensional dynamics, and has to be evaluated case by case, see [18]- [21]. Furthermore, finding the input decoupling state variables in this case requires solving a system of nonlinear partial differential equations [16,Chap.…”

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confidence: 99%

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Input Decoupling of Lagrangian Systems via Coordinate Transformation: General Characterization and Its Application to Soft Robotics

Pustina,

Santina,

Boyer

et al. 2024

IEEE Trans. Robot.

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Suitable representations of dynamical systems can simplify their analysis and control. On this line of thought, this paper aims to answer the following question: Can a transformation of the generalized coordinates under which the actuators directly perform work on a subset of the configuration variables be found? Not only we show that the answer to this question is yes, but we also provide necessary and sufficient conditions. More specifically, we look for a representation of the configuration space such that the right-hand side of the dynamics in Euler-Lagrange form becomes [I O] T u, being u the system input. We identify a class of systems, called collocated, for which this problem is solvable. Under mild conditions on the input matrix, a simple test is presented to verify whether a system is collocated or not. By exploiting power invariance, we provide necessary and sufficient conditions that a change of coordinates decouples the input channels if and only if the dynamics is collocated. In addition, we use the collocated form to derive novel controllers for damped underactuated mechanical systems. To demonstrate the theoretical findings, we consider several Lagrangian systems with a focus on continuum soft robots.

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