Mixed‐Objective Robust Dynamic Output Feedback Controller Synthesis for Continuous‐Time Polytopic Lpv Systems

This paper investigates the problem of robust H ∞ dynamic output feedback control of 3-phase 4-wire converter with neutral bridge arm in the application of smart grid and distributed generation. Based on Lyapunov functions, a novel sufficient Linear Matrix Inequality condition analysis was performed on the dynamic output feedback stabilisation controllers. Meanwhile, some auxiliary slack variables with special structure and wellestablished performance conditions are employed to reduce design conservatism. This topology along with the H ∞ controller can solve the DC link balancing problem and maintain the deviation between the neutral point and the midpoint of DC supply very small. The achievable performance is analysed quantitatively and the controller design method was conducted and verified both in MATLAB simulation and the real-time simulation platform built by StarSim and MT, respectively.

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“…Lemma (Finsler's lemma) If

G=G^{\mathrm{T}}

M , N

and I are real constant matrices with appropriate dimensions, then the following two matrix inequalities are equivalent [26]:

\begin{align*} &(a){\left[ \def\eqcellsep{&}\begin{array}{l}I \\[7pt] N \end{array} \right]}^{\mathrm{T}} P{\left[ \def\eqcellsep{&}\begin{array}{l}I \\[7pt] N \end{array} \right]}&lt;0 \nonumber \\ &(b){P}+{\left[ \def\eqcellsep{&}\begin{array}{c}N^{\mathrm{T}} \\[7pt] -{I} \end{array} \right]}{G}^{\mathrm{T}}+{G}[{N} \quad {-I}]&lt;\mathbf {0} . \nonumber \end{align*}

…”

Section: Control Synthesismentioning

confidence: 99%

Robust H∞$H_\infty$ dynamic output feedback control of the DC–AC converter with a neutral leg

Zhao

Dong

2022

IET Power Electronics

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“…Example Consider the following system, adapted from previous studies [23,31] described by

A (θ) = [\begin{array}{ccc} 1.5 + 0.5 θ & 3 & θ \\ - 2.2 + θ & - 1.8 + 0.5 θ & 0.2 θ \\ 0.1 & 0.5 & - θ \end{array}], B (θ) = [\begin{array}{c} 2 θ \\ 0.1 + θ \\ 0.2 \end{array}],

B_{w} = {[\begin{array}{ccc} 0.2 & 0.02 & 0.1 \end{array}]}^{⊤}, C = [\begin{array}{ccc} 1 & 1 & 0 \\ 0 & 0 & 1 \end{array}], D_{w} = {[\begin{array}{cc} 0 & 0 \end{array}]}^{⊤},

where

θ = 0.5 \sin false(0.2 t false) + 0.5

is a time‐varying parameter,

\overset{θ}{true} false(t false) \leq 0.1

and the exogenous disturbance input is

w = \exp false(- t false) \sin false(0.5 t false)

as given in Cai et al [31]. Under these circumstances, it is possible design state‐feedback controllers by using Theorem 4.1 and Theorem 7 proposed in Cai et al [...…”

Section: Numerical Experimentsmentioning

confidence: 99%

ISS control for continuous‐time systems with filtered time‐varying parameter and saturating actuators

Ferreira

Figueiredo

Lacerda

et al. 2022

Asian Journal of Control

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This paper presents new convex conditions to design robust and linear parameter varying (LPV) gains for continuous time-varying systems subject to saturating actuator and energy bounded disturbances. The input-to-state stability conditions are used to design controllers ensuring the minimization of the  2 -gain between the disturbance input and the controlled output. Furthermore, optimization procedures to maximize the estimate of the region of attraction, and the bound to the control signal as well, are formulated. The efficacy of the proposed methods is illustrated with numerical examples, including a reference tracking problem, where realistic simulations are performed.

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“…The LMI condition (11) for testing whether a matrix polynomial P(x) is SOS can be simplified in some cases by using Lemma 2. Indeed, let P ∶ R n →  s×s be a matrix polynomial with P(x) = P(x) H and deg(P(x)) = 2h, h ∈ N. Let b np (x) ∈ R np be a vector whose entries are all the monomials x w (l) with w (l) satisfying (16)…”

Section: Newton's Polytopementioning

confidence: 99%

“…In this example we consider the problem of establishing robust stability of a polytopic system, see for instance about polytopic systems. Specifically, let us consider Example 2 in .…”

Section: Examplesmentioning

confidence: 99%

On the Complexity of SOS Programming and Applications in Control Systems

Chesi

2017

Asian Journal of Control

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The minimization of a linear cost function subject to the condition that some matrix polynomials depending linearly on the decision variables are sums of squares of matrix polynomials (SOS) is known as SOS programming. This paper proposes an analysis of the complexity of SOS programming, in particular of the number of linear matrix inequality (LMI) scalar variables required for establishing whether a matrix polynomial is SOS. This number is analyzed for real and complex matrix polynomials, in the general case and in the case of some exact reductions achievable for some classes of matrix polynomials. An analytical formula is proposed in each case in order to provide this number as a function of the number of variables, degree and size of the matrix polynomials. Some tables reporting this number are also provided as reference for the reader. Two applications in control systems are presented in order to show the usefulness of the proposed results.

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Mixed‐Objective Robust Dynamic Output Feedback Controller Synthesis for Continuous‐Time Polytopic Lpv Systems

Cited by 9 publications

References 26 publications

Robust H∞$H_\infty$ dynamic output feedback control of the DC–AC converter with a neutral leg

Robust H∞$H_\infty$ dynamic output feedback control of the DC–AC converter with a neutral leg

ISS control for continuous‐time systems with filtered time‐varying parameter and saturating actuators

On the Complexity of SOS Programming and Applications in Control Systems

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