Robust H? static output feedback controller design for parameter dependent polynomial systems: An iterative sums of squares approach

Krug, Matthias; Saat, Shakir; Nguang, Sing Kiong

doi:10.1016/j.jfranklin.2012.11.010

Cited by 33 publications

(33 citation statements)

References 29 publications

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“…In this section, the procedure to obtain the speed controller for normal operation is explained. The design strategy has been developed by using Lyapunov methods and applying optimization techniques over polynomials (see for the details on the technique and for other recent applications). For these techniques, a dynamical polynomial model of the system is assumed to be available, fulfilling

\begin{matrix} leftalign \\ rightalign-odd ẋ & align-even = f MathClass-open(x MathClass-close) + g MathClass-open(x MathClass-close) w, f MathClass-open(0 MathClass-close) = 0 & rightalign-label (12) \end{matrix}

where x is the state vector, w are the inputs and f ( x ) and g ( x ) are given polynomial vectorial functions.…”

Section: Controller Designmentioning

confidence: 99%

Synthesis of nonlinear controller for wind turbines stability when providing grid support

Peñarrocha

Dolz

Aparicio

et al. 2013

Int. J. Robust. Nonlinear Control

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SUMMARYThis paper presents a new nonlinear polynomial controller for wind turbines that assures stability and maximizes the energy produced while imposing a bound in the generated power derivative in normal operation (guarantees a smooth operation against wind turbulence). The proposed controller structure also allows eventually producing a transient power increase to provide grid support, in response to a demand from a frequency controller. The controller design uses new optimization over polynomials techniques, leading to a tractable semidefinite programming problem. The ability of the wind turbine to increase its power under partial load operation has been analysed. The above optimization techniques have allowed quantifying the maximum transient overproduction that can be demanded to the wind turbine without violating minimum speed constraints (that could lead to unstable behaviour), as well as the total generated energy loss. The ability to evaluate this shortfall has permitted the development of an optimization procedure in which wind farm overproduction requirements are divided into individual turbines, assuring that the total energy loss in the wind farm is minimum, while complying with the maximum demanded power constraints.

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\begin{matrix} leftalign \\ rightalign-odd ẋ & align-even = f MathClass-open(x MathClass-close) + g MathClass-open(x MathClass-close) w, f MathClass-open(0 MathClass-close) = 0 & rightalign-label (12) \end{matrix}

where x is the state vector, w are the inputs and f ( x ) and g ( x ) are given polynomial vectorial functions.…”

Section: Controller Designmentioning

confidence: 99%

Synthesis of nonlinear controller for wind turbines stability when providing grid support

Peñarrocha

Dolz

Aparicio

et al. 2013

Int. J. Robust. Nonlinear Control

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“…Zhao and Wang proposed a stabilizing output feedback via a polynomial Lyapunov function where the effect the nonlinear term on

\overset{P}{true} false(x false)

is minimized by imposing a bound to deal with the nonconvex term in the stabilizing condition. Krug et al studied an iterative SOS approach for a robust H ∞ SOF control of parameter dependent polynomial systems. Meng et al proposed a linear Lyapunov function for positive polynomial fuzzy systems where fuzzy system rules and fuzzy controller rules do not share the same premises.…”

Section: Introductionmentioning

confidence: 99%

“…(2) Imposing a bound on the nonlinear derivative term

\overset{P}{true} false(x false)

and forming an optimization problem to obtain zero optimum . (3) An iterative SOS procedure is proposed for the SOF being genetically nonconvex . (4) To use constant Lyapunov P methods instead.…”

Section: Introductionmentioning

confidence: 99%

Polynomial static output feedback H_∞ control via homogeneous Lyapunov functions

Liu

2019

Intl J Robust & Nonlinear

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Summary In this paper, we study a polynomial static output feedback (SOF) stabilization problem with H∞ performance via a homogeneous polynomial Lyapunov function (HPLF). It is shown that the quadratic stability ascertaining the existence of a single constant Lyapunov function becomes a special case. With the HPLF, the proposal is based on a relaxed two‐step sum of square (SOS) construction where a stabilizing polynomial state feedback gain K(x) is returned at the first stage and then the obtained K(x) gain is fed back to the second stage, achieving the SOF closed‐loop stabilization of the underlying polynomial fuzzy control systems. The SOS equations obtained thus effectively serve as a sufficient condition for synthesizing the SOF controllers that guarantee polynomial fuzzy systems stabilization. To demonstrate the effectiveness of the proposed polynomial fuzzy SOF H∞ control, benchmark examples are provided for the new approach.

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“…It should be noted that the nonlinearities of the systems of the related works are restricted by constraint conditions and some boundary conditions are needed for the sake of solving some dynamic equations in the work of Ghaffari et al Besides the general nonlinear systems, there exists an important class of nonlinear systems, ie, polynomial nonlinear systems. Recently, along with the research progress on the control of nonlinear polynomial systems, several sum of squares–based approaches are presented to solve the H ∞ control problem of nonlinear polynomial systems . However, the disadvantage of the method of sum of squares is that it is incapable to solve the polynomial inequality containing nonlinear combination of unknown values.…”

Section: Introductionmentioning

confidence: 99%

Robust H_∞ control for uncertain switched nonlinear polynomial systems: Parameterization of controller approach

Zhu

Hou

2018

Intl J Robust & Nonlinear

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Summary This paper considers the global feedback exponential stabilization and L2 gain disturbance attenuation problems of the switched nonlinear polynomial systems with passive and nonpassive subsystems for any given average dwell time. In the existing result, it needs that there exists at least one open loop passive subsystem in the switched nonlinear system, which is unnecessary for the switched nonlinear polynomial system in this paper because the passivity of the subsystem can be obtained according to the passivity‐based feedback dissipative Hamiltonian realization. In addition, a parameterization of controller approach–based feedback exponential stabilization method of nonlinear polynomial system is described and utilized such that the Lyapunov function of the passive subsystem possesses the required decay rate to exponentially stabilize the switched nonlinear polynomial system. Comparing with the controller designed with the existing method, the obtained controller in this paper has much simpler structure and better performance. An example simulation is provided to illustrate the effectiveness of the proposed approach.

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Robust H? static output feedback controller design for parameter dependent polynomial systems: An iterative sums of squares approach

Cited by 33 publications

References 29 publications

Synthesis of nonlinear controller for wind turbines stability when providing grid support

Synthesis of nonlinear controller for wind turbines stability when providing grid support

Polynomial static output feedback H_∞ control via homogeneous Lyapunov functions

Robust H_∞ control for uncertain switched nonlinear polynomial systems: Parameterization of controller approach

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Robust H? static output feedback controller design for parameter dependent polynomial systems: An iterative sums of squares approach

Cited by 33 publications

References 29 publications

Synthesis of nonlinear controller for wind turbines stability when providing grid support

Synthesis of nonlinear controller for wind turbines stability when providing grid support

Polynomial static output feedback H∞ control via homogeneous Lyapunov functions

Robust H∞ control for uncertain switched nonlinear polynomial systems: Parameterization of controller approach

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Product

Resources

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Polynomial static output feedback H_∞ control via homogeneous Lyapunov functions

Robust H_∞ control for uncertain switched nonlinear polynomial systems: Parameterization of controller approach