State-feedback control for LPV systems with interval uncertain parameters

Park, PooGyeon; Kwon, Nam Kyu; Park, Bum Yong

doi:10.1016/j.jfranklin.2015.08.025

Cited by 18 publications

(21 citation statements)

References 13 publications

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“…Note that (34) also leads toṖ 1 ( ) =Ṗ 2 ( ) =Ṗ 3 ( ) = 0 and one can see that (28) is equivalent to (17). To summarize, we see that, for the choice (31)(a) if (28) and either (29) or (30) hold, then (17) and (18) with s = 1 are satisfied with the same value of . Similarly, choosing (31)(b) will result (17) and (18) for s = 2.…”

Section: Theorem 2 If the Conditions In Lemma 3 Hold For Some Positimentioning

confidence: 64%

“…g = 9.8 m/s 2 is the gravity constant, m p = 0.22 kg is the mass of the pendulum, M c = 1.3282 kg is the mass of the cart, L = 0.304 m is the length from the center of mass of the pendulum to the shaft axis, u is the force (N) applied to the cart, also define a = 1/( m p + M c ). The aforementioned nonlinear equation can be exactly represented by the following LPV model:

\{\begin{matrix} {\overset{x}{true}}_{1} = x_{2} \\ {\overset{x}{true}}_{2} = α_{1} x_{1} + α_{2} u, \end{matrix}

where

\begin{matrix} alignleft \\ align-1 α_{1} : = \frac{g - a m_{p} L x_{2}^{2} \cos (x_{1})}{4 L / 3 - a m_{p} L c o s {(x_{1})}^{2}} \frac{\sin (x_{1})}{x_{1}}, α_{2} : = \frac{- a \cos (x_{1})}{4 L / 3 - a m_{p} L \cos {(x_{1})}^{2}} . & align-2 \end{matrix}

In addition, we suppose that x 1 ( t ) = φ ( t ) is measurable and

x_{2} false(t false) = \overset{ϕ}{true} false(t false)

is unmeasurable and

- \frac{π}{3} \leq x_{1} (t) \leq \frac{π}{3}, - 10 \leq x_{2} (t) \leq 10,

which immediately implies that one can consider

15.1329 \leq α_{1} \leq 27.0617, - 1 .

…”

Section: Numerical Examplesmentioning

confidence: 99%

“…For a prescribed positive value , if there exist a positive scalar and positive definite matrices X, Y ∈ S n , and parametrically affine matrices L 1 (̂) ∈ ℝ n×n , L 2 (̂) ∈ ℝ n×r , L 3 (̂) ∈ ℝ p×n , L 4 (̂) ∈ ℝ p×r such that either (28), (29) or (28), (30) hold, then the controller (̂) whose state space matrices are given in (32) makes the closed-loop system  cl ( ,̂) exponentially stable and ensures (4) for all combinations of admissible trajectories and[…”

Section: Lemma 3 (See the Work Of Sato And Peaucelle 6 )mentioning

confidence: 99%

“…The aforementioned nonlinear equation can be exactly represented by the following LPV model 19,28 : In addition, we suppose that x 1 (t) = (t) is measurable and x 2 (t) =̇(t) is unmeasurable and…”

Section: Examplementioning

confidence: 99%

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Gain‐scheduled continuous‐time control using polytope‐bounded inexact scheduling parameters

Sadeghzadeh

2018

Intl J Robust & Nonlinear

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Summary This paper investigates the problem of gain‐scheduled output feedback control design for continuous‐time linear parameter varying systems. The scheduling parameters are supposed to be measured in real time with absolute uncertainties and proportional uncertainties, simultaneously. Using a nonlinear transformation, the problem is formulated in terms of solutions to a set of parameter‐dependent linear matrix inequalities, exploiting parameter searches for two scalar values. H∞‐type problem is treated using parameter‐dependent Lyapunov and auxiliary matrices. One of the advantages of the presented method lies in its less conservatism in comparison with the available approaches. Some numerical examples are given to illustrate the effectiveness and advantage of the proposed method.

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Section: Theorem 2 If the Conditions In Lemma 3 Hold For Some Positimentioning

confidence: 64%

\{\begin{matrix} {\overset{x}{true}}_{1} = x_{2} \\ {\overset{x}{true}}_{2} = α_{1} x_{1} + α_{2} u, \end{matrix}

where

\begin{matrix} alignleft \\ align-1 α_{1} : = \frac{g - a m_{p} L x_{2}^{2} \cos (x_{1})}{4 L / 3 - a m_{p} L c o s {(x_{1})}^{2}} \frac{\sin (x_{1})}{x_{1}}, α_{2} : = \frac{- a \cos (x_{1})}{4 L / 3 - a m_{p} L \cos {(x_{1})}^{2}} . & align-2 \end{matrix}

In addition, we suppose that x 1 ( t ) = φ ( t ) is measurable and

x_{2} false(t false) = \overset{ϕ}{true} false(t false)

is unmeasurable and

- \frac{π}{3} \leq x_{1} (t) \leq \frac{π}{3}, - 10 \leq x_{2} (t) \leq 10,

which immediately implies that one can consider

15.1329 \leq α_{1} \leq 27.0617, - 1 .

…”

Section: Numerical Examplesmentioning

confidence: 99%

Section: Lemma 3 (See the Work Of Sato And Peaucelle 6 )mentioning

confidence: 99%

Section: Examplementioning

confidence: 99%

See 2 more Smart Citations

Gain‐scheduled continuous‐time control using polytope‐bounded inexact scheduling parameters

Sadeghzadeh

2018

Intl J Robust & Nonlinear

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“…Here, P(a(t)) is the augmented plant in the H ' framework and will be developed in the latter part of this article. Note that the normally induced L 2 -norm is used instead of the H N -norm for the LPV systems in equation (15), since the LPV systems are not LTI. Now considering the LPV systems (equation 14), the quadratic stability of equation 14can be defined by the important quadratic induced L 2 -norm performance index g as follows:…”

Section: Robust Lpv Control Algorithmmentioning

confidence: 99%

Robust gain-scheduled linear parameter-varying control algorithm for a lab helicopter: A linear matrix inequality–based approach

Jafar

Bhatti

Ahmad

et al. 2018

Proceedings of the Institution of Mechanical Engineers, Part I:

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The control performance of aerial vehicles can be easily affected by measurement error in sensor output, dynamic model error, model parameter variation, parametric uncertainty, external disturbance, and dynamic coupling. This article presents a design of robust linear parameter-varying control technique with induced L 2-norm performance combined with linear matrix inequality pole region constraints for a lab-scale helicopter. A linear parameter-varying disturbance rejection observer is constructed that characterizes the L 2-norm performance of the linear parameter-varying system, which enables to estimate state information not only in the presence of external disturbance but also in case of fault occurrence or unavailability of some sensor output. Therefore, the proposed robust linear parameter-varying control scheme has the tendency to provide an adaptive control solution for stability proof and robust tracking performance. The performance of the proposed technique is confirmed both in simulation and in real time. Compared to conventional output feedback H N control technique, the proposed control technique yields a good tracking performance in the presence of disturbance, parameter variation, and dynamic coupling.

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Simultaneous design of robust gain‐scheduled static output‐feedback controller and scaling matrices for linear parameter varying systems with inexact scheduling parameters

Niu,

Lu,

2023

Intl J Robust & Nonlinear

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This article presents a design method of the robust gain‐scheduled static output‐feedback controller exploiting inexact measured scheduling parameters for multi‐affine linear parameter‐varying systems with structured uncertainty blocks. Performance scaling matrices are introduced in the design process to reduce conservatism. By introducing auxiliary variables and properly utilizing projection lemma, a parameter‐dependent linear matrix inequality with a single line search parameter is derived to synthesize the static output‐feedback controller gains and scaling matrices simultaneously. Based on vertices of the convex polytope covering the admissible region of scheduling parameters and inexact ones, the given parameter‐dependent synthesis condition is further expressed as a set of linear matrix inequalities at the vertices of the polytope to guarantee the robustness against inaccurate scheduling parameters. Several examples show the effectiveness of the proposed algorithm.

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State-feedback control for LPV systems with interval uncertain parameters

Cited by 18 publications

References 13 publications

Gain‐scheduled continuous‐time control using polytope‐bounded inexact scheduling parameters

Gain‐scheduled continuous‐time control using polytope‐bounded inexact scheduling parameters

Robust gain-scheduled linear parameter-varying control algorithm for a lab helicopter: A linear matrix inequality–based approach

Simultaneous design of robust gain‐scheduled static output‐feedback controller and scaling matrices for linear parameter varying systems with inexact scheduling parameters

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