Stabilization of linear time-varying systems using proportional-derivative state feedback

Abdelaziz, Taha H. S.

doi:10.1177/0142331217697787

Cited by 5 publications

(5 citation statements)

References 25 publications

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“…In addition, the introduction of ρ ¯ models a randomly occurring gain perturbation. When ρ ¯ → 0 , the non-fragile controller becomes a common fragile controller proposed by Abdelaziz (2018); when ρ ¯ ∈ ( 0 , 1 ) , the controller perturbation randomly occurs; when ρ ¯ = 1 , the controller becomes a common non-fragile controller proposed by Shi et al (2015). Considering these three cases, the controller in this paper is more general than those in the references.…”

Section: Problem Statementmentioning

confidence: 96%

A novel robust non-fragile control approach for a class of uncertain linear systems with input constraints

Shi

Liu

Sun

et al. 2018

Transactions of the Institute of Measurement and Control

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This paper addresses the non-fragile control problem for a class of uncertain linear systems subject to model uncertainty, controller perturbations, fault signals and input constraints. The controller to be designed is supposed to have additive gain perturbations. A novel state feedback controller is proposed based on the exact available expectation of a Bernoulli random variable, which is introduced to model the feature of the controller gain perturbation that randomly occurs. By using Lyapunov stability theory, new sufficient conditions are derived to design non-fragile controller for a class of uncertain linear systems considering input constraints. Compared with the existing non-fragile state feedback controller methods, the non-fragile property is fully considered to improve the tolerance of uncertainties in the controller, where the conservativeness can be reduced via the Bernoulli random variable. The effectiveness of the proposed control strategy is illustrated by two numerical examples.

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Section: Problem Statementmentioning

confidence: 96%

A novel robust non-fragile control approach for a class of uncertain linear systems with input constraints

Shi

Liu

Sun

et al. 2018

Transactions of the Institute of Measurement and Control

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“…Similar to the earlier continuous time treatment, the discrete time optimal state feedback controller gain matrix s K can be achieved as (26) using the matrix P that minimizes the discrete quadratic cost function (24). Therefore we have: (26) This gives the control law as (27): (27) Using (23)…”

Section: G I a H B A I B A I A I B B (22)mentioning

confidence: 99%

“…The optimum weight selection has also been extended for the noisy tracking (integral) problem using linear quadratic Gaussian (LQG) control with loop transfer recovery (LTR) for improved stability margins [24]. Also, optimal statefeedback PD controller design has been previously studied with minimum norm controller gain to reduce noise amplification in [25], [26], [27]. But previous literatures shown above, do not provide the transformation to directly map time domain specifications (usually adopted in dominant pole placement design) onto the discrete time LQR weights, which is the main contribution of this paper over existing literatures.…”

Section: Introductionmentioning

confidence: 99%

Transformation of LQR Weights for Discretization Invariant Performance of PI/PID Dominant Pole Placement Controllers

Halder¹,

Das

Gupta³

2019

Robotica

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SummaryLinear quadratic regulator (LQR), a popular technique for designing optimal state feedback controller, is used to derive a mapping between continuous and discrete time inverse optimal equivalence of proportional integral derivative (PID) control problem via dominant pole placement. The aim is to derive transformation of the LQR weighting matrix for fixed weighting factor, using the discrete algebraic Riccati equation (DARE) to design a discrete time optimal PID controller producing similar time response to its continuous time counterpart. Continuous time LQR-based PID controller can be transformed to discrete time by establishing a relation between the respective LQR weighting matrices that will produce similar closed loop response, independent of the chosen sampling time. Simulation examples of first/second order and first-order integrating processes exhibiting stable/unstable and marginally stable open loop dynamics are provided, using the transformation of LQR weights. Time responses for set-point and disturbance inputs are compared for different sampling times as fraction of the desired closed loop time constant.

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“…For LTV systems, people have made a series of research results. [9][10][11] In the field of observer design, Trabet et al 12 presented a constructive method to ensure the synergy of observation errors in the new coordinate system to design interval observers. Zhang et al 13 designed an improved high-gain adaptive observer for a class of LTV systems with parameter uncertainties.…”

Section: Introductionmentioning

confidence: 99%

Parametric design to reduced-order functional observer for linear time-varying systems

Sun

Liu

2021

Measurement and Control

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This article studies the parametric design of reduced-order functional observer (ROFO) for linear time-varying (LTV) systems. Firstly, existence conditions of the ROFO are deduced based on the differentiable nonsingular transformation. Then, depending on the solution of the generalized Sylvester equation (GSE), a series of fully parameterized expressions of observer coefficient matrices are established, and a parametric design flow is given. Using this method, the observer can be constructed under the expected convergence speed of the observation error. Finally, two numerical examples are given to verify the correctness and effectiveness of this method and also the aircraft control problem.

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Stabilization of linear time-varying systems using proportional-derivative state feedback

Cited by 5 publications

References 25 publications

A novel robust non-fragile control approach for a class of uncertain linear systems with input constraints

A novel robust non-fragile control approach for a class of uncertain linear systems with input constraints

Transformation of LQR Weights for Discretization Invariant Performance of PI/PID Dominant Pole Placement Controllers

Parametric design to reduced-order functional observer for linear time-varying systems

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