New Design of Robust LQR-State Derivative Controllers via LMIs

Beteto, Marco Antonio Leite; Assunção, Edvaldo; Teixeira, Marcelo Carvalho Minhoto; Silva, Emerson R.P.; Buzachero, Luiz Francisco Sanches; Caun, Rodrigo P.

doi:10.1016/j.ifacol.2018.11.149

Cited by 15 publications

(14 citation statements)

References 18 publications

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“…Since t 𝛼 is a known constant, and in the performance index (15), there is not any expression in term of z(t 𝛼 ) out of the integral, it is easy to get…”

Section: Preview Repetitive Control Of Nominal Systemmentioning

confidence: 99%

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Preview repetitive control with equivalent input disturbance for continuous‐time linear systems

Lan

Zhao

She

2021

IET Control Theory & Appl

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This paper investigates the problem of preview repetitive control with equivalent‐input‐disturbance for a class of continuous‐time linear systems in the presence of unknown external disturbances. First, an augmented delay system is constructed by using the nominal state equation with error system and the state equation of a modified repetitive controller, which is then transformed into a non‐delayed one by state transformation. Next, by using optimal control theory, a preview repetitive control law is obtained. It is composed of state feedback, tracking error compensation, output of modified repetitive controller and preview compensation. Furthermore, in order to achieve a good disturbance estimation and attenuation performance, by applying the results of the standard equivalent‐input‐disturbance theory, a preview repetitive control law with equivalent‐input‐disturbance is offered for the uncertain system with unknown external disturbance. Finally, the numerical simulation example is provided to illustrate the effectiveness of the proposed method.

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“…Since t 𝛼 is a known constant, and in the performance index (15), there is not any expression in term of z(t 𝛼 ) out of the integral, it is easy to get…”

Section: Preview Repetitive Control Of Nominal Systemmentioning

confidence: 99%

“…𝜎 max (G d ) means the maximum singular value of G d . Then under the performance index (15), the optimal PRC law with EID for the uncertain system ( 1) is given by (47), where u f (t ) is defined in (16) and d (t ) is obtained from (46).…”

Section: Optimal Prc With Eid Of Uncertain Systemmentioning

confidence: 99%

Preview repetitive control with equivalent input disturbance for continuous‐time linear systems

Lan

Zhao

She

2021

IET Control Theory & Appl

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“…This assumption has been considered in the linear state derivative designs, as can be seen for instance in Rossi et al 2018, Beteto et al (2018) and references.…”

Section: Stabilizationmentioning

confidence: 99%

“…Regarding contributions concerning state derivative feedback, it is important to highlight that most research efforts have been devoted to the design of continuous-time controllers (Duan et al (2005), Faria et al (2009), Tseng and Hsieh (2013), Beteto et al (2018), among others). On the other hand, several methods treat the problem of discretization of uncertain systems through of the first order Taylor series expansion to circumvent the difficulty of dealing with the exponential of an uncertain matrix (Cardim et al (2009), Rossi et al (2018)).…”

Section: Introductionmentioning

confidence: 99%

Robust state derivative feedback LMI-based designs for discretized systems.

Leandro¹,

Pereira

Kienitz

2020

Anais Do Congresso Brasileiro De Automática 2020

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This work addresses novel Linear Matrix Inequality (LMI)-based conditions for thedesign of discrete-time state derivative feedback controllers. The main contribution of this work consists of an augmented discretized model formulated in terms of the state derivative, such that uncertain sampling periods and parametric uncertainties in polytopic form can be propagated from the original continuous-time state space representation. The resulting discrete-time model is composed of homogeneous polynomial matrices with parameters lying in the Cartesian product of simplexes, plus an additive norm-bounded term representing the residual discretization error. Moreover, the referred condition allows for the closed-loop poles allocation of the augmented system in a D-stable region. Finally, numerical simulations illustrate the effectiveness of the proposed method.

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“…For more than five decades, the most extensive research into preview control has focused on the linear quadratic optimal control problem with preview compensation [1][2][3][4][5], especially for discrete-time systems. Subsequently, linear matrix inequality (LMI) technique has been extensively used to handle the PC problems for uncertain discrete-time systems [6]. Combining LMI-based PC with other control schemes, some new concepts are proposed, such as adaptive PC [7], fault tolerant PC [8], H ∞ PC [9], observer-based PC [10], and distributed PC [11].…”

Section: Introductionmentioning

confidence: 99%

Padé-Approximation-Based Preview Repetitive Control for Continuous-Time Linear Systems

Zhao

Wang

Yan

et al. 2021

Mathematical Problems in Engineering

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This paper concerns a Padé-approximation-based preview repetitive control (PRC) scheme for continuous-time linear systems. Firstly, the state space representation of the repetitive controller is transformed into a nondelayed one by Padé approximation. Then, an augmented dynamic system is constructed by using the nominal state equation with the error system and the state equation of a repetitive controller. Next, by using optimal control theory, a Padé-approximation-based PRC law is obtained. It consists of state feedback, error integral compensation, output integral of repetitive controller, and preview compensation. Finally, the effectiveness of the method is verified by a numerical simulation.

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New Design of Robust LQR-State Derivative Controllers via LMIs

Cited by 15 publications

References 18 publications

Preview repetitive control with equivalent input disturbance for continuous‐time linear systems

Preview repetitive control with equivalent input disturbance for continuous‐time linear systems

Robust state derivative feedback LMI-based designs for discretized systems.

Padé-Approximation-Based Preview Repetitive Control for Continuous-Time Linear Systems

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