Robust control synthesis using coefficient diagram method and µ-analysis: an aerospace example

Abtahi, Seid Farhad; Yazdi, Ehsan Azadi

doi:10.1007/s40435-018-0462-7

Cited by 7 publications

(4 citation statements)

References 22 publications

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“…A(s), B(s) can be obtained by Equations (17) and (21). F(s) can be obtained by Equation (16). Remark 2.…”

Section: Overall Design Ideasmentioning

confidence: 99%

“…At the same time, all algebraic equations in the CDM are expressed in the form of polynomials, which facilitates the elimination of poles and zeros in the design and analysis of the control systems. CDM has been proven to be a method to ensure the robustness of the control system, and its effectiveness has been proven through a series of experiments [ 15 , 16 , 17 ]. Therefore, with the continuous improvement of CDM, CDM has been continuously applied to existing control systems.…”

Section: Introductionmentioning

confidence: 99%

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Robust Controller Design for Multi-Input Multi-Output Systems Using Coefficient Diagram Method

Meng

et al. 2021

Entropy

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The coupling between variables in the multi-input multi-output (MIMO) systems brings difficulties to the design of the controller. Aiming at this problem, this paper combines the particle swarm optimization (PSO) with the coefficient diagram method (CDM) and proposes a robust controller design strategy for the MIMO systems. The decoupling problem is transformed into a compensator parameter optimization problem, and PSO optimizes the compensator parameters to reduce the coupling effect in the MIMO systems. For the MIMO system with measurement noise, the effectiveness of CDM in processing measurement noise is analyzed. This paper gives the control design steps of the MIMO systems. Finally, simulation experiments of four typical MIMO systems demonstrate the effectiveness of the proposed method.

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“…A(s), B(s) can be obtained by Equations (17) and (21). F(s) can be obtained by Equation (16). Remark 2.…”

Section: Overall Design Ideasmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Robust Controller Design for Multi-Input Multi-Output Systems Using Coefficient Diagram Method

Meng

et al. 2021

Entropy

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“…Many researchers have worked on this problem since the years 1950s and 1960s, among whom can be cited as Aizerman (1947), with the well known Aizerman conjecture, and Krasovskii (1953), Popov (1961), and Kalman (1963). In a way, research on the Lurie’s problem took a bigger leap in the 1980s, when works began to appear that linked the problem to other areas and approaches such as neural networks (Liao and Yu, 2008; Pinheiro and Colón, 2019); complex network (Li et al, 2012); chaos and chaos synchronization (Kazemy and Farrokhi, 2017); convex approach to the Lurie problem (Gapski and Geromel, 1994); linear parameter varying (LPV) system (Yu and Liao, 2019); uncertain systems (Tan and Atherton, 2003); Integral Quadratic Constraints (IQC) and Zames-Falb multipliers (Carrasco et al, 2016); μ analysis (Abtahi and Yazdi, 2019; Lee and Juang, 2005); and more recently the application of Lurie’s problem in modern control systems such as Hopfield neural network controls (Pinheiro and Colón, 2021), modeling Alzheimer’s disease (Pinheiro and Colón, 2020), tracking differential extended state observer (Wang et al, 2020) and in control rates of the extended state observer (ESO) for speed control system for the pitching axis of a remote sensing camera (Liu, 2020). In addition to all these new lines of application and study of the Luries problem, its study remains current in the aeronautical field, as can be seen in Imani and Montazeri-Gh (2019).…”

Section: Introductionmentioning

confidence: 99%

Analysis and synthesis of single-input-single-output Lurie type systems via H∞ mixed-sensitivity

Pinheiro

Colón

2021

Transactions of the Institute of Measurement and Control

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The goal of this paper is to present a different approach to the analysis of the absolute stability of Lurie type systems in the single-input-single-output (SISO) case using robust control theory. The proposed technique enables the design of controllers via [Formula: see text] mixed-sensitivity (S/KS/T), where, besides making the system absolutely stable, the performance problem can also be solved. In addition, it is also demonstrated that it is possible to make use of this new approach in time-delay Lurie type systems. Thus, through a new methodology, this work paves the way to the study of the absolute stability of multiple-inputs-multiple-outputs (MIMO) systems, aiming at a better generalization of the theory and enabling applications in other areas, such as neural networks. Examples, numerical simulations and application in Chua’s circuit are given to illustrate the results.

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“…This problem was studied for many researchers, as Krasovskii (1953), Popov (1961), and Kalman (1963). Research on the LP also went on to other areas, such as chaos synchronization (Liao and Yu, 2008); convex approach (Gapski and Geromel, 1994); neural networks (Pinheiro and Colón, 2019); linear parameter varying (LPV) system (Yu and Liao, 2019); and µ analysis (Abtahi and Yazdi, 2019). In works like Liao and Yu (2008) and Pinheiro and Colón (2019) is shown that HNN is a particular case of Lurie type system.…”

Section: Introductionmentioning

confidence: 99%

Relating Lurie's problem, Hopfield's network and Alzheimer's disease

Pinheiro¹,

Colón

Reinoso

2020

Anais Do Congresso Brasileiro De Automática 2020

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Alzheimer's disease is a degenerative brain disorder that affects millions of people around the world and still without cure. A very common application of Hopfield neural networks is to simulate a human memory as well as to evaluate problems of degeneration and memory loss. On the other hand, from the control area, one has Lurie's problem, which emerged in the 1940s and which still does not have a general solution. However many works and results came in an attempt to solve it. In this paper, the Hopfield's network is shown as a particular case of Lurie's problem, then one of the consequences of Alzheimer's disease, memory failure, is modeled using Hopfield's networks and nally a recent result of Lurie's problem is applied to the computationally modeled disease to correct the problem of memory loss. The correction is made using a controller via DK-iteration. Simulations are performed to validate the computational model of the disease and to demonstrate the effectiveness of the application of the recent Lurie's problem theorem. Therefore, in addition to the results presented, this work aims at encouraging the researches in the area, so that in the future, better diagnostic and treatment conditions will be achieved.

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Robust control synthesis using coefficient diagram method and µ-analysis: an aerospace example

Cited by 7 publications

References 22 publications

Robust Controller Design for Multi-Input Multi-Output Systems Using Coefficient Diagram Method

Robust Controller Design for Multi-Input Multi-Output Systems Using Coefficient Diagram Method

Analysis and synthesis of single-input-single-output Lurie type systems via H∞ mixed-sensitivity

Relating Lurie's problem, Hopfield's network and Alzheimer's disease

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