Digital redesign via the generalised bilinear transformation

Chen, Xiang; Chen, Tongwen

doi:10.1080/00207170802247728

Cited by 13 publications

(3 citation statements)

References 22 publications

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“…where the state 𝜔 𝑢 and 𝜔 𝑦 creates the signal 𝜑 𝑢𝑦 (𝑡) = 𝜔 𝑦 (𝑡) 𝜔 𝑢 (𝑡) (see Appendix A for definition of 𝐹, 𝑙). Then, to calculate the state in discrete space, the above filters are converted to a discrete system by a generalized bilinear transformation with coefficient 0.5 [29]:…”

Section: Identification Schemamentioning

confidence: 99%

The buffered optimization methods for online transfer function identification employed on DEAP actuator

2023

Archives of Control Sciences

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Identification plays an important role in relation to control objects and processes as it enables the control system to be properly tuned. The identification methods described in this paper use the Stochastic Gradient Descent algorithms, which have so far been successfully presented in machine learning. The article presents the results of the Adam and AMSGrad algorithms for online estimation of the Dielectric Electroactive Polymer actuator (DEAP) parameters. This work also aims to validate the learning by batch methodology, which allows to obtain faster convergence and more reliable parameter estimation. This approach is innovative in the field of identification of control systems. The research was supplemented with the analysis of the variable amplitude of the input signal. The dynamics of the DEAP parameter convergence depending on the normalization process was presented. Our research has shown how to effectively identify parameters with the use of innovative optimization methods. The results presented graphically confirm that this approach can be successfully applied in the field of control systems.

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Section: Identification Schemamentioning

confidence: 99%

The buffered optimization methods for online transfer function identification employed on DEAP actuator

2023

Archives of Control Sciences

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“…Many scholars have proposed methods to obtain the matrix for bilinear transform, of which the literatures [4][5][6] were to derive coefficient matrix of different order under the discussion of relationships between the matrix elements, while [7,8] used method of induction to derive coefficient matrix of order n from coefficient matrix of order zero. Other relative reference as [9][10][11][12][13][14] also studied quick algorithms for different forms of linear -to-transform.…”

Section: Problems To Bementioning

confidence: 99%

Transformation Matrix for Time Discretization Based on Tustin’s Method

Jiang

2014

Mathematical Problems in Engineering

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This paper studies rules in transformation of transfer function through time discretization. A method of using transformation matrix to realize bilinear transform (also known as Tustin’s method) is presented. This method can be described as the conversion between the coefficients of transfer functions, which are expressed as transform by certain matrix. For a polynomial of degreen, the corresponding transformation matrix of ordernexists and is unique. Furthermore, the transformation matrix can be decomposed into an upper triangular matrix multiplied with another lower triangular matrix. And both have obvious regularity. The proposed method can achieve rapid bilinear transform used in automatic design of digital filter. The result of numerical simulation verifies the correctness of the theoretical results. Moreover, it also can be extended to other similar problems. Example in the last throws light on this point.

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“…ESIGNING classical and/or fractional order control laws involving integral and differential actions [1,2] often requires formulation of a discrete model of the process by using methods of invariable response to a pulse or Heaviside excitation and a series of other approximate methods [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Since a process can, in general, is represented by a transfer function G p (s) which is not a rational function [21,22], the problem of rational approximation and discretization in general becomes complex.…”

Section: Introductionmentioning

confidence: 99%