Identification from step response – The integral equation approach

Ahmed, Salim

doi:10.1002/cjce.22645

Cited by 8 publications

(17 citation statements)

References 74 publications

(163 reference statements)

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“…Then, eq 6 can be transformed into the form of the integral equation as eq 7 , and then, eq 8 is obtained through the inverse Laplace transform, which can be written as the matrix form as eq 9 . 18 …”

Section: Process Modelingmentioning

confidence: 99%

“…By integrating eq 8 on both sides to increase the number of equations, the unknown steady-state value is solved. 18 However, multiple integrations will increase the error, and the solution effect may be not good.…”

Section: Process Modelingmentioning

confidence: 99%

“… 26 Step response may be not available, and step response can be obtained from nonstep response with a filter as in eq 15 . 18 However, this kind filter is hard to be implemented when the controller output U is not an explicit expression. …”

Section: Process Modelingmentioning

confidence: 99%

See 2 more Smart Citations

Proportional–Integral–Derivative Controller Performance Assessment and Retuning Based on General Process Response Data

Sheng

2021

ACS Omega

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In this paper, the current research status of controller performance assessment is reviewed in brief. Solving the problem of proportional–integral–derivative performance assessment usually requires step response data, and several methods are combined and extended. Using the integral of signals, implicit model information contained in process response data becomes explicit, and then the least squares approach is adopted to construct a detailed low-order process model based on process response data in more general types. A one-dimensional search algorithm is used to attain better estimation of process time delay, and integral equation approach is extended to be useful for more general process response. Based on the obtained model, a performance benchmark is established by simulating model output. Appropriate retuning methods are selected when the index of absolute integral error (IAE) indicates bad performance. Simulations and experiments verify the effectiveness of the proposed method. Issues about estimation of process time delay, data preprocessing, and parameter selection are studied and discussed.

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Section: Process Modelingmentioning

confidence: 99%

Section: Process Modelingmentioning

confidence: 99%

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Proportional–Integral–Derivative Controller Performance Assessment and Retuning Based on General Process Response Data

Sheng

2021

ACS Omega

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“…From step‐response tests, the auxiliary information regarding overshoot, the period between damped oscillations and the settling time seems to be a reasonable way to define the LMI regions in practice. Step response data are often employed to estimate second‐order dynamical models [20–23]. However, the auxiliary information obtained from experimental data may be uncertain due to many reasons, e.g., the measurement noise on data and the complexity of the system dynamics.…”

Section: Introductionmentioning

confidence: 99%

Mapping prior information onto LMI eigenvalue‐regions for discrete‐time subspace identification

Ricco

Teixeira

2020

IET Control Theory & Applications

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In subspace identification, prior information can be used to constrain the eigenvalues of the estimated state-space model by defining corresponding LMI regions. In this paper, first we argue on what kind of practical information can be extracted from historical data or step-response experiments to possibly improve the dynamical properties of the corresponding model and, also, on how to mitigate the effect of the uncertainty on such information. For instance, prior knowledge regarding the overshoot, the period between damped oscillations and settling time may be useful to constraint the possible locations of the eigenvalues of the discrete-time model. Then, we show how to map the prior information onto LMI regions and, when the obtaining regions are non-convex, to obtain convex approximations.

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“…The step identification approach is to estimate the parameters of CT models from step responses. Typical technologies related to this approach include the two‐point fitting method, the integral equation method [4], the frequency domain method [5], and so on [6]. The defect of this approach is that only the lower‐order models plus time delay such as first‐order plus time delay (FOPTD) and second‐order plus time delay (SOPTD) can be identified from step responses.…”

Section: Introductionmentioning

confidence: 99%

A two‐stage searching method for continuous time‐delay systems identification

Meng

2019

Asian Journal of Control

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This paper presents a novel method to estimate the unknown parameters of continuous‐time systems with time delay. In the proposed method, the time delay and plant parameters are estimated separately. To estimate the time delay, a one‐dimensional searching method with variable step size is proposed to improve computational efficiency. The searching method consists of two stages: the coarse stage and the refined searching stage. To analyze the convergence of the searching method, the concept of significant interval is proposed. By defining the significant interval, a sufficient condition for global convergence of the searching method is provided. Based on the two‐stage searching method, a novel identification algorithm is developed in which the simplified refined instrumental variable for continuous‐time models algorithm is used to estimate the plant parameters. Simulation results demonstrate that the proposed identification method can estimate the unknown parameters of continuous‐time system with time delay efficiently. The estimation results under different noisy conditions verify the reliability and robustness of the proposed method. The applicability of the developed identification method is demonstrated by a practical example.

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Identification from step response – The integral equation approach

Cited by 8 publications

References 74 publications

Proportional–Integral–Derivative Controller Performance Assessment and Retuning Based on General Process Response Data

Proportional–Integral–Derivative Controller Performance Assessment and Retuning Based on General Process Response Data

Mapping prior information onto LMI eigenvalue‐regions for discrete‐time subspace identification

A two‐stage searching method for continuous time‐delay systems identification

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