Continuous time model identification using sinusoidal response

Fahim, Shaikh Mohammad (2018) Continuous time model identification using sinusoidal response. Masters thesis, Memorial University of Newfoundland.

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Abstract

System identification is an interface that unites the mathematical world of control theory and practical applications of control; as such its significance is omnipresent. Identification techniques involve differential equations where the coefficients are closely related to the physical parameters in the system; continuous time models have greater appeal than its discrete-time counterpart in understanding these interpretations. In this study, we have considered sinusoidal input for identification purpose as it has been discussed in the context of designing optimal input and also because it facilitates to excite processes with particular frequencies of interest. The primary objective of this work focuses on process parameter estimation. At first, integer order model is studied due to its simplicity, as order estimation is not necessary and thus the structure of the model. In addition, a comparison between different identification methods for better parameter estimates is performed on integer order model. Following on, fractional order model is taken into consideration with known and unknown order estimates. When solving for unknown model order, more emphasis is given on the logarithmic derivative term. According to literature, the unknown model order is estimated numerically whereas we provide an analytical expression of logarithmic derivative of sinusoidal inputs considering deterministic approach. For integer order model, although satisfactory results were achieved in terms of parameter estimates for different approaches varying different input constraints, it was evident that the performances varied with data length, and more importantly with the frequency of the input signal. The developed methodology for fractional order model identification with known model order lead fairly accurate estimates of the process parameters and when extended for unknown model order, exhibited highly satisfactory results as well but with higher computational time. The main challenge of this study was optimizing process parameters based on convergence; this issue was studied in simulation and corresponding numerical results for diverse noise levels met our expectations.

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