Abstract
The present research develops the parametric estimation of a second-order transfer function in its standard form, employing metaheuristic algorithms. For the estimation, the step response with a known amplitude is used. The main contribution of this research is a general method for obtaining a second-order transfer function for any order stable systems via metaheuristic algorithms. Additionally, the Final Value Theorem is used as a restriction to improve the velocity search. The tests show three advantages in using the method proposed in this work concerning similar research and the exact estimation method. The first advantage is that using the Final Value Theorem accelerates the convergence of the metaheuristic algorithms, reducing the error by up to 10 times in the first iterations. The second advantage is that, unlike the analytical method, it is unnecessary to estimate the type of damping that the system has. Finally, the proposed method is adapted to systems of different orders, managing to calculate second-order transfer functions equivalent to higher and lower orders. Response signals to the step of systems of an electrical, mechanical and electromechanical nature were used. In addition, tests were carried out with simulated signals and real signals to observe the behavior of the proposed method. In all cases, transfer functions were obtained to estimate the behavior of the system in a precise way before changes in the input. In all tests, it was shown that the use of the Final Value Theorem presents advantages compared to the use of algorithms without restrictions. Finally, it was revealed that the Gray Wolf Algorithm has a better performance for parametric estimation compared to the Jaya algorithm with an error up to 50% lower.
Highlights
Transfer functions are widely used in engineering and other fields to represent physical systems of various natures
The case of second-order transfer functions is unique since they represent a large number of physical systems
The results show that the algorithm can recreate the signal of the transfer function with real signals
Summary
Transfer functions are widely used in engineering and other fields to represent physical systems of various natures. Identification is essential for industrial processes, as mentioned in [6,7,8,9] Another example is [10], where a fractional transfer function is used for modeling and control applications, implementing a low-order algorithm for their application. Investigations [11,12,13,14,15] work with systems described by a second-order transfer function. An option that presents greater simplicity and ease of implementation is the so-called metaheuristic algorithms [16] This type of algorithm has the advantage of its relative simplicity and the disadvantage that the process is iterative [16].
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