Optimal Setting and Control Strategy for Industrial Process Based on Discrete-Time Fractional-Order PI$^{\lambda}$ D$^{\mu}$

Abstract

Generally, the main task of the optimal operation in the industrial process is to satisfy the process technical requirements, and the PID controller is a well-known controller in industrial control applications. Nevertheless, due to the complicated mechanisms and the dynamic characteristics of a complex industrial process, the conventional PID controller fails to provide effective control to such systems. In this paper, we develop a novel discrete-time fractional order PID (DFOPID) control strategy to achieve the technical requirements of the complex industrial process. The proposed work is conducted through a combination of three novel interdependent efforts. First, on the basis of the widely used Tustin operator and its Taylor series, a digital structure of the DFOPID is proposed. Second, in order to solve the stability problem of the complex industrial process, an optimal setting of the approximation function's order (N) and five parameters (λ, μ, K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> , K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> , K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> ) is necessary. Hence, an integral time absolute error (ITAE) criterion is applied to convert the optimal setting problem to a nonconvex optimization problem. Finally, a novel intelligent optimization search algorithm called state transition algorithm is employed to carry out the aforementioned design procedure. Furthermore, the performance of the DFOPID control strategy in some practical industrial control systems, including the copper removal process and the electrochemical process of zinc are also investigated.