1#. • Basis Weight Control System
` )NTRODUCTION The basis weight control loop of the papermaking process has the characteristics of large time-delay and external interference; hence, it is difficult to establish an accurate mathematical model [1] . Previous studies [2 3] have demonstrated that its model is usually approximated to a low-order transfer function with time-delay, including first-order-plus-dead-time (FOPDT) or second-order- plus-dead-time (SOPDT) structures. Because these models not only effectively reflect the basic dynamics of the paper industry process, they can also contribute to the design of the controller. With the extensive use of model-based advanced control methods in the papermaking process, the high-precision identification of models is one of the challenges that urgently needs to be solved in the control field. Therefore, it is very important to identify the FOPDT or SOPDT models for designing the controller and maintaining stable operation of the papermaking process. Several effective system identification techniques [4 9] have been proposed. The least square method (LSM) [10] is an effective method to identify models of time-delay. This method is an identification algorithm based on discrete systems; therefore, the continuous transfer function needs to be discretized. The improper selection of sampling intervals and non-integer optimization problem of systems with time-delay can increase the difficulty of identification. A frequency domain identification method [11] is proposed to identify the parameters of a system with time-delay. It requires a small amount of calculation and strong robustness, but ignores the high-frequency dynamics of the system, and is easy to converge locally. Filter-based adaptive identification algorithm [12] is the most commonly employed method to identify time-delay systems and avoid local minima under full excitation; however, full excitation is not suitable for practical industrial processes. Therefore, it is meaningful to determine a system identification method with strong identification ability, good robustness, and suitable for engineering practice. Recently, intelligent optimization technologies have
garnered significant attention in system identification [13 17] . One of the most popular optimization algorithms for system identification is particle swarm optimization (PSO)-based algorithm [18] . PSO algorithm is a population-based optimization algorithm introduced by Kennedy and Eberhart in 1995 [19] . It is used to identify time-delay model parameters and achieved good results [20] . However, classical PSO is easily classified as local optimal value and its local search ability is relatively poor. To improve the performance of PSO algorithm, various versions of the improved PSO algorithm have been proposed. Zou et al [21] proposed an improved PSO algorithm to identify the infinitive impulse response (IIR) system. Using the golden section rate to divide the solution space, different inertia weights and normal distribution improve the global search ability and convergence speed of the algorithm to obtain high-quality solutions. Feng et al [22] proposed a modified PSO algorithm to identify micro piezoelectric actuators. This method improves the ability of global optimization and ensures the accuracy of parameter identification. Strange nonchaos [23 28] is an unstable dynamic behavior with randomness and ergodicity in deterministic nonlinear systems, which is highly sensitive to system parameters. Based on the strange nonchaotic behavior, it can perform the overall search faster than the probability-dependent random ergodic search. In this study, an strange nonchaotic particle swarm optimization (SNPSO) algorithm is proposed to identify the papermaking process. First, random particles are initialized by strange nonchaotic sequences to obtain high-quality solutions. Furthermore, the weights updating with strange nonchaotic features and time-varying acceleration coefficient are used to improve the global search ability and search speed. Finally, a mutation individual with strange nonchaotic characteristics is utilized to further improve the global search ability. Simulation results demonstrate the effectiveness of the algorithm. To highlight the advantages of the proposed algorithm, a comparative study is also implemented, and it is proved that the convergence speed, global search ability, and robustness of SNPSO are superior to classical PSO [19] , PSO with
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