In this paper, a nonlinear PID (NLPID) controller is used to replace a traditional PID controller to overcome the influence of nonlinear factors in the computer numerical control (CNC) system. A particle swarm optimization based on a generalized opposition-based learning (G-PSO) algorithm is proposed to optimize the NLPID controller. The convergence speed and global optimization ability of the particle swarm optimization (PSO) algorithm are improved by introducing generalized opposition-based learning. The natural selection mutation is introduced into the G-PSO algorithm to further avoid the particles falling into local optimization. Different from the existing research, this paper designs a special fitness function according to the control objectives of improving system response speed and suppressing overshoot. By comparing the differential evolution (DE) algorithm, the ant lion optimizer (ALO) and the genetic algorithm (GA) through simulation, it is proven that the G-PSO algorithm has a faster convergence speed and better global optimization ability. Compared to Fuzzy PID and MRAC PID, G-PSO NLPID is shown to be more suitable for CNC systems. Additionally, it is proven through experiments that the rise time and settling time of the NLPID controller optimized by the G-PSO algorithm are 22.22% and 24.52% faster, respectively, than the traditional PID controller, and the system overshoot is successfully suppressed.

The robustness of the control algorithm plays a crucial role in the precision manufacturing and measurement of the CNC machine tool. This paper proposes a fuzzy PID controller based on a sparse fuzzy rule base (S-FPID), which can effectively control the position of a nonlinear CNC machine tool servo system consisting of a rotating motor and ball screw. In order to deal with the influences of both the internal and external uncertainties in the servo system, fuzzy logic is used to adjust the proportion, and integral and differential parameters in real-time to improve the robustness of the system. In the fuzzy inference engine of FPID, a sparse fuzzy rule base is used instead of a full-order fuzzy rule base, which significantly improves the computational efficiency of FPID and saves a lot of RAM storage space. The sensitivity analysis of S-FPID verifies the self-tuning ability of its parameters. Furthermore, the proposed S-FPID has been compared with the PID and FPID via simulation and experiment. The results show that compared with the classical PID controller, the overshoot of the S-FPID controller is reduced by 74.29%, and the anti-interference ability is increased by 62.43%; compared with FPID algorithm, the efficiency of the SPID is improved by 87.25% on the premise of a slight loss in robustness.

NURBS curves have been widely applied in the field of data points approximation, and their fitting accuracy can be improved by adjusting the values of their weights. When applying the NURBS curve, it is difficult to obtain the optimal weights values due to the nonlinearity of the curve fitting problem with NURBS. In this paper, a weights iterative optimization method for NURBS curve fitting is proposed, where the geometric property of weight has been adopted to iteratively obtain the adjusting values of the weights with the least square method. The effectiveness and convergence of the proposed method are demonstrated by numerical experiments. The results show that the proposed method can obtain higher fitting accuracy than other iterative optimization methods. Meanwhile, it has the merits of data noise robustness, high accuracy with small-scale knots, and flexibility. Hence, the proposed method is suitable for applications including noisy data approximation and skinned surface generation.

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The physical optics (PO) method treats the outer surface of airborne radomes in front of antennas as a secondary source region when analyzing the electromagnetic performance. The effective reduction of the secondary source region can significantly improve the computational efficiency, which is helpful for the rapid analysis and design of airborne radomes. In this paper, we present a cylindrical equivalent source-based PO method by introducing an antenna radiation cylinder that can cover the main near-field radiation characteristics of the antenna. The cubic-spline interpolation technique is used to standardize the solution method for the boundary of the cylindrical equivalent source of different antennaradome systems. The results of a tangent-ogival radome verify the validity of the proposed method. Compared with the conical equivalent source-based PO method, the proposed method improves the efficiency by 71.83%. It can be applied to airborne antenna-radome systems with antenna diameters of 12.14 times of wavelength and above, using 10% as the error threshold.