Modified Nonlinear Proportional–Integral Retarded controller for precision positioning in nano-scale systems
摘要
Precision positioning regulation tasks in nano-scale systems demand exceptional precision and stability, which are fundamental for applications in nanotechnology, biotechnology, and advanced manufacturing. This study aims to enhance nano-scale position regulation by introducing a Modified Nonlinear Proportional–Integral Retarded controller that eliminates the need for reference signal filtering. In addition, the proposed controller ensures that control signal values remain within the manufacturer’s specified range, thereby preventing damage, overshoot, or oscillations that could compromise nano-scale positioning accuracy. The proposed method integrates nonlinear dynamics and delayed control strategies, enabling the Modified Nonlinear Proportional–Integral Retarded controller to improve precision and robustness, effectively addressing challenges related to measurement noise, system disturbances, and parameter uncertainties. Experimental and theoretical analyses confirm its ability to optimize positioning accuracy. Furthermore, its performance is compared with that of a Proportional–Integral Retarded controller, highlighting the advantages of the modified approach in achieving reliable, high-precision regulation for nano-scale positioning tasks, resulting in smoother control effort and reduced overshoot and oscillatory behavior. To provide a thorough assessment, the error expressed in pulses was analyzed. This metric directly measures the deviation in terms of actuator resolution, offering a practical gauge of positioning accuracy. By incorporating pulse error into the analysis, the study highlights not only the robustness of the proposed controller against disturbances and uncertainties but also its capability to minimize positioning errors at the nanometer scale, achieving errors as low as 50 nm.