Non-Parametric Loop-Shaping Algorithm for High-Order Servo Systems Based on Preset Frequency Domain Specifications

Loop shaping the controller for high-order systems, especially in the presence of flexible transmission components such as elastic shafts, gearboxes, and belts commonly found in servo systems, poses significant challenges. Therefore, developing a non-parametric, versatile tuning algorithm that adapts to multi-order systems is essential for general control applications. This article first obtains the frequency characteristics of plants through a frequency sweep. Then, based on preset frequency domain specifications, the boundaries representing disturbance rejection and stability constraints are defined in the complex plane with explicit mathematical and graphical expressions. Subsequently, a system of equations is developed based on the tangency between the open-loop curve of the system and the boundaries in the complex plane. On this basis, a versatile tuning algorithm is designed to calculate parameters of a PI controller cascaded with a low-pass filter that ensures the system meets the preset constraints. The proposed approach does not rely on parametric modeling, and the zeros and poles of the controller can be flexibly placed. Experimental validation is carried out on mechanical platforms.