Design of Robust Adaptive Fuzzy Controller for a Class of Single-Input Single-Output (SISO) Uncertain Nonlinear Systems

In order to solve the precision and stability control problems of nonlinear uncertain systems applied in machining systems, in this paper, a robust adaptive fuzzy control technique based on Dynamic Surface Control (DSC) method is proposed for the generalized single-input single-output (SISO) uncertain nonlinear system. A first-order low-pass filter is introduced in each step of the traditional robust control method to overcome the “calculation expansion” problem, and Takagi–Sugeno (T-S) fuzzy logic system is applied to approximate an uncertain nonlinear function of unknown structure in the system. The designed robust adaptive fuzzy controller is applied to the 3D elliptical vibration cutting (3D EVC) device system model, and the effectiveness of the controller design is verified by analysis of position tracking, speed tracking, and tracking error. The results of studies show that the robust adaptive fuzzy controller can effectively suppress the jitter problem of the three-dimensional elliptical vibration cutting device so that the control object can be stabilized quickly even if it has a little jitter at the beginning. It can be smoothed to move along the ideal displacement and velocity signals. It is verified that the designed controller has strong robust adaptability.