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

Abstract

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. e 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. e 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. adaptive control and robust control methods cannot be used for controller design. However, for such problems, neural networks and fuzzy control can approximate uncertain continuous functions of the unknown structure in the system [11,12]. Ge et al. researched a robust adaptive neural network control method for a perturbed strictly feedback nonlinear system, which can guarantee the final boundedness in the case of unknown structural uncertainty [13]; Cao et al. proposed a new system control strategy using the global approximation property of the fuzzy system to approximate the unknown function of the designed system and ensure the stability of the whole system [14].However, in the system described above, it is satisfied that the unknown nonlinearity and the control input appear in the same state space model equation. In order to overcome the limitations of such systems, relevant research scholars have proposed adaptive post-push technology [4,6,15,16], furthermore successfully solved the constraint

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