Nonlinear adaptive robust control with continuous error reduction mapping

Abstract Achieving high stability and high-precision control by traditional control algorithms is difficult due to the strong nonlinearity, parameter uncertainty, and random disturbance characteristics of electro-hydraulic proportional servo systems. Herein, we developed a nonlinear adaptive control algorithm based on Lyapunov functions. By estimating the parameters and converging their errors, this algorithm solved the parameter adaptation problem. Additionally, based on convergence inference from the nonnegativity of the derivative of Lyapunov functions, the algorithm designed a disturbance mapping through the derived function. The random disturbance was reduced through the mapping, improving the stability of the system under random disturbance. Finally, we carried out continuous derivation and moved the mapping relationship out of the intermediate temporary controller. This reduced the complexity of the calculation during controller design, prevented performance degradation of the error convergence algorithm after complex calculation, and enhanced the robustness of the algorithm. The algorithm was verified through the simulation model established by Simulink and experience. Results showed that the nonlinear adaptive control algorithm demonstrates fast response, high accuracy, and strong anti-interference ability compared with the high-gain robust control algorithm. It realizes the adaptation of unknown parameters and reduces the control error introduced by random disturbance.