Indirect Adaptive Robust Backstepping Control for Input Delay Systems With Unknown Periodic Disturbances: Theory and Experiments

This article proposes an indirect adaptive robust backstepping control method for trajectory tracking of input delay systems with unknown plant parameters and periodic disturbances. By modeling the delay as a transport PDE and using the backstepping boundary control technique for PDEs, the underlying robust control is established including the model compensation, predictor feedback and nonlinear robust feedback, ensuring the robust stability in the coexistence of delay and uncertainties. Periodic disturbances are addressed by their finite Fourier series expansion with unknown Fourier coefficients. Meanwhile, the upper-layer adaptation law based on the actual system dynamics, is utilized to estimate unknown plant parameters and Fourier coefficients in batches to reduce parametric uncertainties. The adaptation law is constructed totally independent from the design of underlying robust control law, which allows practical modifications, such as the on-line explicit monitoring, of signal excitation levels to improve the accuracy of parameter estimates in implementation. Comparative experiments on a voice coil motor setup confirm the effectiveness of the proposed controller.