Spline adaptive inverse control scheme with filtered error feedback

This paper presents a new scheme for the control of unknown block-oriented nonlinear systems using spline adaptive filter (SAF). The principle of adaptive inverse control (AIC) is utilized as the control structure in this scheme. First, the mathematical model of the unknown controlled plant was established through SAF, which consists of a linear FIR filter and a nonlinear spline interpolation function. The controller is obtained by adaptively establishing the inverse model of linear FIR filter and nonlinear spline function, respectively. In this process, a shift form DCT-LMS with variable learning rate (VL-DCTS-LMS) algorithm is proposed in order to adapt the inverse of FIR filter, and a modified Newton–Raphson method is used for directly calculating the inverse of spline interpolation function. Considering the steady-state error resulted by the plant modeling inaccuracy, filtered error feedback is introduced into the plant input in order to eliminate the control error. The effectiveness of the proposed control scheme is verified by several numerical examples, including some additional discussions and a comparison with other control methods.