A new adaptive backstepping control algorithm for motion control systems ― an implicit and symbolic computation approach

摘要

A new adaptive integral backstepping control algorithm for motion control systems is proposed. The design approach is non-conventional in that it only implicitly incorporates error states into a design Lyapunov function and computes time derivative of the Lyapunov function symbolically to the point of getting parameter estimate update laws on which desirable structures are imposed. The closed-loop error system turns out to be linear and time-varying and can be reformulated as a linear-non-linear cascade system. Uniform exponential stability or absolute stability can be achieved. The design is robust against system parameter variations. The effectiveness and robustness of the control algorithm are verified by numerical examples.