A new adaptive backstepping control algorithm for motion control systems

A new adaptive integral backstepping control algorithm for motion control systems is proposed. Integral action is utilized to ensure the convergence of tracking error to zero at steady state in the presence of model inaccuracy and disturbance. The proposed design is a nonstandard approach in that it only implicitly and symbolically incorporates the error states into the Lyapunov function and computes the 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 a linear time-varying system and can be reformulated as a linear-nonlinear cascade system. The proposed control design is robust against system parameter variations. The robustness of the control system is verified by numerical examples that contain time-varying system parameters