Publikationen

In this paper, an eigenvalue-based discretization scheme is applied to a novel adaptive super-twisting-algorithm. Following the proposed procedure the discretization chattering effect is avoided entirely. An attractive property of the adaptation law is the insensitivity of the closed-loop system to overly large gains which in existing laws potentially leads to instability. Using Lyapunov's direct method the stability of the feedback loop is shown. Numerical examples underline the beneficial properties of the proposed methodology.

A discrete-time implementation of a continuous-time adaptive gain sliding mode control law for a system with matched disturbance is presented. The discrete-time control algorithm is derived from the solution of the nominal continuous-time closed-loop dynamics. This approach ensures elimination of discretization chattering as well as proper disturbance rejection. Slight modifications of the resulting discrete-time control law are proposed to guarantee ultimate boundedness of the sliding variable and the adaptive gain which is formally proven by means of Lyapunov arguments. Prevention of discretization chattering and disturbance attenuation properties are validated in a simulation and compared to other approaches.