Abstract
SummaryThis paper proposes a technique to extend a nominal homogeneous state‐feedback control law by continuous or discontinuous integral terms. Compared to pure state feedback, this permits to suppress non‐vanishing perturbations that are either constant or Lipschitz continuous with respect to time. The proposed technique seeks to do this while maintaining nominal performance in the sense that the nominal control signal and closed‐loop behavior is not modified in the unperturbed case. The class of controllers thus obtained is shown to include the well‐known super‐twisting algorithm as a special case. Simulations comparing the technique to other approaches demonstrate its intuitive tuning and show a performance preserving effect also in the perturbed case.
Highlights
Rejecting disturbances acting on a plant is one of the main goals of feedback control
Linear state feedback can usually attenuate very small disturbances or disturbances that vanish with vanishing state to a satisfactory degree, but fails to suppress large nonvanishing disturbances
The integral controller is constructed in such a way that the nominal performance is recovered in the unperturbed case
Summary
Rejecting disturbances acting on a plant is one of the main goals of feedback control. Homogeneous state-feedback control laws improve on the disturbance rejection capability of linear controllers due to their increase in (linearized) gain close to the equilibrium.[1] they fail to completely reject nonvanishing (even constant) disturbances. Handling such disturbances typically requires techniques such as disturbance observers or integral control. It is shown that global finite-time stability of the closed loop is achieved in the presence of constant or slope bounded, that is, Lipschitz continuous perturbations For the latter disturbance class in particular, the technique yields integral state-feedback control laws with discontinuous integrands
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