An Asymptotic Second‐order Smooth Sliding Mode Control

Presented is a method of smooth sliding mode control design to provide for an asymptotic second‐order sliding mode on the selected sliding surface. The control law is a nonlinear dynamic feedback that in absence of unknown disturbances provides for an asymptotic second‐order sliding mode. Application of the second‐order disturbance observer in a combination with the proposed continuous control law practically gives the second‐order sliding accuracy in presence of unknown disturbances and discrete‐time control update. The piecewise constant control feedback is “smooth” in the sense that its derivative numerically taken at sampling rate does not contain high frequency components. A numerical example is presented.