Harmonic oscillator utilizing double-fold integral, traditional and second-order sliding mode control

To stabilize both amplitude and frequency of the second-order harmonic oscillator double-fold sliding mode control is employed. The first, integral sliding mode control, is used to compensate for the disturbance/uncertainty, which is unmatched by the second control. The second sliding mode control is designed to achieve the stabilization of the harmonic oscillator system while the system is in the integral sliding mode. The first (integral) and second sliding mode controls are implemented in both formats: traditional sliding mode control that requires high-frequency oscillating control action and second-order sliding mode (super-twisting) control that is continuous and provides for the higher accuracy of stabilization. It is shown that the output of the double-fold sliding mode controlled second-order harmonic oscillator is robust to bounded disturbances and model parameter uncertainties. Computer simulations are performed to manifest the theoretical analysis.