Sliding mode control using a switching function incorporating the state trajectory approach angle

This dissertation work presents a novel continuous switching term to be used as part of a sliding mode controller. The novel continuous switching term incorporates the state approach angle, which is a measure of the orientation of the state trajectory with respect to the sliding surface. By incorporating the state approach angle into the continuous switching term, the continuous switching term behaves similar to a discontinuous switching term, as the state trajectory nears the sliding surface. The mimicing of a discontinuous switching term ensures that the continuous switching sliding mode control achieves asymptotic stability; which is usually not the case for a traditional continuous switching sliding mode control. Since the novel sliding mode control is continuous switching-based, system chattering is kept to a minimal level. The theory is developed for a second order system of regular form; this theory is then extended to a general nth order system, that has nonlinear system function components. Asymptotic stability of the novel continuous switching sliding mode control is verified in the Lyapunov-sense. The novel sliding mode control is applied to some examples; along with a discontinuous switching sliding mode control and a traditional continuous switching sliding mode control, to demonstrate its merit. A detailed case study on wheel slip control is included as one of the application examples. A historical background on controlled braking is given and formulations of the numerical models used for simulations are included as part of the case study. Algorithms are given in the Appendices to determine the state approach angle for various system orders.