Near time-optimal control with smooth mode-switching for uncertain time-varying systems

This paper proposes a scheme of near time-optimal control with smooth mode switching. A near time-optimal switching curve is first determined for second-order systems with uncertain time-varying parameters and external disturbances. Instead of utilizing an extreme bang-bang control, a sliding-mode control is proposed to ensure the existence of a sliding motion on the switching curve while alleviating the chatter phenomenon. Around the goal state, a mode-switching control (MSC) transfers the active controller from the near time-optimal control to global sliding-mode control (GSMC) that maintains the near time-optimal behavior during the period between the mode-switching instant and the terminal time when the representative point (RP) just arrives at the origin in the phase plane. The proposed initial value compensation (IVC) performed at the mode-switching instant is insensitive to plant parameter variations and utilizes only the information on system output, instead of all state variables, leading to a more precise IVC. After the terminal time, an integral action is introduced to improve the steady-state performance while diminishing possible overshoot. Experimental results show the effectiveness as well as the feasibility of the proposed scheme.