Title Discrete-Time Fast Terminal Sliding Mode Control Based on Generalized Implicit Reaching Law for Electronic Throttle

To achieve precise tracking control under the hardware of electronic throttle digital control, this paper proposes a novel implicit discrete-time fast terminal sliding mode control method for electronic throttles. Specifically, a recursive discrete-time fast terminal sliding surface is adopted, which can ensure that the system error converges to a smaller error bandwidth. To further eliminate the chattering problem in actual systems, a new generalized implicit discrete reaching law is designed. Compared with the traditional explicit Euler reaching law, the proposed implicit reaching law can effectively suppress the chattering caused by discretization through backward discretization (implicit discretization). Meanwhile, compared with existing implicit discrete reaching laws, the proposed reaching law has an explicit recursive equation, avoiding the problems of high computational complexity and difficult engineering implementation. Subsequently, strict theoretical analysis proves the existence of the quasi-sliding mode (QSM) and the convergence of the system tracking error. Moreover, experimental results demonstrate that the proposed controller achieves faster transient response, smaller steady-state tracking error, and significantly reduced chattering compared with DFSM, DSTWISTING, and DLSMC, highlighting its clear performance advantages over existing sliding mode methods.