This paper proposes a robust control for wheeled inverted pendulum (WIP) taking into account the wheel position and pendulum angle in the presence of uncertain disturbances. The proposed control algorithm is a combination of time-varying sliding mode control (TVSMC), exponential reaching law (ERL), and nonlinear feedback control (NFC) to eliminate the chattering phenomenon and arrive at better stability and tracking performance. For consistency, the nonlinear dynamic model of WIP is derived using Lagrangian and Newtonian approaches. The convergence and stability of the proposed control scheme are proved using Lyapunov theorem. The study also presents a comparative analysis of linear and nonlinear control strategies based on investigation of time response, tracking error, and control energy. The WIP system has been subjected to various rigorous initial conditions and disturbances to characterize the stability and tracking performance of the implemented controllers. The simulation results demonstrate the promising performance of the proposed control scheme in eliminating the chattering phenomenon, suppressing the uncertain disturbances effect, and improving the stability and tracking performance.

本文提出了一种对轮式倒立摆 (WIP) 的鲁棒控制，在存在不确定干扰的情况下，考虑了车轮位置和摆角。所提出的控制算法是时变滑模控制（TVSMC）、指数到达律（ERL）和非线性反馈控制（NFC）的组合，以消除颤振现象并达到更好的稳定性和跟踪性能。为了一致性，WIP 的非线性动态模型是使用拉格朗日和牛顿方法导出的。使用李雅普诺夫定理证明了所提出的控制方案的收敛性和稳定性。该研究还基于对时间响应、跟踪误差和控制能量的研究，对线性和非线性控制策略进行了比较分析。WIP 系统经受了各种严格的初始条件和干扰，以表征所实施控制器的稳定性和跟踪性能。仿真结果表明，所提出的控制方案在消除颤振现象、抑制不确定扰动效应、提高稳定性和跟踪性能方面具有良好的性能。