Integral Sliding Mode Control for Self-balancing of a Two-Wheeled Mobile Robot with Uncertainties

Abstract

An inverted pendulum concept is used in two-wheeled self-balancing robots. TWMR system is a strongly coupled, nonlinear, and unstable system. The cart and pendulum system state space design model is the foundation upon which the model is built. The primary goal of this work is to develop an effective controller for robot that can tackle constant and time varying disturbances and parameter variations through the whole response in a real-time setting. In this thesis an optimal integral sliding mode controller (OISMC) is proposed to solve the reaching phase problem with SMC (Sliding Mode Controller) and keep the robustness during the entire motion. This controller distinguished in two parts: optimal controller for stabilizing the nominal system and discontinuous controller to assess the system in the presence of uncertainties. The stability of the system constructs the reachability of sliding mode and ensured by the Lyapunov theorem. Then, this applied to the nonlinear model of two wheeled mobile robot and performance is observed under different transient and uncertainty conditions. The results demonstrate that the technique offers a best performance to overcome parametric uncertainties and disturbance without modifying the integral sliding variable in sliding mode controller algorithm. The Integral sliding mode algorithm makes the robot immune to matched as well mismatched uncertainties means, when the uncertainties affects the system from different input channels or enter the robot through channels different from control input. A comparison also made with one of the best prevalent Optimal controllers Linear Quadratic Regulator (LQR)since both have same state feedback techniques and the proposed controller achieves a satisfactory control performance with robustness as compared to the LQR. Accordingly with uncertainties, the ISMC has a settling time of 1.0780sec, a rise time of 0.2267sec, and the LQR has a settling time of 4.4969sec, a rise time of 0.5741sec, for the tilt angle of TWMR , while the ISMC has a settling time of 0.8294sec, a rise time of 0.5870 sec, and the LQR has a settling time of 3.7646sec, a rise time of 0.6523 sec, for position response of the robot . On the other hand, the ISMC has a settling time of 1.8172sec, a rise time of 0.9783 sec, and the LQR has a settling time of 9.7382sec, a rise time of 1.8487sec, for yaw angle response. The overall system with the proposed method is simulated on MATLAB 2023a software.