Robust control and optimized parallel control double loop design for mobile robot

Robots have been used in many applications in the past few decades. Moreover, due to high nonlinearity behavior of these systems, an optimal and robust control design approaches have been considered to stabilize and improve their performance and robustness. The uncertainties of the time delay on the output states of the mobile robot system have a significant influence on the system nominal performance. As a result, the work becomes here to address the influence of these uncertainties on the robot system performance. In order to achieve this objective, the nonlinear controller via sliding mode control (SMC) is designed by selecting a suitable sliding surface dynamics in which the considered robot displacement and tilt angle are sliding on. The lyapunov function is considered here to accomplish the design of the sliding control signals for robot stabilization. Furthermore, the stability of the considered system is guaranteed due to convergence of the lyapunov functions into zero when the state trajectories tend to desired set points. In addition, we consider the trajectory tracking and stabilization of TWBMR system using parallel double loop PID controllers whose controllers gains are tuning via Linear Quadratic Regulator (LQR) approach.  Finally, to demonstrate the effectiveness of SMC and PID-LQR design methods, the comparison is carried out when the nominal and uncertain conditions.