Fault-tolerant control of the self-balancing two-wheeled trolley with actuator saturation

The actuator saturation problem is very common in the real system, owing to the actuators are limited by physical factors. The balance and stability of the two-wheeled trolley is also plagued by the problem of actuator saturation. In order to establish its nonlinear mathematical model, we can change the stability issues into a standard control problem. Using the LMI to give a method of control algorithm design about fixed gain and adaptive gain. In conclusion, it's clear that adaptive control algorithm can make the closed-loop system to get a greatest attraction area under the normal and fault mode. The results show that adaptive control has the better effect by using the simulation.