Nonlinear Optimal Control of a Two Wheeled Self Balancing Robot

Two wheeled self balancing robots have dynamic behaviour and are unstable in nature. Due to this, stabilizing of these robots has become a field of interest to many researchers. Around the equilibrium point of two wheeled self balancing mobile robot, the pitch angles are very small. Hence the balancing is achieved commonly by using linear control methods such as LQR(Linear Quadratic Regulator) control, PID(Proportional Integral Derivative) control etc. But the robots with large pitch angles tends to be in a region of high nonlinear behavior. Hence the linear control techniques fails in maintaining the balance of the robot. To remedy this problem and for improving the performances of the robot, an SDRE(State Dependent Riccati Equation) controller is designed along with SDC (State Dependent Coefficient) Matrix. Simulations are done to check the stability using SDRE controllers. A comparison is done using SDRE, PID and LQR controllers for the system with nonlinear dynamics. Also a comparison is done using PID and LQR controllers for the system with linear dynamics. From the simulations it is clear that SDRE controller shows excellent balancing for the two wheeled self balancing robot when compared to PID and LQR controllers.