Stabilization of Cart-Pole System-A Linear Quadratic Gaussian Control and Robust H-infinity Control Design and Comparative Approach

A cart-pole system is a highly nonlinear as well as an unstable system, which can be utilized as a benchmark system for the testing and designing purposes of different control efforts and it is the widely used application of control system and robotics. For getting the stability of cart-pole system Linear Quadratic Gaussian optimal control problem is formulated which is based on the design of state observer. According to the principal of separation of the problem, at the beginning the control law is generated just after solving ARE using Schur Decomposition to design a controller, which is totally based on principal of state feedback and the point of time comes when all the states of the system can not be measured at the same time there is a presence of process noise as well as measurement noise, optimal state estimator (i.e. Kalman Filter) is made for cart-pole system. Robust \({H}_{\infty }\) controller has been designed using plant augmentation with weighting functions for the system to carry out the frequency domain analysis of the given system. The simulation results reveal that the controllers can stabilize the cart-pole system at the same time it eliminates noise presents in the system and makes the system robust. Numerical experimentation has been carried out to compare the different approaches.