Suboptimal control of a 3 dof helicopter with state dependent riccati equations

The paper presents the application of State Dependent Riccati Equation (SDRE) based optimal controller design for nonlinear systems. Optimal controller is designed in local sense to minimize a given quadratic performance index, leading to well-known Linear Quadratic Regulator (LQR) problem and the optimal controller is updated at each sampling time to cope with the nonlinear dynamics. Since the SDRE based optimal controller is designed by freezing the nonlinear system at some sampling periods, the effect of sampling period on the performance index is studied. The SDRE based optimal controller is designed for an experimental setup of a 3 DOF Helicopter and implemented on the setup for different working frequencies. The performance index and therefore the values of the cost function is then computed for different working frequencies. Experimental studies reveals that an increased sampling period results in decreased value of the cost function.