The SDRE controller and estimator design for flexible joint manipulators in presence of noise and disturbance

Full feedback data is mostly essential in control design. The measurement of the variation of flexible joint robot (FJR) actuators is not easy as the measurement of the changes of FJR links’ angles. The measurement of the states is also affected by noise, and the disturbance in the workspace of the robot is not ignorable. Hence a state observer or a nonlinear estimator is necessary to improve the performance of the dynamic system. The state-dependent Riccati equation (SDRE) is one of the most promising nonlinear optimal control methods for estimating variables of systems. Systematic procedure, simple structure, and incorporating wide range of systems (under observability condition) are some advantages of SDRE method. The majority of nonlinear techniques linearize the model, but the SDRE directly uses the nonlinear state space; it is one of the reasons for its precision and flexibility in design with respect to other methods. The goal of this work is to merge the SDRE controller and estimator simultaneously to reduce the state error of the system in presence of external disturbance and measurement noise. So, first, the controller and the observer formulation has been stated. Then, the procedure has been applied to design and to simulate a 3 DOF robot arm with flexible joints. Next, the process has been tested experimentally using Scout robot and the simulation results have been verified. Finally, the proposed method of this paper has been compared with the optimal sliding mode.