Nonlinear Optimal Control for the Translational Oscillator with Rotational Actuator

Abstract

In this article, the problem of nonlinear optimal (H-infinity) control for a translational oscillator with rotating actuator (TORA) system is treated. The dynamic model of a translational oscillator with rotational actuator is generated through Euler-Lagrange analysis. This model undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the computation of the associated Jacobian matrices. For the linearized state-space model of the system, a stabilizing optimal (H-infinity) feedback controller is designed. This controller stands for the solution to the nonlinear optimal control problem under model uncertainty and external perturbations. To compute the controller’s feedback gains, an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis. Finally, to implement state estimation-based control without the need to measure the entire state vector of the TORA the H-infinity Kalman Filter is used as a robust state estimator.