Derivative State Constrained Optimal H₂ Control for Oscillatory Systems and its Application

Abstract

The optimal H₂ control of oscillatory systems via the constraints of the derivatives of state variables is discussed and applied to a physical system in this paper. It is shown that the derivative state constrained optimal H₂ control can be reduced into the standard optimal H₂ control problem with modified controlled output equations. The solution to the modified standard problem has salient features for controlling oscillatory systems that have been a tough subject in state space as well as in classical frequency domain controls.
The results obtained in the paper suggest the directions how to select the constraining weights in the standard state space control designs of oscillatory systems.
The application of this approach to the control of a two-inertia resonance system is shown to demonstrate the proposed schemes.