State Feedback in the Context of a Gyroscopic Rotor using a Disturbance Observer

In this article, a Disturbance Observer is utilized to realize state feedback in the context of a rotor test rig. The rotor is actively supported by means of piezoelectric stack actuators and subject to unbalance excitation and gyroscopic effect. The presence of gyroscopic effect leads to a dependence of the system dynamics on rotary frequency of the shaft. Due to unknown disturbances in the form of unbalance excitation and system deviation due to gyroscopic effect, ordinary linear time invariant observers fail to observe the system states accurately for gyroscopic rotors, possibly leading to significant control performance reduction. To overcome this problem, a Disturbance Observer is applied to the problem. It is shown that the gyroscopic effect can be approximated accurately by an additive term in the state space equation and can thus be treated as an additional disturbance in Disturbance Observer design. Due to high steady state estimation accuracy, the presence of the Disturbance Observer does not affect steady state control performance and thus, controller and observer design are decoupled regarding control performance. Due to this fact, the controller can be designed prior to the observer despite system deviation due to gyroscopic effect and disturbances. However, since the separation principle does not hold for the system, stability proof has to be carried out by consideration of the entire closed loop system for all rotational frequencies within the operating range. A Linear Quadratic Regulator is used as a controller for the sake of simplicity. However, the proposed observer structure is applicable to arbitrary state space controllers. The resulting controller-observer combination is validated in simulation and experiment.