Active vibration control for ship pipeline system based on PI-LQR state feedback

An active vibration control method based on PI-LQR (Proportional Integral-Linear Quadratic Regulator) state feedback is studied to suppress the vibration of ship pipeline systems. LQR is a common optimal calculation method of proportional active control. However, PI active control may cause the uncontrollability of the extended system, which leads to the failure of combination of PI and LQR. To solve this problem, a PI-LQR controller is designed and proposed in this paper. Firstly, an arrangement method of sensors and controllers is introduced according to the Gramian theory of observability and controllability. Then, Based on a modified system matrix, the revised extended system achieves to be controllable, such that LQR becomes available to the quick calculation of the approximate control gains. Moreover, the proof and example simulations of the provided method are given. Compared with the classical LQR-based proportional control in the example simulation, PI-LQR control makes the vibration acceleration levels of the sensors decrease 0.29 dB on average and 2.00 dB maximally, which verifies the effectiveness and superiority of the obtained results.