Active Vibration Control of Container Cranes against Earthquake by the Use of LMI Based Mixed H 2 / H ∞ State-Feedback Controller

This paper studies the design of a linear matrix inequality (LMI) based mixed H 2 / H ∞ state-feedback controller for vibration attenuation problem of seismic-excited container cranes. In order to show effectiveness of the designed controller, a six-degree-of-freedom container crane structural system is modeled using a spring-mass-damper subsystem. The system is then simulated against the real ground motion of El Centro and Northridge earthquakes. Finally, the time history of the crane parts displacements, accelerations, control forces, and frequency responses of both uncontrolled and controlled cases are presented. Additionally, the performance of the designed controller is also compared with a nominal state-feedback H ∞ controller performance. Simulations of the designed controller show better seismic performance than a nominal state-feedback H ∞ controller. Simulation results show that the designed controller is all effective in reducing vibration amplitudes of crane parts.