Feedforward and feedback optimal control with memory for offshore platforms under irregular wave forces

This paper studies the vibration suppression of actively controlled jacket-type offshore platforms with fixed delay in the control. Based on the wave theory and Morison equation, an exosystem is designed to describe the irregular wave forces. Through a particular transformation, the original delay system is reduced into a non-delay system. Based on the reduced system, the paper develops a feedforward and feedback optimal control law with memory (FFOCLM). The memory terms in FFOCLM compensate the time-delay in control input. The feedforward term of the controller includes the information of the irregular wave forces. The feedback loop incorporates the displacement and velocity of structure into the control law. The FFOCLM is proved to be existent and unique, and able to stabilize the time-delay system. The feasibility and effectiveness of the presented control law is demonstrated by a numerical example of a jacket-type offshore structure.