Simultaneous optimal design of structural and control systems for cantilevered pipes conveying fluid

We consider a shape optimization problem for a cantilevered pipe conveying fluid. The outer diameter distribution of the pipe and the location of the sensor and the actuator are optimized such that the critical flow velocity of the closed-loop system is maximized. The outer diameter distribution is optimized such that the total volume of the pipe is unchanged with the initial diameter distribution. The critical flow velocity of the closed-loop system is defined as the flow velocity which cannot be stabilized by active control law with a predetermined energy quantity. By this definition, it is physically reasonable comparing the quality of several design candidates since all candidates are actively controlled with the same energy consumption. We propose a method for obtaining the critical flow velocity with consideration of the amount of computation for the optimal design. This optimal design problem results in a maximization problem with equality and inequality constraints. We adopt simulated annealing method which is known as one of discrete optimization techniques for obtaining the optimal design.