Convergence Control For Topology Optimization

Proportional-Integral-Derivative (PID) control theory is applied to the evolutionary rate of the Bi-Directional Evolutionary Structural Optimization (BESO) method to control aspects of the convergence such as the rise time, stability, and other convergence characteristics. When the PID controller is applied to the BESO topology optimization method, its behavior resembles that of a second order linear system and its response depends on whether it is an overdamped, critically damped or underdamped system. The new algorithm replaces the evolutionary rate control parameter with the three gain values of the controller, namely, the proportional gain, the integral gain and the derivative gain for further control the structure’s evolution.