Optimal control and design optimization methods are used to optimize mechanical systems and decices, respectively. An offline optimal control of a two-link ball pitching robot is considered. The aim is to determine the optimal motor torque and release line that enables the robot to throw the ball as far as possible. The system is modeled based on the Euler-Lagrange formulation. Constraints on the motor torque and power as well as the angular velocity of the motor shaft are included in the model. We solve the resulting optimal control problem numerically by using an interior point method.
Design optimization is used to determine the structure of a reactive muffler. A material distribution approach is developed to optimize the layout of sound-hard material inside the expansion chamber of a cylindrical symmetric muffler with the objective of minimizing the acoustic energy at the muffler outlet. The acoustic propagation is modeled by Helmholtz equation with a transmission impedance, which models the effects of the perforated pipe in the muffler. The equation is solved using a finite element method in which the impedance is included using a mortar function. The material distribution is modeled by a material indicator function which is a variable coefficient in the governing equation. Gradient-based optimization algorithm is used to solve the optimization problem. Design restriction is included to the problem by using an anisotropic filter.