kể từ khi họ chỉ sử dụng thông tin địa phương về chức năng chi phí và các dẫn xuất của nó trong quá trình tìm kiếm. Phương pháp để tìm kiếm toàn cầu cực tiểu được mô tả trong | x -------- Base Motion FIGURE E14-20 Cantilever structure with mass at the tip. For the optimal control problem of minimization of error in the state variable formulated and solved in Section study the effect of including a 1 percent critical damping in the formulation. For the minimum control effort problem formulated and solved in Section study the effect of including a 1 percent critical damping in the formulation. For the minimum time control problem formulated and solved in Section study the effect of including a 1 percent critical damping in the formulation. For the spring-mass-damper system shown in Fig. E14-29 formulate and solve the problem of determining the spring constant and damping coefficient to minimize the maximum acceleration of the system over a period of 10 s when it is subjected to an initial velocity of 5m s. The mass is specified as 5 kg. The displacement of the mass should not exceed 5 cm for the entire time interval of 10 s. The spring constant and the damping coefficient must also remain within the FIGURE E14-29 Damped single-degree-of-freedom system. 510 INTRODUCTION TO OPTIMUM DESIGN limits 1000 k 3000N m 0 c 300N-S m. Hint The objective of minimizing the maximum acceleration is a min-max problem which can be converted to a nonlinear programming problem by introducing an artificial design variable. Let a t be the acceleration and A be the artificial variable. Then the objective can be to minimize A subject to an additional constraint a t A for 0 t 10 . Formulate the problem of optimum design of steel transmission poles described in Kocer and Arora 1996b . Solve the problem as a continuous variable optimization problem. Design Optimization Applications with Implicit Functions .
