sp eeeeee

1
Algorithm: The following steps are implemented in order 1. Initialize D to the desired transfer function and x0 to the starting values of coefficients. 2. The gain K and the phase m are also initialized to some constants. The values of x0, K, m are chosen such that the resulting bi-quadratic transfer function is stable. 3. From Eq. 2.1, compute H, the pole zero approximated transfer function. 4. Next, we use Eq. 3.6 to 3.8 find the optimal values of K and m using D and H, obtained in step 1 and 3 respectively. 5. Use the optimal values obtained in the previous step in Eq. 2.8 – 2.9 to compute the values of logarithmic error in both magnitude and phase. 6. The gradient with respect to x, the optimal coefficient vector, is then computed from Eq. 3.10 – 3.11. 7. The hessian matrix with respect to x,|delta^2(x) is computed using Eq. 3.14 to 3.19. 8. Form the matrix Bx as shown in the below equation such that Bx is positive definite , where \sigma is a small quantity that converts Hessian to a positive definite matrix. 9. Update the optimal coefficient vector x using the below equation. 10. If the error < \epsilon then stop the process , else go to step 3.

Upload: vighnesh-s-bhat

Post on 15-Nov-2015

212 views

Category:

Documents


0 download

TRANSCRIPT

Algorithm: The following steps are implemented in order 1. Initialize D to the desired transfer function and x0 to the starting values of coefficients.2. The gain K and the phase m are also initialized to some constants. The values of x0, K, m are chosen such that the resulting bi-quadratic transfer function is stable.3. From Eq. 2.1, compute H, the pole zero approximated transfer function. 4. Next, we use Eq. 3.6 to 3.8 find the optimal values of K and m using D and H, obtained in step 1 and 3 respectively.5. Use the optimal values obtained in the previous step in Eq. 2.8 2.9 to compute the values of logarithmic error in both magnitude and phase.6. The gradient with respect to x, the optimal coefficient vector, is then computed from Eq. 3.10 3.11.7. The hessian matrix with respect to x,|delta^2(x) is computed using Eq. 3.14 to 3.19.8. Form the matrix Bx as shown in the below equation such that Bx is positive definite , where \sigma is a small quantity that converts Hessian to a positive definite matrix.9. Update the optimal coefficient vector x using the below equation.10. If the error < \epsilon then stop the process , else go to step 3.