9c66dd29-f1c6-4196-b473-65c383535604 13 3 5 decimal

&[DATE] &[TIME] - &[FILENAME]

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 31 line for data r3 r4 r5 augment 21 line :

3 appVersion 0.98.6179 ≡ Timing 5 min ≡ 21 mat

r ≠ 1 r 1.001 :

Sensible to integrator acc [1000] n # X x r n^2 π * / r i u * exp * X n u * i * exp * u 02 π * int * :

n 120 range :

Kp 0.5 :

z H z Kp + z 2^z - Kp + / z z 1 - / (* :

# X

unary 20 z H x eval abs : 3.047

Y n 120 range U n el n z H x eval : for 1 unary / U abs vectorize * 21 line :

Z n Y augment : Ω Z o 5 black plot : 21 sys

x c 10 x ≤ cases :

Z 1 Ω 3 1 sys x H x c * 1 100 1 100 - 2 2 mat 2 1 sys

=========== Complete 'Z' plot =========

Kp 0.625 :

sol z 2^z - Kp + (z 1 - (* z solve maple : 2 i 6 sqrt * + 4 / 2 i 6 sqrt * - 4 / 131 mat

z H z Kp + z 2^z - Kp + / z z 1 - / (* :

z H A z r1 - / B z r2 - / + C z r3 - / + ≡

r1 sol 1 el : r2 sol 2 el : r3 sol 3 el : 31 sys

A B + C + 1 ≡ A r2 r3 + (* B r1 r3 + (* + C r1 r2 + (* + Kp - ≡ A r2 r3 * (* B r1 r3 * (* + C r1 r2 * (* + 0 ≡ 31 line

A B C 31 mat 111 r2 r3 + r1 r3 + r1 r2 + r2 r3 * r1 r3 * r1 r2 * 33 mat 1 -^1 Kp - 031 mat * :

A B C 31 mat 0.8 - 0.674 i * - 0.8 - 0.674 i * + 2.6 31 mat

N 20 : m 0 N 0.05 range : p 1 el 0 : m p p 1 el A r1 m 1 -^* + B r2 m 1 -^* + C r3 m 1 -^* + : 41 sys

unary m p abs vectorize m rows row 1 el : response m 1 unary / m p abs vectorize * augment : 21 sys

n 020 range : data n 1 unary / n p abs vectorize * augment : 21 sys

Unary response to 'Z' transform

response 1 data o 5 black plot 3 1 sys