Pole Placement Explorer — Eigenvalue Design

Interaction Mode

k1 18.0

k2 6.0

Closed-Loop Readout

-4.0

lambda1

-5.0

lambda2

0.95

zeta (damping)

4.47

omega_n [rad/s]

A-BK = [[0, 1], [-20.0, -9.0]]
char poly: s^2 + 9.0s + 20.0

Open-Loop Plant

A = [[0, 1], [-2, -3]] B = [[0], [1]]
open-loop lambda: -1, -2
x'' + 3x' + 2x = u C = [1, 0]

Presets

Simulation

Initial x(0)=[1,0]

Ref step (r=1)

s-Plane Pole Map — click to place desired poles

Closed-Loop Response

With K=[18, 6], closed-loop poles move from open-loop [-1, -2] to [-4, -5]. The system is 4-5x faster but uses more control effort. The eigenvalues of A-BK determine everything.