Pole-Zero Map Simulator

Load Example

Response Type

\(K\), System Gain

0.1 10

Real Pole A \((s+1.00)\)

\(p_a\), Location

-5 3

Real Pole B \((s+2.00)\)

\(p_b\), Location

-5 3

Complex Pole Pair \(s^2+2.00s+5.00\)

\(\sigma\), Real Part

-4 2

\(\omega\), Imaginary Part (rad/s)

0.1 5

Real Zero A \((s+0.50)\)

\(z_a\), Location

-5 3

Real Zero B \((s+3.00)\)

\(z_b\), Location

-5 3

Stable oscillatory response

Pole-Zero Map

\[\displaystyle G(s) = \frac{1.00}{s^2+2.00s+5.00}\]

Characteristic	Formula	Value	Annotation
Enabled poles	\(n_p\)	N/A	cross markers
Enabled zeros	\(n_z\)	N/A	circle markers
Transfer function order	\(\deg D(s)\)	N/A	denominator order
Dominant pole real part	\(\max \operatorname{Re}(p_i)\)	N/A	violet vertical line
Stability status	\(\operatorname{Re}(p_i) < 0\)	N/A	left-half plane is stable
Oscillation tendency	\(\operatorname{Im}(p_i) \ne 0\)	N/A	complex poles oscillate
Expected speed	\(-1/\operatorname{Re}(p_d)\)	N/A	dominant decay rate
Zero effect	\(s-z_i\)	N/A	zeros shape response