signals
Transfer functions. Bode plots. Stability. Step response. PID. Filters.
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Transfer Function G(s) = N(s) / D(s)
Numerator
coefficients low→high: "1" = 1, "1, 0, 1" = 1+s²
Denominator
"2, 3, 1" = 2+3s+s²
Analyze System
Quick Tools
Close Loop
Routh Table
Minreal
Bandwidth
State-Space
Controllability
C → D
PID Tune
Pole Placement
LQR
Butterworth
Chebyshev
Filter Design
Type
Butterworth
Chebyshev I
Chebyshev II
Order
Cutoff
Ripple (dB)
Stopband (dB)
Design Filter
PID Controller
Kp
Ki
Kd
Apply PID
Continuous → Discrete
Sample Time
seconds
Convert
Pole Placement (Ackermann)
Desired Poles
comma-separated
Compute K
LQR Optimal Control
Q diagonal
state cost weights
R
input cost
Compute K
Step
Impulse
Bode Mag
Bode Phase
Nichols
Example Systems
1/(s²+3s+2) — overdamped
25/(s²+2s+25) — underdamped
1/(s³+6s²+11s+6)
10/(s²+5s+10) — 2nd order
1/(s+1) — 1st order
100/(s²+10s+100) — fast
(1+s)/(s²+s+1)
1/(s³+s²) — marginal