Control Theory Visualiser
PID tuning, root locus, Bode plots, Nyquist diagrams, and state-space analysis
PID Tuning
Root Locus
Bode Plot
Nyquist
State-Space
Plant G(s)
1/s (Integrator)
1/(s+1) (First Order)
1/(s²+s+1) (Second Order)
1/(s(s+1)) (Integrator+FO)
1/(s+1)² (Double Pole)
Custom coefficients
Num coeffs (high to low):
Den coeffs (high to low):
PID Gains
Kp
1.00
Ki
0.00
Kd
0.00
Reference Input
Unit Step
Ramp
Sinusoid
Performance Metrics
Rise Time
--
Settling Time
--
Overshoot
--
SS Error
--
Closed-Loop Block Diagram
Presets
DC Motor Speed
Mass-Spring-Damper
Inverted Pendulum
Temperature Ctrl
Cruise Control
Step Response
Open-Loop G(s)H(s)
Num coeffs (high to low):
Den coeffs (high to low):
Gain K
K
1.0
Open-Loop Poles & Zeros
--
Closed-Loop Poles (at current K)
--
Root Locus
Transfer Function
Num coeffs (high to low):
Den coeffs (high to low):
Options
Show asymptotic approximation
Stability Margins
Gain Margin
--
Phase Margin
--
Add Series Element
Integrator 1/s
Differentiator s
Lag 1/(s+1)
Lead (s+1)
Magnitude (dB)
Phase (degrees)
Transfer Function G(s)
Num coeffs (high to low):
Den coeffs (high to low):
Animation
Trace
100%
Animate
Stability Analysis
--
Margins
Gain Margin
--
Phase Margin
--
Nyquist Diagram
System Order
2nd order
3rd order
A Matrix
B Vector
C Vector
D Scalar
System Properties
--
Eigenvalues of A (System Poles)
Step Response