Controls & Robotics
Frequency Response & Stability Simulators
A focused Controls & Robotics hub for frequency response & stability tools, keeping related formulas, assumptions, and engineering checks together.
24 simulators
Adjacent categories
Simulator list
Adaptive Control MRAC Simple Simulator
Frequency Response & Stability
Compare reference response, tracking error, and adaptive-gain history to see how stronger adaptation improves or destabilizes tracking.
Attitude Control Thruster Sizing Simulator
Frequency Response & Stability
A tool for sizing the Reaction Control System (RCS) thrusters and propellant budget of a satellite or spacecraft.
Bode Lead Lag Compensator Simulator
Frequency Response & Stability
Link magnitude, phase, and pole-zero views to see how zero-pole spacing changes stability margin.
Bode Plot Generator (Frequency Response)
Frequency Response & Stability
Real-time Bode plot generator for transfer functions. Automatically calculates gain margin, phase margin, and crossover frequencies for stability analysis.
Bode Plot Simulator — Transfer Function Gain & Phase Response
Frequency Response & Stability
Generate Bode plots from a transfer function in real time. Visualize gain margin, phase margin, cutoff frequency, and resonance peaks for control system design.
Disturbance Observer (DOB) Simulator — DOB+PI vs. PI Alone
Frequency Response & Stability
Visualize how a disturbance observer estimates an input disturbance from the nominal model and a Q filter, then cancels it. Compare DOB+PI with PI alone and see the effe…
Gain Scheduling Control Simulator
Frequency Response & Stability
Control a nonlinear plant whose gain changes with the operating point. Switch between fixed-gain and scheduled control and move the operating point to watch the actual l…
Inverse Response Simulator — Step Response of an RHP-Zero Process
Frequency Response & Stability
A process with a right-half-plane zero first moves opposite to the setpoint on a step input — the inverse response. Vary the process gain and zero time constant to see h…
Jury Stability Test Simulator
Frequency Response & Stability
Enter the coefficients of a discrete-time (digital) control system's characteristic polynomial and the tool builds the Jury table automatically, deciding whether every r…
Loop Shaping Simulator — Bode Plot and Stability Margins
Frequency Response & Stability
Draw the open-loop frequency response L=C*G_p of a PI controller on a second-order process in real time. Change parameters and watch crossover frequency, phase margin, g…
Nichols Chart Simulator
Frequency Response & Stability
Plot the open-loop frequency response on a single diagram with phase on the horizontal axis and gain on the vertical axis. Adjust the gain, time constants and dead time …
Nyquist Diagram & Stability Margin Calculator
Frequency Response & Stability
Interactive Nyquist plot calculator. Adjust gain K to visualize stability margins and encirclements in real time. Learn the Nyquist stability criterion.
Padé Approximation of Time Delay Simulator
Frequency Response & Stability
Explore the Padé approximation, which replaces a pure time delay e^(−sT) with a rational transfer function. Change the approximation order or the delay and watch the pha…
Particle Filter Simulator
Frequency Response & Stability
A tool for estimating a hidden state buried in noise with a swarm of weighted particles — the particle filter, or sequential Monte Carlo method. Change the particle coun…
Pole Placement Simulator — State Feedback Design
Frequency Response & Stability
Design the state-feedback gain K of u=-Kx by pole placement for a 2nd-order single-input system ẋ=Ax+Bu.
Robot Arm Jacobian Singularity Simulator
Frequency Response & Stability
Interactively change joint angles and link lengths of a 2-link planar arm to see the Jacobian det(J), Yoshikawa manipulability w, singular values σ_max/σ_min and conditi…
2-Link Robot Arm Kinematics Simulator — FK & IK
Frequency Response & Stability
Adjust joint angles for FK, or click the canvas to set an IK target and toggle between elbow-up and elbow-down configurations.
Root Locus Control System Designer
Frequency Response & Stability
Design and analyze root locus plots in real time. Set poles and zeros, sweep gain K, and visualize stability margins with asymptotes and centroid formulas.
Routh-Hurwitz Stability Criterion Simulator
Frequency Response & Stability
Enter the coefficients of a control system's characteristic equation and the tool builds the Routh array automatically, counts the sign changes in the first column, and …
Second-Order Step Response Simulator
Frequency Response & Stability
Visualise the time response of a standard second-order system to a step input. Adjust the natural frequency ωn and the damping ratio ζ to see the percent overshoot, peak…
Sliding Mode Control — VSC and Robustness
Frequency Response & Stability
Apply SMC to a 2nd-order plant under disturbance. Adjust the sliding surface coefficient c, switching gain k, boundary layer width phi and disturbance amplitude d to fee…
Smart Grid Frequency Droop Control Simulator
Frequency Response & Stability
Watch how each generator's droop response and the grid inertia H hold the frequency when the load suddenly changes.
State-Space Controllability Simulator
Frequency Response & Stability
For a 2nd-order linear time-invariant system ẋ=Ax+Bu, this tool checks whether the input u alone can steer every direction of the state space — its controllability.
Steady-State Error vs System Type Simulator
Frequency Response & Stability
A classical-control playground that shows how the steady-state error of a unity-feedback loop is determined by the system type N (the number of integrators) and the inpu…
How to Use
- Select filter topology (Butterworth, Chebyshev, or Bessel) from the dropdown
- Set cutoff frequency (Hz) and filter order (2–8) using numeric inputs
- Enter system input signal frequency range (0.1–10 kHz) to sweep the magnitude and phase response
- Run simulation; view Bode plot, pole-zero map, and step-response overshoot
- Export stability margin data (gain margin in dB, phase margin in degrees) for control system verification
Worked Example
Design a 4th-order Butterworth low-pass filter with cutoff at 500 Hz for a robotic servo motor feedback loop. Applying the simulator: cutoff fc=500 Hz, order n=4. At 100 Hz (−3 dB point), magnitude = −3.01 dB, phase = −45°. At 5 kHz (10× cutoff), attenuation = −80 dB, phase ≈ −360°. Gain margin = 12 dB, phase margin = 58°—sufficient stability for 0.2 kg payload with 50 rad/s natural frequency.
Practical Notes
- Butterworth filters suit servo control (maximally flat passband); Chebyshev allows steeper rolloff but introduces ripple and phase distortion—avoid for precision trajectory tracking
- Verify nyquist stability by checking pole locations remain in left half-plane; simulator flags instability if any pole Re > 0
- Cross-reference phase margin ≥ 45° and gain margin ≥ 6 dB for industrial robotic arms operating at ±10% load variation
- Filter delay (group delay) at cutoff ≈ 1/(2πfc × n); account in real-time closed-loop sampling at 1 kHz and above