Simulator Library
Controls and Robotics Simulators
Control simulators for PID, stability, state-space models, observers, Kalman filters, and robot control.
47 simulators
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Simulator list
Two-Degree-of-Freedom Control — Independent Setpoint and Disturbance Design
Tune PI feedback and a reference pre-filter independently. Compare against the classic 1-DoF response to see how feedforward shaping kills overshoot without weakening di…
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.
Anti-Lock Braking System (ABS) Slip Ratio Simulator
See how an Anti-lock Braking System keeps wheels rolling at the optimal slip ratio instead of locking up. Set initial speed, road surface and vehicle mass to compare ABS…
Anti-Windup PI Controller Simulator
PID & Servo Control
Compare standard PI, back-calculation anti-windup PI, and ideal PI responses on a 1st-order plant with input saturation. See how integral reset prevents overshoot caused…
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.
Bang-Bang Control Simulator — Time-Optimal Control
A tool that visualizes bang-bang control, which drives the double integrator ẍ = u to the origin in minimum time under the input bound |u| ≤ u_max.
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.
Cascade Control Simulator — Dual-Loop PID Step Response
PID & Servo Control
Inner loop $G_i(s) = \\frac{K_i}{\\tau_i s+1}$ nested inside an outer loop — see how dual-loop PID outperforms single-loop in rise time, overshoot, and settling time.
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.
Control System Step Response Simulator
Simulate and visualize 1st & 2nd order control system step responses in real-time. Adjust damping, frequency, and PID parameters to explore transient behavior.
Describing Function Simulator
Replace relay, saturation and dead-zone nonlinearities with an amplitude-dependent equivalent gain N(A), then predict the amplitude and frequency of a limit cycle (self-…
Digital PID Discretization Simulator
PID & Servo Control
Digital PID Discretization Simulator updates live numeric results and charts as inputs change, supporting early design checks and model review.
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…
Quadrotor Drone Thrust Allocation Simulator
A quadrotor turns four motor thrusts into total lift plus three body moments (roll, pitch, yaw) — four inputs, four degrees of freedom. This tool solves the X / + / H fr…
Feedforward Compensation Simulator — Disturbance Rejection
The feedforward compensation simulator compares PI-only and PI plus feedforward control under a step disturbance, with peak deviation and settling time in real time.
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…
H-Infinity Control Simulator — Mixed Sensitivity Design
Visualize the sensitivity S, complementary sensitivity T, and the mixed sensitivity peak under W_S and W_T weights for a PI controller on G_p = 1/(T_p s + 1). Explore th…
Haptic Feedback Device Bandwidth & Z-Width Simulator
Design the force-feedback devices used in VR, surgical robots and haptic gloves.
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…
Kalman Filter Simulator — State Estimation & Noise Reduction Visualization
Visualize how the Kalman filter recovers true state from noisy data. Adjust process and measurement noise to intuitively understand its operation.
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…
LQR Inverted Pendulum Simulator — Optimal State Feedback
LQR inverted pendulum simulator: optimal feedback u=-Kx on a 4D cart-pole. Tune Q and R weights to see settling time, overshoot, and peak input trade off in real time.
Model Predictive Control Simulator — Finite-Horizon Optimization
Discretize a first-order process and compute, at every step, the optimal input that minimizes the predicted output error over a finite horizon. Compare MPC with a baseli…
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.
State-Space Observability Simulator
For a 2nd-order linear time-invariant system ẋ=Ax+Bu, y=Cx, this tool answers the question "can the full internal state x be known from the measurable output y alone?" A…
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…
PID Controller Simulator
PID & Servo Control
Tune PID controller parameters (Kp, Ti, Td) in real time. Compare P, PI, and PID control to master step response and closed-loop system tuning.
PID Tuning Method Comparison (Z-N / IMC / SIMC)
PID & Servo Control
Set FOPDT process parameters (Kp, τ, θ) and compare four PID tuning methods simultaneously: Ziegler-Nichols, Cohen-Coon, IMC, and SIMC. Real-time step response, integral…
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.
PWM Motor Control Calculator
Calculate PWM duty cycle, frequency, voltage, ripple current, losses & LC filter design for motor control. Answers the question:
Relative Gain Array (RGA) Simulator
When a multivariable process with several inputs and outputs is controlled with decentralized single loops, this tool decides which input to pair with which output.
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 …
Servo Mechanism Calculator
PID & Servo Control
Calculate servo system performance: bandwidth, phase margin, Bode plots, settling time, and PID tuning for optimal 45° stability.
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.
Smith Predictor Simulator — Dead-Time Compensation vs PI
The Smith predictor simulator compares the step response of a standard PI controller and a Smith predictor on a first-order plus dead-time process, in real time.
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.
State Space Analysis
Analyze state-space systems: Check controllability & observability, compute state feedback gain K, and visualize eigenvalues. Enter your A, B, C, D matrices.
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 system type (PID servo, state-space, or Kalman filter) from the dropdown menu
- Enter plant parameters: for a DC motor, input Kp=0.5, Tm=0.1s (motor time constant), and damping ratio 0.3
- Define controller gains: Kp (proportional), Ki (integral), Kd (derivative) or state feedback matrix K
- Set reference input (step, ramp, or sinusoidal) and simulation duration in seconds
- Click Run Simulation to generate time-domain response plots and stability margins (gain/phase at crossover frequency)
- Export step response data (rise time, settling time, overshoot %) for design documentation
Worked Example
Industrial robotic arm joint control: Plant transfer function G(s)=10/(s(s+2)), target settling time 0.5s, overshoot under 5%. Apply PID tuning: Kp=2.4, Ki=12, Kd=0.08. Simulator shows closed-loop poles at -6±4j, phase margin 52 degrees, step response settling in 0.48s with 3.2% overshoot. For Kalman filter on the same system with measurement noise covariance R=0.01 and process noise Q=0.1, filter gain L stabilizes at [9.8, 1.2] and reduces position error from 0.85mm to 0.12mm under 0.1rad/s sinusoidal disturbance.
Practical Notes
- Verify Nyquist stability criterion before hardware deployment: ensure encirclement count matches unstable pole count
- For electro-hydraulic actuators (nonlinear friction), increase Ki by 15-20% to overcome static pressure losses
- Kalman filter performance degrades if measurement noise statistics are unknown; use white-noise identification testing on live sensor data first
- State-space representation requires observable/controllable systems; check rank of observability matrix [C; CA; CA^2] equals system order
- Export bode plots at critical frequencies (0.1-100 rad/s) to validate anti-aliasing filter cutoff for real-time control loops running at 1-10 kHz