Mechanical Systems
Mass–spring–damper, rotational dynamics, gears, multi-DOF models, friction, backlash and saturation.
mẍ + bẋ + kx = F(t)DYNAMIC SYSTEMS • CONTROL • SIMULATION
Model the physics.
Control the response.
A multi-domain engineering project for mechanical, electrical, pneumatic and hydraulic systems — from governing equations to closed-loop control.
5engineering notebooks
4+physical domains
30+control & analysis topics
closed_loop_responseSTABLE
responsereferenceζ = 0.42
DIFFERENTIAL EQUATIONS • TRANSFER FUNCTIONS • STATE SPACE • POLE–ZERO • ROOT LOCUS • BODE • NYQUIST • PID • LQR • DIGITAL CONTROL
PROJECT OVERVIEW
One framework across physical domains.
Derive, model, simulate, analyze, control and compare.
Electrical Systems
RC/RL/RLC circuits, DC motors, converters, transformers, generators and electromechanical coupling.
Lq̈ + Rq̇ + q/C = V(t)Pneumatic Systems
Compressible-air cylinders, chamber pressure, valve flow, leakage and spool dynamics.
mẍ + bẋ + kx = AΔP − FₗHydraulic Systems
Compressibility, nonlinear orifice flow, cylinders, leakage, accumulators and cavitation checks.
ΔṖ = β/Vₜ(Q − 2Aẋ − CₗΔP)INTERACTIVE MULTI-DOMAIN SIMULATOR
Change parameters. Watch the dynamics change.
A lightweight browser companion to the Jupyter notebooks.
Mechanical step responsenormalized displacement
StablePROJECT NOTEBOOKS
The website is the front door. The notebooks are the engineering core.
01
Mechanical Systems Modeling, Simulation and ControlClassical control • state space • nonlinearities
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02Electrical Systems Modeling, Simulation and ControlRLC • DC motor • converters • generators
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03Pneumatic Systems Modeling, Simulation and ControlPressure dynamics • valves • nonlinear actuator
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04Hydraulic Systems Modeling, Simulation and ControlOrifice flow • compressibility • cylinders
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05Multi-Domain Dynamic Systems Modeling, Simulation and ControlElectromechanical • electro-pneumatic • electro-hydraulic
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ANALYSIS & CONTROL METHODS
Beyond simple time-response plots.
Classical and modern control methods, robustness, digital control and nonlinear simulation.
Step / Impulse / RampPole–ZeroRouth–HurwitzRoot LocusBodeNyquistNicholsPIDLead / LagFeedforwardCascadeState FeedbackObserversLQRKalman / LQGJury Stability
Pole–Zero Map
Bode Magnitude
MATLAB / SIMULINK COMPARISON
Comparable concepts, a more transparent workflow.
MATLAB/Simulink remains stronger for graphical block diagrams and Simscape physical libraries.
Capability
Python / Jupyter
MATLAB / Simulink
Transfer functions & state space
✓
✓
Bode, Nyquist, Nichols & root locus
✓
✓
PID, observers, state feedback & LQR
✓
✓
Interactive tuning
ipywidgets / browser controls
Apps / Simulink
Graphical physical libraries
Limited
Excellent
Equation / source visibility
Fully open
Toolbox workflow
FULL REPOSITORY
Explore the complete engineering project.
Five notebooks, interactive models, controller design, frequency analysis, nonlinear dynamics and multi-domain integration.