Engineering

The registered systems of skcomplex.systems.engineering. The page of each shows its factory, its component types with their states, parameters, and laws as written, and, for the forms that have them, its equations as SymbolicAnalysis returns them, so it serves as the pattern for a system of your own.

Circuits

• Chua double and multiple scrolls: Chua's circuit, whose double-scroll or multiscroll attractor is chaotic.
• Circuits under periodic impulses: An RLC circuit driven by a periodic train of current impulses, L C x'' + R C x' + x = A Σ δ(t - k T).
• Coupled Colpitts oscillators: Two detuned chaotic Colpitts oscillators coupled through the difference of their second variables.
• Memristive mixed-mode oscillator: A slow-fast circuit with a cubic flux-controlled memristor, whose oscillations mix two amplitudes.
• Memristor oscillator: The simplest memristor oscillator: a capacitor, an inductor, and a memristor in series.
• Modified Chua with mixed-mode oscillations: A modified Chua circuit on three time scales, whose oscillations mix small and large amplitudes.
• RLC circuit: A series RLC circuit written as Kirchhoff's voltage law, L q'' + R q' + q / C = V cos(ω t).
• Tunnel-diode oscillator: A tunnel-diode oscillator: an inductor and a capacitor in parallel with a negative-resistance diode.
• Vibration energy harvester: A dual-mass piezoelectric harvester in a car suspension, driven by the roughness of the road.

Control

• Heated room with a thermostat: A room assembled from thermal and electrical components, heated under a thermostat with hysteresis.
• Linear-quadratic regulated oscillator: A harmonic oscillator that a linear-quadratic regulator brings to rest.
• Minimum-time control of a free particle, a harmonic oscillator, and a saddle: A linear plant steered to the origin of its phase space in minimum time by a sampled bang-bang control.
• Model predictive control of Duffing, Van der Pol, and a bilinear DC motor through Koopman surrogates: A plant that a discrete-time controller steers with model predictive control on a fitted surrogate.
• PID governance loop: A work process whose output a PID controller keeps at a set point against a disturbance.
• PID-stabilised inverted pendulum: An inverted pendulum on a cart that a PID controller of its angle keeps upright.
• Pendulum swing-up: A pendulum swung up to its inverted position by a bang-bang acceleration of its pivot.
• Satellite transfer: A satellite moved between Kepler orbits of equal angular momentum by radial thrust.
• Thermostat: A room heated by a furnace under a thermostat while heat leaks to the outside.

Mechatronics

• DC motor with an inertia: A DC motor whose armature circuit of components drives an inertia on a Lagrangian coordinate.
• Electromagnetic vibrating table: An electromagnetic vibrating table, a shaker driven by a sinusoidal supply after its switch closes.
• Magnetic levitation under alternating impulses: A conductive ball levitated in a vacuum by a field that pushes and pulls it with alternating impulses.
• Quarter-car suspension: A quarter-car suspension driving over a road step.

Power systems

• Faraday-disk charger: A battery charger driven by a Faraday disk generator whose own current strengthens its field.
• Regenerative braking: A car braked by a Faraday disk generator on its wheel, which charges a supercapacitor.
• Swing-equation power grid with Braess paradox: A ring power grid in the swing-equation system, where more transmission capacity can break synchrony.
• Wheel and rail contact: A rail segment on a sleeper, loaded by the wheels of passing bogies.

Processes

• Bathtub: A bathtub, one stock of water with an inflow from the faucet and an outflow through the drain.
• Cascade classifier: A cascade classifier, a column of stages that separates a narrow size class of particles by an air flow.
• Food relief system: A food relief system, a pipeline that ships food to a warehouse and distributes it to people in need.
• Grain storage system: A retail grain store, whose orders through a supply line make its stock oscillate.
• Irrigation system: An irrigation system, a reservoir and an aquifer that keep the root zone of the crops supplied.
• Rice milling system: A rice milling system, a mill that buys paddy, mills it into rice and by-products, and sells them.
• Solid waste system: A solid waste system, the waste of a growing city collected, recycled, composted, and landfilled.

Robotics

• Light-emitting robots with sensory delay: Light-emitting robots, which cluster when they sense the light of the others late and spread when early.
• Light-sensitive robots with sensory delay: Light-sensitive robots in a circular well, whose sensory delay decides whether they gather in the light.
• Swarmtaxis: The swarmtaxis algorithm, which moves a swarm of robots towards a beacon that only some of them see.

Traffic

• Car following with delay: A chain of cars that react to the speed difference to the car ahead after a reaction time.
• Charbonneau traffic: Charbonneau's traffic system, where random braking of single drivers sets off traffic jams.
• GKT non-local traffic: The gas-kinetic-based traffic system, where drivers brake on the traffic at an interaction point ahead.
• Intelligent driver system: The intelligent driver system of cars on a ring road.
• Kerner-Konhäuser system: The Kerner-Konhäuser system, where viscous traffic flow forms dense moving clusters.
• Langevin car-following toward a density-dependent speed: Cars on a ring road whose speeds relax with noise towards a desired speed set by the local density.
• Lighthill-Whitham-Richards: The Lighthill-Whitham-Richards system, the conservation of cars with the Greenshields speed law.
• Moment equations of Langevin traffic with a jam instability: The density and flux equations of Langevin traffic on a ring road, whose uniform flow breaks into jams.
• Nagel-Schreckenberg: The Nagel-Schreckenberg traffic system on a ring road, where jams emerge above a critical density.
• Optimal velocity: The optimal velocity system of cars on a ring road, where uniform flow breaks into stop-and-go waves.
• Payne system: The Payne system, where the speed of traffic relaxes to the Greenshields speed and anticipates density.
• Ridesharing: Riders who request trips on a city grid and cabs that a stable matching sends to them.
• Ring-road driver agents: Drivers on a circular highway, where small random errors of speed set off traffic jams.