Control_theory - Wikiparency

# Control theory Control theory develops models and algorithms that apply inputs to a [[Dynamical_system|dynamical system]] so as to drive it toward desired states while minimizing error, delay, overshoot, and instability. [[Feedback|Feedback]] (closed-loop), feedforward, PID, optimal, robust, adaptive, and intelligent controllers exploit controllability, observability, and stability criteria (Lyapunov, Nyquist, Bode) for engineered and natural processes.  ## Microsims (promoted from legacy — three.js first) ### MicroSim spec ### Parameters (tunable controls) - `Kp (proportional)` · 0–10 · stiffness of the proportional response - `Kd (derivative)` · 0–5 · [[Damping|damping]] that reacts to error rate - `Setpoint` · 0–100 · target the controlled state should track ### What animates A step response curve rises, overshoots, and settles depending on the gains. ### Learning objective Show how PID-style gains shape the transient response of a [[Dynamical_system|dynamical system]]. ### MicroSim spec - **Recommended sim type:** [[Control_system|control system]] - **Microsimmability score:** 88/100 - **Layout:** drawing region (canvas) on top; control region (sliders/buttons) below. ### Parameters (tunable controls) - `Setpoint` - `Proportional gain` - `Integral gain` ### What animates A controlled output overshoots, settles, or oscillates as the controller gains are tuned. ### Learning objective Show how controller gains shape a system's response to its setpoint. ### MicroSim spec - **Recommended sim type:** control-system [[Block_diagram|block diagram]] - **Microsimmability score:** 100/100 - **Layout:** controller-plant block diagram on top with a response plot; sliders below. ### Parameters (tunable controls) - `Proportional gain Kp` - `Integral gain Ki` - `Setpoint` ### What animates A controller drives a plant toward the setpoint; the error trace and step response update live as the gains change. ### Learning objective Relate controller gains to rise time, overshoot, and steady-state error. ### MicroSim spec - **Recommended sim type:** [[Control_system|control system]] - **Microsimmability score:** 90/100 - **Layout:** drawing region (canvas) on top; control region (sliders/buttons) below. ### Parameters (tunable controls) - `Setpoint` - `Gain` - `System lag` ### What animates A controller drives a plant's output toward a setpoint and you watch the error shrink or oscillate. ### Learning objective Relate controller gain and [[System|system]] lag to closed-loop stability and tracking.   ## Microsims — p5.js ### Control theory (p5.js) · `feedback` <div class="microsim-player"> <iframe src="https://editor.p5js.org/sciencenibber/full/DtAoGXBbj" width="100%" height="480" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Control theory — p5.js microsim"></iframe> </div> *The mathematics of steering a system to a desired state despite disturbances.* **Open in the editor:** [▶ fork this sketch](https://editor.p5js.org/sciencenibber/sketches/DtAoGXBbj) · movement *VI · Control theory & estimation* · library `p5js` ### Related microsims Live sims on neighbouring articles — 6 of them inside this article's own Wikipedia link tree: - [[Analog_signal]] *(in tree)* - [[Autocorrelation]] *(in tree)* - [[Bifurcation_theory]] *(in tree)* - [[Calculus]] *(in tree)* - [[Chaos_theory]] *(in tree)* - [[Communication_channel]] *(in tree)* *Sim hosted off-article; the article owns the reference, not the runtime (WIKI_RULES §10.4). Placed by `g08_place_microsims.py`.*   ## Images <figure class="wt-gifplate"> <img src="https://commons.wikimedia.org/wiki/Special:FilePath/Buck_switching_regulator_with_feedback_control.gif" alt="Feedback Regulation" loading="lazy" decoding="async"> <figcaption><strong>Feedback Regulation</strong> — Watch voltage oscillate around a target value, correcting itself. This is negative feedback.<br> <span class="wt-credit">Wikimedia Commons · <strong>licence pending verification</strong> (run <code>g17_gif_verify.py</code> on a networked lane) · <a href="https://commons.wikimedia.org/wiki/File:Buck_switching_regulator_with_feedback_control.gif">Details</a></span></figcaption> </figure> *The hub concept of [[PORTAL_Control_theory]]. Still companion to the 1 live microsim above — §15 keeps the player first, the plate sits in the image slot.*  ## Reveal %%REVEAL:p5%% %%REVEAL:svg%% --- *Concept aligned with [Wikipedia](https://en.wikipedia.org/wiki/Control_theory); adapted text, where present, is licensed [CC BY-SA 4.0](https://creativecommons.org/licenses/by-sa/4.0/).* ## Overview The regulation story is [[Cybernetics|cybernetics]] made rigorous: [[Norbert_Wiener|Norbert Wiener]]'s circular causality, [[W._Ross_Ashby|W. Ross Ashby]]'s requisite variety, and [[Stafford_Beer|Stafford Beer]]'s management cybernetics all read as control loops, and homeostasis in an [[Ecosystem|ecosystem]] or organism reads the same way through [[Systems_biology|systems biology]]. Design mathematics leans on [[Statistics|statistics]], optimization shared with [[Operations_research|operations research]] and [[Decision_theory|decision theory]], and structure from [[Graph_theory|graph theory]] and [[Information_theory|information theory]]. Modern practice extends through [[Multi-agent_system|multi-agent systems]], [[Game_theory|game-theoretic]] control, [[Neural_network_(machine_learning)|neural-network]] and [[Machine_learning|learning-based]] controllers inside [[Artificial_intelligence|artificial intelligence]], and system-level integration in [[Systems_engineering|systems engineering]], with behavior-over-time intuition borrowed from [[System_dynamics|system dynamics]] and [[Systems_thinking|systems thinking]].  *Built to the [[WT!P5_js_Microsim_Master_Class|p5.js Master Class]].*  ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Control_theory) : [Wikitube](https://en.wikitube.io/wiki/Control_theory) ## Previous hub tags Hubs: `Systems`. Portals: [[PORTAL_Systems]], [[PORTAL_Control_theory]].