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Misalai na Naukukan da Kowane da Ba Kowane Bane

Naukukan da kowane da ba kowane bane ne farkon abubuwa masu muhimmanci a cikin littattafan kontrol. Naukukan da kowane sun nuna halayen da ke dace da sashe na superposition, amma naukukan da ba kowane ba. Duk da cewa, wadannan ne misalai na mafi yawan naukukan da kowane da ba kowane bane:

Naukukan da Kowane

Naukukan da kowane suka nuna halaye da ya fiye waɗanda ke tsariwa da al'amuran input da output, zan iya cewa suke taimaka da sashe na superposition da homogeneity. Misalai na mafi yawan naukukan da kowane sun haɗa:

Circuit mai Resistor:

• Bayani: Circuit mai resistor, capacitor, da inductor, wadannan halayen suke bayyana da tushen differential linear.

• Misalai: RC circuits, RL circuits, LC circuits.

Spring-Mass-Damper Systems:

• Bayani: Masana'antu mai springs, masses, da dampers, wadannan tushen motion suna taimaka da tushen differential linear na biyu.

• Misalai: Automotive suspension systems.

Heat Conduction Systems:

• Bayani: Tsariyar hawa a lokacin da tsariyar gida suke bayyana da tushen partial differential linear.

• Misalai: One-dimensional heat conduction equation.

Signal Processing Systems:

• Bayani: Linear filters da Fourier transform methods a signal processing.

• Misalai: Low-pass filters, high-pass filters, band-pass filters.

Control Systems:

• Bayani: Models of linear control systems suke bayyana da tushen differential linear.

• Misalai: PID controllers, state feedback controllers.

Naukukan da Ba Kowane Bane

Naukukan da ba kowane bane suka nuna halaye da ba fiye waɗanda ke tsariwa da al'amuran input da output, zan iya cewa su ba su taimaka da sashe na superposition. Misalai na mafi yawan naukukan da ba kowane bane sun haɗa:

Saturation Systems:

• Bayani: Idan input ya kawo karfin adadin, output ya ƙarƙashinsu ba ta ciwo shiga, amma yake ƙarƙasha.

• Misalai: Current saturation in motor drive systems, output saturation in amplifiers.

Friction Systems:

• Bayani: Al'amuran friction force da velocity ba fiye, musamman yana nuna static da dynamic friction.

• Misalai: Friction in mechanical transmission systems.

Hysteresis Systems:

• Bayani: Al'amuran magnetization da magnetic field strength yana nuna hysteresis.

• Misalai: Hysteresis effects in magnetic materials.

Biological Systems:

• Bayani: Yawancin al'amuran biological processes ba fiye, kamar enzymatic reactions da neuronal firing.

• Misalai: Enzyme kinetics models, neural network models.

Economic Systems:

• Bayani: Al'amuran economic variables ba fiye, kamar supply and demand, market volatility.

• Misalai: Stock market price fluctuations, macroeconomic models.

Chaotic Systems:

• Bayani: Wasu naukukan da ba kowane bane sun nuna halaye chaotic a wurare mai ma'aikata, suke da yawa ga initial conditions.

• Misalai: Lorenz system, double pendulum system.

Chemical Reaction Systems:

• Bayani: Rate of chemical reactions ba fiye waɗanda ke tsariwa da concentrations of reactants.

• Misalai: Enzyme-catalyzed reactions, chemical oscillators.

Mafarin Muhimmiyar

• Naukukan da Kowane: Al'amuran input da output ya fiye, tana taimaka da sashe na superposition. Misalai na mafi yawan naukukan da kowane sun haɗa circuit mai resistor, spring-mass-damper systems, heat conduction systems, signal processing systems, da control systems.

• Naukukan da Ba Kowane Bane: Al'amuran input da output ba fiye, ba tana taimaka da sashe na superposition. Misalai na mafi yawan naukukan da ba kowane bane sun haɗa saturation systems, friction systems, hysteresis systems, biological systems, economic systems, chaotic systems, da chemical reaction systems.

Fahimtata daban-daban da ke kara a naukukan da kowane da ba kowane bane yana taimaka wajen zaba hanyoyi da models masu daidai don analysis da design a yankunan lissafi.