Funkar da Tattalin Aiki: Tatabbacin Sistomi na Koyarwa
Karamin describing function yana haka shi ne kalmomin kimiyya mai gaba da yanayin kawo rigar tushen cikakken kontrolu a control engineering. Idan an yi nasara, zaka iya nuna takamaddini na biyuwar tushen cikakken kontrolu. Tushen cikakken kontrolu suna da principle of superposition (idandanan inputs ke amfani a lokacin tsohon, za a ci gaba da ci abubuwa daban-daban) yana da damar. A lokacin tushen cikakken kontrolu masu kimiyya mai gaba, ba a zan iya amfani da principle of superposition.
Amfani da tushen cikakken kontrolu masu kimiyya mai gaba ita ce mafi karfi saboda irin al'amuran da suke. Ba a zan iya amfani da tattalin bayanai masu gida kamar Nyquist stability criterion ko pole-zero method don in bayyana waɗannan tushen kimiyya, domin waɗannan tattalin bayanai suna da nasara a tushen cikakken. Duk da haka, akwai muhimmanci masu kimiyya:
Tushen kimiyya suna da kyau a matsayin tushen cikakken kontrolu.
Tushen kimiyya suna da lalacewa a matsayin tushen cikakken kontrolu.
Sun fi yawa da kuma fitaccen girman a matsayin tushen cikakken kontrolu.
A cikin rayuwa, duka masana'antar jihohin suna da wata irin kimiyya. Yanzu kuma ana iya tabbatar da inganta kimiyya ta hanyar da aka bari don in taimaka wajen kirkiro tushen ko in taimaka wajen haɗaƙi tushen. Da haka, tushen ya zama da lalacewa a matsayin tushen cikakken kontrolu.
Wata misali na biyuwar tushen da ake amfani da kimiyya a tsafta ita ce tushen da ake kontrola da relay ko ON/OFF. Misali, a cikin tushen tsirrai a tashar mutanen, ana sauki furnance a lokacin da tsirrai yana koma zuwa harshe da aka sani, kuma ana kashe a lokacin da tsirrai yana koma zuwa harshe da aka sani. A wannan lokaci, zan iya magana game da biyar tattalin bayanai ko tattalin bayanai don in bayyana tushen kimiyya. Biyar tattalin bayanai suna nufin aiki da misali.
Describing function method in control system
Phase plane method in control system
Common Non Linearities
A cikin types of control systems, ba a zan iya haɓaka cewa akwai wata irin non-linearities. Waɗannan zan iya faɗinsu a matsayin static ko dynamic. Tushen da ake amfani da kimiyya daban-daban a kan input da output, ba ake amfani da differential equation ba, ana kiran static nonlinearity. Duk da haka, input da output zan iya amfani da differential equation. Wannan tushen ana kiran dynamic nonlinearity.
A wannan lokacin, zan iya magana game da irin non-linearities in a control system:
Saturation nonlinearity
Friction nonlinearity
Dead zone nonlinearity
Relay nonlinearity (ON OFF controller)
Backlash nonlinearity
Saturation Nonlinearity
Saturation nonlinearity ita ce irin kimiyya na biyu. Misali, a cikin saturation a kurban magnetizing curve na DC motor. Don in fahimta wannan irin kimiyya, zan iya magana game da saturation curve ko magnetizing curve wanda aka bayyana a cikin:
Daga cikin wannan kurba, zan iya nuna cewa output yana da shiga linear a farkon, amma a nan, ana iya samun saturation a cikin kurba wanda yana da kimiyya a cikin tushen. Ana iya nuna approximated curve.
Irinsu na biyu na saturation non linearity zan iya nuna a amplifier, inda output yana da shiga proportional to the input only for a limited range of values of input. Idan input yana koma zuwa harshe, output yana koma zuwa kimiyya.
Friction Nonlinearity
Wannan da ake amfani da ita don in haɗaƙi relative motion da body, ana kiran friction. Ita ce wata irin kimiyya a cikin tushen. Wannan misali a cikin electric motor, inda ake amfani da coulomb friction drag saboda rubbing contact between the brushes and the commutator.
Friction zan iya da tasiri uku, kuma waɗannan suka rubuta a cikin:
Static Friction : A harshen kalma, static friction take amfani a cikin body idan body yana da shiga rest.
Dynamic Friction : Dynamic friction take amfani a cikin body idan akwai relative motion between the surface and the body.
Limiting Friction : Ita ce maximum value of limiting friction that acts on the body when it is at rest.
Dynamic friction zan iya faɗinsu a (a) Sliding friction (b) Rolling friction. Sliding friction take amfani idan biyuwan bodies slides over each other while rolling takes amfani idan biyuwan bodies rolls over another body.
A cikin tushen mechanical, akwai biyu irin friction na (a) Viscous friction (b) Static friction.
Dead Zone Nonlinearity
Dead zone nonlinearity ita ce wata irin kimiyya a cikin electrical devices kamar motors, DC servo motors, actuators, etc. Dead zone non linearities refers to a condition in which output becomes zero when the input crosses certain limiting value.
Relays Nonlinearity (ON/OFF Controller)
Electromechanical relays are frequently used in control systems where the control strategy requires a control signal with only two or three states. This is also called as ON/OFF controller or two state controller.
Relay Non-Linearity (a) ON/OFF (b) ON/OFF with Hysteresis (c) ON/OFF with Dead Zone. Fig (a) shows the ideal characteristics of a bidirectional relay. In practice, relay will not respond instantaneously. For input currents between the two switching instants, the relay may be in one position or other depending upon the previous history of the input. This characteristic is called ON/OFF with hysteresis that shows in Fig (b). A relay also has a definite amount of dead zone in practice that show in Fig (c). The dead zone is caused by the fact that the relay field winding requires a finite amount of current to move the armature.
Backlash Nonlinearity
Another important nonlinearity commonly occurring in the physical system is hysteresis in mechanical transmissions such as gear trains and linkages. This nonlinearity is somewhat different from magnetic hysteresis and is commonly referred to as backlash nonlinearities. Backlash in fact is the play between the teeth of the drive gear and those of the driven gear. Consider a gearbox as shown in below figure (a) having backlash as illustrated in fig (b).
Fig (b) shows the teeth A of the driven gear located midway between the teeth B1, B2 of the driven gear. Fig (c) gives the relationship between input and output motions. As the teeth A is driven clockwise from this position, no output motion takes place until the tooth A makes contact with the tooth B1 of the driven gear after traveling a distance x/2. This output motion corresponds to the segment mn of fig (c). After the contact is made the driven gear rotates counterclockwise through the same angle as the drive gear if the gear ratio is assumed to be unity. This is illustrated by the line segment no. As the input motion is reversed, the contact between the teeth A and B1 is lost and the driven gear immediately becomes stationary based on the assumption that the load is friction controlled with negligible inertia.
The output motion, therefore, causes till tooth A has traveled a distance x in the reverse direction as shown in fig (c) by the segment op. After the tooth A establishes contact with the tooth B2, the driven gear now mores in a clockwise direction as shown by segment pq. As the input motion is reversed the direction gear is again at standstill for the segment qr and then follows the drive gear along rn.
