ÃÐºº¤Çº¤ØÁ Start, Stop, PD

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ÃÐºº¤Çº¤ØÁª¹Ô´Ç§¨Ãà»Ô´ (Open Loop Control System)
ÃÐºº¤Çº¤ØÁª¹Ô´Ç§¨Ã»Ô´ (Close Loop or Feedback Control System)

»ÃÐÊÔ·¸ÔÀÒ¾¢Í§ÃÐºº¤Çº¤ØÁ

Steady State Performance
Transient Performance

Characteristic Function ¢Í§ÃÐºº¤Çº¤ØÁª¹Ô´»éÍ¹¡ÅÑº
µÑÇÍÂèÒ§¡ÒÃÇÔà¤ÃÒÐËì´éÇÂ Characteristic Function
ÃÐºº¤Çº¤ØÁáºº PD
ÃÐºº¤Çº¤ØÁáºº Start Stop
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àÍ¡ÊÒÃÍéÒ§ÍÔ§

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¡ÒÃ¤Çº¤ØÁà¤Ã×èÍ§¨Ñ¡ÃËÃ×ÍÍØ»¡Ã³ìÍÐäÃ¡çµÒÁ ÊÒÁÒÃ¶ãªéÍØ»¡Ã³ì·Ò§ÍÔàÅ¤·ÃÍ¹Ô¤¤Çº¤ØÁÍØ»¡Ã³ìàËÅèÒ¹Ñé¹ä´é ¡ÒÃ¤Çº¤ØÁ´éÇÂÍØ»¡Ã³ì ÍÔàÅ¤·ÃÍ¹Ô¤ÍÂèÒ§§èÒÂ·ÕèÊØ´ ¤×Í¡ÒÃãªéÍØ»¡Ã³ì·Ò§ÍÔàÅ¤·ÃÍ¹Ô¤¤Çº¤ØÁ¡ÒÃà»Ô´(Start), ¡ÒÃ»Ô´(Stop) ¢Í§ÍØ»¡Ã³ìàËÅèÒ¹Ñé¹ â´Â·ÕèÍØ»¡Ã³ì·Ò§ ÍÔàÅ¤·ÃÍ¹Ô¤·Õè¶Ù¡ãªéã¹¡ÒÃ¤Çº¤ØÁ¹ÕéÁÕËÅÒÂª¹Ô´àªè¹ ·ÃÒ¹«ÔÊàµÍÃì(Transistor), CMOS, FET, Relay ÎÅÎ ¹Í¡¨Ò¡¹ÕéËÒ¡à»ç¹ÍØ»¡Ã³ì·ÕèµéÍ§¡ÒÃ ¡ÓÅÑ§ä¿¿éÒÊÙ§¡ç¨Ðãªé¾Ç¡ Thyristor àªè¹ SCR, Triac ÎÅÎ

¡ÒÃ¤Çº¤ØÁ·ÕèÁÕ¤ÇÒÁ«Ñº«éÍ¹¡çÊÒÁÒÃ¶¤Çº¤ØÁ´éÇÂÍØ»¡Ã³ìÍÔàÅ¤·ÃÍ¹Ô¤ä´é â´ÂÍÒÈÑÂËÅÑ¡¡ÒÃ¤Çº¤ØÁª¹Ô´»éÍ¹¡ÅÑº àªè¹ P, PD, PID â´Âã¹·Õè¹Õé¨Ð¡ÅèÒÇ¶Ö§ ÃÐºº¤Çº¤ØÁ Start, Stop, PD

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        ã¹ÃÐºº¤Çº¤ØÁâ´Â·ÑèÇä»áÅéÇ ¨Ðà»ç¹¡ÒÃ¤Çº¤ØÁáººÍÑµâ¹ÁÑµÔ·Õè·Ó§Ò¹â´ÂÍØ»¡Ã³ì¤Çº¤ØÁ·Ò§ ÍÔàÅ¤·ÃÍ¹Ô¤ à¹×èÍ§¨Ò¡ËÒ¡ãªéÁ¹ØÉÂìÁÒ¤ÍÂ¤Çº¤ØÁ¡ÒÃ·Ó§Ò¹¢Í§à¤Ã×èÍ§¨Ñ¡ÃàÍ§áÅéÇ ÍÒ¨ãËé¼Å·ÕèäÁè´Õ¾Í à¹×èÍ§¨Ò¡¢Õ´¨Ó¡Ñ´¢Í§Á¹ØÉÂìàªè¹ ¤ÇÒÁÅÐàÍÕÂ´ã¹¡ÒÃÊÑ§à¡µÊÔè§·Õèà»ÅÕèÂ¹á»Å§, ¡ÒÃµÑ´ÊÔ¹ã¨·ÕèãªéàÇÅÒ äÁèà·èÒ¡Ñ¹à»ç¹µé¹
        ÃÐºº¤Çº¤ØÁ´éÇÂÍØ»¡Ã³ì·Ò§ÍÔàÅ¤·ÃÍ¹Ô¤¹Ñé¹ ÍÒ¨¨Ðáºè§ÍÍ¡ä´éà»ç¹ 2 »ÃÐàÀ·
                    1. ÃÐºº¤Çº¤ØÁª¹Ô´Ç§¨Ãà»Ô´ (Open-Loop Control System)
                    2. ÃÐºº¤Çº¤ØÁª¹Ô´Ç§¨Ã»Ô´(ËÃ×Í»éÍ¹¡ÅÑº) (Close-Loop or Feedback Control System)
        ¤ÇÒÁËÁÒÂ¢Í§ÃÐºº¤ÇÁ¤ØÁ ¤×ÍàÍÒ·ì¾Øµ¢Í§ÃÐºº·Õèä´é¨ÐµéÍ§à»ç¹ä»µÒÁÍÔ¹¾Øµ·ÕèàÃÒ»éÍ¹ãËé¡ÅÑºÃÐºº
ËÁÒÂ¤ÇÒÁÇèÒ àÃÒ¨ÐµéÍ§ÊÒÁÒÃ¶¤Çº¤ØÁàÍÒ·ì¾ØµãËéà»ç¹ä»µÒÁ¤ÇÒÁµéÍ§¡ÒÃä´é â´Â¡ÒÃ»éÍ¹ÍÔ¹¾Øµ ºÒ§ÍÂèÒ§à¾×èÍÊÑè§¡ÒÃá¡èÃÐºº ÊèÇ¹ÁÒ¡ÃÐºº¤ÇÁ¤ØÁ¨ÐÁÕ¼ÅµÍºÊ¹Í§µèÍàÇÅÒ (Time Domain Response) ËÁÒÂ¤ÇÒÁÇèÒ ÍÔ¹¾Øµ·Õè»éÍ¹ãËé¡ÑºÃÐºº«Öè§â´ÂÁÒ¡¨Ðà»ç¹ÊÑÒ³·Ò§ä¿¿éÒ (Signal)áÅÐ ¾ÄµÔ¡ÃÃÁ¢Í§ ÃÐºº ¨Ð¶Ù¡ÈÖ¡ÉÒà»ç¹¿Ñ§¡ìªÑ¹¢Í§àÇÅÒ ËÒ¡áµèàÃÒÍÒ¨¨ÐµéÍ§¾Ô¨ÒÃ³Òà»ç¹¿Ñ§¡ìªÑ¹¢Í§¤ÇÒÁ¶Õè «Öè§·ÓãËé   ÊÒÁÒÃ¶¤Ó¹Ç³·Ò§¤³ÔµÈÒÊµÃìä´é§èÒÂ¡ÇèÒ

ÃÐºº¤Çº¤ØÁª¹Ô´Ç§¨Ãà»Ô´ (Open Loop Control System)

ÃÐºº¤Çº¤ØÁª¹Ô´Ç§¨Ãà»Ô´ ¤×ÍÃÐºº¤Çº¤ØÁ·ÕèäÁèÁÕ¡ÒÃ¹Ó¤èÒàÍÒ·ì¾Øµ·Õèä´éÁÒ¤Ó¹Ç³ ËÃ×Í¼èÒ¹ ¡ÃÐºÇ¹¡ÒÃºÒ§ÍÂèÒ§à¾×èÍ¹ÓÁÒãªé¾Ô¨ÒÃ³ÒËÒ¤èÒÍÔ¹¾Øµ·ÕèàËÁÒÐÊÁ à¾×èÍãªéã¹¡ÒÃ¤Çº¤ØÁàÍÒ·ì¾Øµ â´ÂÁÕÃÙ»áºº´Ñ§á¼¹ÀÒ¾ ÃÙ»·Õè 1

ÃÙ»·Õè 1 á¼¹ÀÒ¾áÊ´§ÃÐºº¤Çº¤ØÁª¹Ô´Ç§¨Ãà»Ô´

x(t) = ÊÑÒ³ÍÔ¹¾Øµ (Input Signal)
y(t) = ÊÑÒ³àÍÒ·ì¾Øµ (Output Signal) ËÃ×Í Time Response
h(t) = »¯Ô¡ÔÃÔÂÒµÍºÊ¹Í§¢Í§ÃÐºº (System's Response)

ËÃ×Í ¿Ñ§¡ìªÑ¹ÃÐºº (System Function)

ÃÐºº¤Çº¤ØÁª¹Ô´¹ÕéäÁè¤èÍÂä´éÃÑº¤ÇÒÁ¹ÔÂÁÁÒ¡¹Ñ¡ à¹×èÍ§ÁÒ¨Ò¡ÇèÒàÃÒäÁèÊÒÁÒÃ¶·ÃÒºä´éÇèÒàÍÒ·ì¾Øµ ¢Í§ÃÐºº·Õèä´éÁÕ¤ÇÒÁ¶Ù¡µéÍ§ÊÍ´¤ÅéÍ§¡ÑºÍÔ¹¾Øµ·ÕèàÃÒ»éÍ¹ãËéá¡èÃÐººÁÒ¡¹éÍÂà¾ÕÂ§ã´ â´Â·Óä´éáµèà¾ÕÂ§ ÊÑ³¹ÔÉ°Ò¹ÇèÒÃÐººÁÕ»ÃÐÊÔ·¸ÔÀÒ¾´Õ¾Í·Õè¨ÐãËéàÍÒ·ì¾Øµä´é¶Ù¡µéÍ§
áµè¶Ö§áÁéÇèÒÃÐºº¨ÐÁÕ»ÃÐÊÔ·¸ÔÀÒ¾´Õ áµèÍÒ¨¨ÐÁÕ»Ñ¨¨ÑÂÍ×è¹·Õè·ÓãËé¤èÒàÍÒ·ì¾Øµ¢Í§ÃÐºº·Õèä´éÁÕ¤ÇÒÁ ¤ÅÒ´à¤Å×èÍ¹ä´é à»ç¹µé¹ÇèÒ ÊÑÒ³Ãº¡Ç¹, áÃ§àÊÕÂ´·Ò¹, áÃ§à©×èÍÂ, ¤ÇÒÁº¡¾ÃèÍ§¢Í§ÍØ»¡Ã³ì ÎÅÎ â´ÂÃÐºº¤Çº¤ØÁª¹Ô´Ç§¨Ãà»Ô´¹Õé ÊèÇ¹ãËè¨ÐãªéÁ¹ØÉÂì¤ÍÂ¤Çº¤ØÁâ´ÂÍÒÈÑÂ¡ÒÃÊÑ§à¡µ¢éÍ¼Ô´¾ÅÒ´¢Í§ àÍÒ·ì¾Øµ

ÃÐºº¤Çº¤ØÁª¹Ô´Ç§¨Ã»Ô´ (Close Loop or Feedback Control System)

ÃÐºº¤Çº¤ØÁª¹Ô´Ç§¨Ã»Ô´ ¤×ÍÃÐºº¤Çº¤ØÁ·ÕèÁÕ¡ÒÃ¹ÓàÍÒ¤èÒàÍÒ·ì¾Øµ·Õèä´éÁÒ¤Ó¹Ç³ ËÃ×Í¼èÒ¹ ¡ÃÐºÇ¹¡ÒÃºÒ§ÍÂèÒ§à¾×èÍ¹ÓÁÒãªéã¹¡ÒÃ¾Ô¨ÒÃ³ÒËÒ¤èÒÍÔ¹¾Øµ·ÕèàËÁÒÐÊÁ à¾×èÍ¤Çº¤ØÁãËéàÍÒ·ì¾Øµ¢Í§ÃÐºº ÁÕ¤ÇÒÁ¶Ù¡µéÍ§ â´ÂÁÕÃÙ»áºº´Ñ§á¼¹ÀÒ¾ ÃÙ»·Õè 2

ÃÙ»·Õè 2 á¼¹ÀÒ¾áÊ´§ÃÐºº¤Çº¤ØÁª¹Ô´Ç§¨Ã»Ô´

x(t) = ÊÑÒ³ÍÔ¹¾Øµ (Input Signal)
y(t) = ÊÑÒ³àÍÒ·ì¾Øµ (Output Signal) ËÃ×Í Time Response
e(t) = ÊÑÒ³¤ÇÒÁ¼Ô´¾ÅÒ´ (Error Signal)
h(t) = »¯Ô¡ÔÃÔÂÒµÍºÊ¹Í§¢Í§ÃÐºº (System's Response)
g(t) = ¿Ñ§¡ìªÑ¹¡ÒÃ»éÍ¹¡ÅÑº (Feedback Function)

ÃÐºº¤Çº¤ØÁª¹Ô´Ç§¨Ã»Ô´¹Õé ¹Í¡¨Ò¡àÍÒ·ì¾Øµ¢Í§ÃÐºº¨ÐÁÕ¤ÇÒÁ¶Ù¡µéÍ§ÁÒ¡¢Öé¹áÅéÇ à¹×èÍ§¨Ò¡ÃÐºº¤Çº¤ØÁà»ç¹áººÍÑµâ¹ÁÑµÔ ·ÓãËéªèÇÂá¡é »ÑËÒÍÑ¹à¹×èÍ§ÁÒ¨Ò¡¢Õ´¨Ó¡Ñ´¢Í§Á¹ØÉÂìä´é àªè¹ãªé¤Çº¤ØÁÃÐºº·ÕèµéÍ§¡ÒÃ¤ÇÒÁÅÐàÍÕÂ´ÊÙ§, ·Ó§Ò¹ä´éÍ´·¹¡ÇèÒ ÎÅÎ ÃÐºº¤Çº¤ØÁáºº»éÍ¹¡ÅÑº¹Õé ÁÕÍÂÙèËÅÒÂª¹Ô´àªè¹ P, PD, PI, PID

»ÃÐÊÔ·¸ÔÀÒ¾¢Í§ÃÐºº¤Çº¤ØÁ

¡ÒÃÇÔà¤ÃÒÐËìÃÐººÇèÒÁÕ»ÃÐÊÔ·¸ÔÀÒ¾ËÃ×ÍäÁè¹Ñé¹ ÁÕ»Ñ¨¨ÑÂ·ÕèáÊ´§¶Ö§»ÃÐÊÔ·¸ÔÀÒ¾¢Í§ÃÐºº·Õè¨ÐµéÍ§¾Ô¨ÒÃ³ÒÍÂÙèËÅÒÂ»Ñ¨¨ÑÂ´éÇÂ¡Ñ¹ â´ÂÍÒÈÑÂ¡ÒÃÇÔà¤ÃÒÐËì¶Ö§¾ÄµÔ¡ÃÃÁ¢Í§àÍÒ·ì¾Øµ¢Í§ÃÐºº â´Â·ÕèàÍÒ·ì¾Øµ¢Í§ÃÐººã¹àªÔ§¢Í§àÇÅÒ(Time Response) ¨Ð»ÃÐ¡Íº´éÇÂ 2 ÊèÇ¹¤×Í "Transient Response" áÅÐ "Steady State Response" ´Ñ§ÊÁ¡ÒÃ

(PD-1)

¤ÓÇèÒ Steady State ÁÕ¤ÇÒÁËÁÒÂä´éËÅÒÂÍÂèÒ§¢Öé¹ÍÂÙè¡ÑºàÃ×èÍ§·Õè¡ÓÅÑ§¾Ô¨ÒÃ³Òàªè¹ ã¹¡ÒÃÇÔà¤ÃÒÐËìÇ§¨Ã·Ò§ä¿¿éÒ Steady State ¨ÐËÁÒÂ¶Ö§ ÃÐ´Ñº»ÃÔÁÒ³·Ò§ä¿¿éÒ·ÕèÁÕ¤èÒ¤§·ÕèäÁèà»ç¹¿Ñ§¡ìªÑ¹¢Í§àÇÅÒËÃ×Í¤ÇÒÁ¶Õè ¢³Ð·Õèã¹ÃÐºº¤Çº¤ØÁ¶éÒàÍÒ·ì¾Øµà¢éÒÊÙèÊ¶Ò¹Ð Steady State áÅéÇàÍÒ·ì¾ØµÂÑ§ÊÒÁÒÃ¶à»ÅÕèÂ¹á»Å§à»ç¹¿Ñ§¡ìªÑ¹¢Í§àÇÅÒä´é â´Â¨Ð¶×ÍÇèÒàÍÒ·ì¾Øµà¢éÒÊÙèÊ¶Ò¹Ð Steady State àÁ×èÍàÇÅÒà»ç¹Í¹Ñ¹µì áµè¶éÒËÒ¡¾Ô¨ÒÃ³Ò ¤Å×è¹ÃÙ» Sine ¡ç¨Ð¶×ÍÇèÒà¢éÒÊÙèÊ¶Ò¹Ð Steady State àªè¹¡Ñ¹à¾ÃÒÐÇèÒ¾ÄµÔ¡ÃÃÁ¢Í§¤Å×è¹ÃÙ» Sine ¨ÐäÁèÁÕ¡ÒÃà»ÅÕèÂ¹á»Å§àÁ×èÍàÇÅÒà¢éÒÊÙèÍ¹Ñ¹µì ¨Ò¡ÊÁ¡ÒÃ PD-1 C_ss(t)¨Ðá·¹àÍÒ·ì¾Øµ¢Í§ÃÐººàÁ×èÍà¢éÒÊÙèÊ¶Ò¹Ð Steady State àÃÕÂ¡ÇèÒ Steady State Response «Öè§¨Ðà»ç¹ÊèÇ¹Ë¹Öè§¢Í§àÍÒ·ì¾Øµ¢Í§ÃÐºº C_t(t)¨ÐËÁÒÂ¶Ö§ Transient Response «Öè§àÁ×èÍàÇÅÒà¢éÒÊÙèÍ¹Ñ¹µìáÅéÇ ¨Ð·ÓãËé C_t(t) ÁÕ¤èÒà»ç¹ÈÙ¹Âì ´ÑÇÊÁ¡ÒÃ·Õè PD-2

(PD-2)

ã¹ÃÐºº¤Çº¤ØÁª¹Ô´»éÍ¹¡ÅÑº ¨ÐÁÕ»Ñ¨¨ÑÂºÒ§ÍÂèÒ§·Õè·ÓãËéàÍÒ·ì¾Øµ¢Í§ÃÐºº äÁèà»ÅÕèÂ¹á»Å§ä»µÒÁÍÔ¹¾Øµ¢Í§ÃÐººã¹·Ñ¹·Õ·Õè ÍÔ¹¾Øµ¶Ù¡»éÍ¹à¢éÒÊÙèÃÐºº àªè¹ ¤ÇÒÁà©×èÍÂ, áÃ§àÊÕÂ´·Ò¹ à»ç¹µé¹ «Öè§¡èÍãËéà¡Ô´¼ÅÅÑ¾¸ì·ÕèàÃÕÂ¡ÇèÒ Transient Response( C_t(t) ) ¹Í¡¨Ò¡¹Õé Steady State Response ¨Ð¶Ù¡µÃÇ¨ÊÍº¡ÑºÍÔ¹¾Øµ·Õè»éÍ¹ãËéá¡èÃÐºº à¾×èÍËÒ¤èÒ¤ÇÒÁ¶Ù¡µéÍ§¢Í§ÃÐºº «Öè§¶éÒàÍÒ·ì¾Øµ Steady State Response ¢Í§ÃÐºº äÁèÊÍ´¤ÅéÍ§¡ÑºÍÔ¹¾Øµ áÊ´§ÇèÒà¡Ô´¤ÇÒÁ¼Ô´¾ÅÒ´ Steady State Error ¢Öé¹

Steady State Performance

àÍÒ·ì¾Øµ Steady State Response ãªéà»ç¹¤èÒÊÓËÃÑºµÃÇ¨ÊÍº¤ÇÒÁ¶Ù¡µéÍ§¢Í§ÃÐºº â´Â¹ÓÁÒ¾Ô¨ÒÃ³Ò¡ÑºÍÔ¹¾Øµ·Õè»éÍ¹ãËéá¡èÃÐºº ÇèÒÁÕ¤ÇÒÁÊÍ´¤ÅéÍ§¡Ñ¹ËÃ×ÍäÁè ¡ÒÃ·´ÊÍº»ÃÐÊÔ·¸ÔÀÒ¾¢Í§ Steady State Performance ¢Í§ÃÐºº·Óä´éâ´Â ãËéÍÔ¹¾ØµÍéÒ§ÍÔ§(Reference Input) «Öè§à»ç¹ Test Signal à¢éÒÊÙèÃÐºº áÅéÇ·Ó¡ÒÃµÃÇ¨ÊÍºàÍÒ·ì¾Øµ Steady State Response à¾×èÍ¾Ô¨ÒÃ³ÒËÒ¤èÒ Steady State Error «Öè§à»ç¹¤èÒ¤ÇÒÁáµ¡µèÒ§ÃÐËÇèÒ§àÍÒ·ì¾Øµ Steady State Response ·Õè¤Ò´ÇèÒ¨Ðà»ç¹¡Ñº àÍÒ·ì¾Øµ Steady State Response ·Õèä´é¨Ò¡¡ÒÃ·´ÊÍº «Öè§¨Ðãªéà»ç¹µÑÇµÑ´ÊÔ¹¤ÇÒÁ¶Ù¡µéÍ§¢Í§ÃÐºº

Transient Performance

»Ã¡µÔ¡ÒÃ·´ÊÍº»ÃÐÊÔ·¸ÔÀÒ¾ Transient Performance ¢Í§ÃÐºº¨Ð¾Ô¨ÒÃ³Ò¨Ò¡àÍÒ·ì¾Øµ Transient Response à¾×èÍ¾Ô¨ÒÃ³ÒËÒÅÑ¡É³Ð ¾ÄµÔ¡ÃÃÁ¢Í§àÍÒ·ì¾Øµ¢Í§ÃÐººã¹¢³Ðã´¢³ÐË¹Öè§ ¡ÒÃËÒ Transient Response ¨Ð·Óä´éâ´Â¡ÒÃãËéÍÔ¹¾ØµÍéÒ§ÍÔ§(Reference Input) ·Õèà»ç¹ Unit Step áÅéÇÃÐºº¨ÐµéÍ§ãËé¤èÒàÍÒ·ì¾ØµÁÒà»ç¹ Unit Step ´éÇÂ ã¹¡ÒÃ¾Ô¨ÒÃ³Ò»ÃÐÊÔ·¸ÔÀÒ¾¢Í§ Transient Performance ¨Ð¾Ô¨ÒÃ³ÒÅÑ¡É³Ð ¾ÄµÔ¡ÃÃÁ¢Í§àÍÒ·ì¾Øµ¢³Ðã´¢³ÐË¹Öè§´Ñ§¹Õé

ÃÙ»·Õè 3 ¡ÃÒ¿áÊ´§ÅÑ¡É³Ð¾ÄµÔ¡ÃÃÁ¢Í§àÍÒ·ì¾Øµ¢Í§ÃÐºº

Overshoot :- à»ç¹¤èÒ·ÕèáÊ´§¶Ö§¤ÇÒÁ¼Ô´¾ÅÒ´·ÕèÁÒ¡·ÕèÊØ´ÃÐËÇèÒ§ÍÔ¹¾ØµáÅÐàÍÒ·ì¾Øµ µÅÍ´ÃÐÂÐàÇÅÒ·ÕèàÍÒ·ì¾ØµÍÂÙèã¹Ê¶Ò¹Ð Transient State (àÍÒ·ì¾ØµÁÕ¡ÒÃà»ÅÕèÂ¹á»Å§à¾×èÍà¢éÒÊÙèÊ¶Ò¹Ð Steady State) ¤èÒ Overshoot ¹ÕéãªéáÊ´§¶Ö§¤ÇÒÁ Stability ¢Í§ÃÐºº ¶éÒ Overshoot ÁÕ¤èÒÁÒ¡áÊ´§ÇèÒ àÍÒ·ì¾Øµ¢Í§ÃÐºº¨Ðà¢éÒÊÙèÊÀÒÇÐ Steady State ä´éªéÒ ¤èÒ Overshoot ÊèÇ¹ÁÒ¡¨Ð¶Ù¡áÊ´§à»ç¹à»ÍÃìà«ç¹¢Í§àÍÒ·ì¾ØµÊØ´·éÒÂ(àÍÒ·ì¾Øµã¹ÊÀÒÇÐ Steady State) ´Ñ§ÊÁ¡ÒÃ PD-3

(PD-3)

Time Delay :- à»ç¹àÇÅÒ·Õèãªéã¹¡ÒÃ·ÓãËéàÍÒ·ì¾ØµÁÕ¤èÒ¶Ö§ 50 à»ÍÃìà«ç¹¢Í§¤èÒàÍÒ·ì¾ØµÊØ´·éÒÂ
Rise Time :- à»ç¹àÇÅÒ·Õèãªéã¹¡ÒÃà¾ÔèÁàÍÒ·ì¾Øµ¨Ò¡ 10 à»ÍÃìà«ç¹ ¶Ö§ 90 à»ÍÃìà«ç¹¢Í§àÍÒ·ì¾ØµÊØ´·éÒÂ
Settle Time :- à»ç¹àÇÅÒ·Õèãªéã¹¡ÒÃÅ´¤èÒàÍÒ·ì¾Øµ·Õèà¡Ô´¡ÒÃ Overshoot ãËéÍÂÙèã¹¢Í§à¢µäÁèà¡Ô¹ 5 à»ÍÃìà«ç¹ ¢Í§àÍÒ·ì¾ØµÊØ´·éÒÂ

¹Í¡¨Ò¡¹ÕéÂÑ§ÁÕ»Ñ¨¨ÑÂÍ×è¹æ·ÕèÊÓ¤Ñàªè¹ Damping ratio, Damping factor áÅÐ Undamped natural frequency «Öè§¨Ð¡ÅèÒÇ¶Ö§ã¹ÀÒÂËÅÑ§ ¤èÒ Time Delay áÅÐ Rise Time ¨ÐáÊ´§¶Ö§¼ÅµÍºÊ¹Í§àÁ×èÍ·Ó¡ÒÃà»ÅÕèÂ¹á»Å§ÍÔ¹¾ØµÇèÒÁÕ¼ÅµÍºÊ¹Í§ä´éäÇà¾ÕÂ§ã´ â´Â¶éÒ Time Delay áÅÐ Rise Time ÁÕ¤èÒ¹éÍÂ¨ÐáÊ´§ÇèÒ ÁÕ¼ÅµÍºÊ¹Í§µèÍÍÔ¹¾Øµä´é´Õ áµèÍÒ¨¨Ð·ÓãËéà¡Ô´ Overshoot ä´éÁÒ¡¢Öé¹ ÊèÇ¹¤èÒ Settle Time ¨ÐáÊ´§¶Ö§àÇÅÒ·Õèãªéã¹ ¡ÒÃ·ÓãËéàÍÒ·ì¾ØµÊÙèÊÀÒÇÐ Stability â´Â¶éÒ¤èÒ Settle Time ÁÕ¤èÒ¹éÍÂáÊ´§ÇèÒ ÃÐºº¨ÐãªéàÇÅÒã¹¡ÒÃ·ÓãËéàÍÒ·ì¾Øµà¢éÒÊÙèÊÀÒÇÐ Stability ä´éàÃçÇ

Charactoristic Function ¢Í§ÃÐºº¤Çº¤ØÁª¹Ô´»éÍ¹¡ÅÑº

¡ÒÃ¾Ô¨ÒÃ³ÒÃÐºº¤Çº¤ØÁ àÃÒÊÒÁÒÃ¶ãªé»ÃÐâÂª¹ì¨Ò¡ ¿Ñ§¡ìªÑ¹¢Í§ÊÑÒ³ÍÔ¹¾Øµ, ¿Ñ§¡ìªé¹¢Í§ÊÑÒ³àÍÒ·ì¾Øµ, ¿Ñ§¡ìªé¹ÃÐºº(System's Response) ¹ÓÁÒÊÃéÒ§ÊÁ¡ÒÃ·Ò§¤³ÔµÈÒÊµÃìà¾×èÍ¹ÓÁÒËÒ Transfer Function ¢Í§ÃÐºº áÅéÇ¹ÓÁÒÇÔà¤ÃÒÐËìÇèÒàÍÒ·ì¾Øµ¨ÐÁÕ¾ÄµÔ¡ÃÃÁàªè¹äÃ ã¹ÍÔ¹¾ØµªèÇ§Ë¹Öè§æ

Transfer Function ¢Í§ÃÐºº ¨ÐáÊ´§¶Ö§ÅÑ¡É³Ð¾ÄµÔ¡ÃÃÁ¢Í§ÃÐºº â´ÂÊÁ¡ÒÃ·Õè PD-4 à»ç¹ÊÁ¡ÒÃ·Ñè§ä»·ÕèãªéËÒ Transfer Function ¢Í§ÃÐºº

(PD-4)

¨ÐÊÑ§à¡µÇèÒ Transfer Function ¨ÐäÁèàËÁ×Í¹¡Ñº ¿Ñ§¡ìªÑ¹¢Í§ÃÐºº(System's Response) â´Â¾Ô¨ÒÃ³Ò¨Ò¡ ÃÙ»·Õè 2 á¼¹ÀÒ¾ÃÐºº¤Çº¤ØÁª¹Ô´Ç§¨Ã»Ô´ ¨Ðä´éÇèÒ ¿Ñ§¡ìªÑ¹¢Í§ÃÐºº ¤×Í h(t) ¢³Ð·Õè Transfer Function ¨ÐÁÕ¤èÒà·èÒ¡Ñº y(t)/x(t)

¤èÒ h(t) ¢Í§ÃÐºº¤Çº¤ØÁª¹Ô´Ç§¨Ã»Ô´ã¹ÃÙ»·Õè 1 ÊÒÁÒÃ¶¤Ó¹Ç³ä´é¨Ò¡¡ÒÃá¡éÊÁ¡ÒÃ·ÕèÁÕ¡ÒÃ·Ó Convolution ´Ñ§ÊÁ¡ÒÃ PD-5

(PD- 5)

áµèËÒ¡àÃÒ·Ó¿Ñ§¡ìªÑ¹ÍÔ¹¾Øµ, ¿Ñ§¡ìªÑ¹àÍÒ·ì¾Øµ, ¿Ñ§¡ìªÑ¹¢Í§ÃÐºº ãËéà»ç¹¿Ñ§¡ìªÑ¹·ÕèÁÕâ´àÁ¹à»ç¹¤ÇÒÁ¶Õè ¡ÒÃ·Ó Convolution ¢Í§¿Ñ§¡ìªÑ¹·ÕèÁÕâ´àÁ¹à»ç¹¤ÇÒÁ¶Õè ¨ÐàËÁ×Í¹¡Ñº¡ÒÃ¤Ù³·ÑèÇä» ·ÓãËé¤Ó¹Ç³ä´é§èÒÂ¡ÇèÒ·ÓãËéá¡ÑÊÁ¡ÒÃËÒ¿Ñ§¡ìªÑ¹ÃÐººä´é§èÒÂ¡ÇèÒ ´Ñ§ÊÁ¡ÒÃ PD-6

(PD-6)

ÊÑ§à¡µä´éÇèÒËÒ¡ÃÐºº¤Çº¤ØÁà»ç¹ª¹Ô´Ç§¨Ãà»Ô´ Transfer Function ¨ÐÁÕ¤èÒà´ÕÂÇ¡Ñ¹¡Ñº¿Ñ§¡ìªÑ¹¢Í§ÃÐºº ¾Ô¨ÒÃ³ÒÃÐºº¤Çº¤ØÁª¹Ô´Ç§¨Ã»Ô´ ·Õèà»ç¹¿Ñ§¡ìªÑ¹¢Í§¤ÇÒÁ¶Õè´Ñ§ÃÙ»·Õè 4 áÅÐÁÕ Transfer Function ¢Í§ÃÐºº¤Çº¤ØÁª¹Ô´»éÍ¹¡ÅÑº à»ç¹´Ñ§ÊÁ¡ÒÃ PD-7

ÃÙ»·Õè 4 á¼¹ÀÒ¾áÊ´§ÃÐºº¤Çº¤ØÁª¹Ô´Ç§¨Ã»Ô´·ÕèÁÕâ´àÁ¹à»ç¹¤ÇÒÁ¶Õè

(PD-7)

¾Ô¨ÒÃ³ÒÊÁ¡ÒÃ PD-7 àÃÒÊÒÁÒÃ¶ËÒÊÁ¡ÒÃ Characteristic equation ¢Í§ÃÐºº¤Çº¤ØÁª¹Ô´»éÍ¹¡ÅÑº ä´é¨Ò¡¡ÒÃ¹ÓÊèÇ¹µÑÇËÒÃ¢Í§ Transfer Function áÅéÇãËé¤èÒà·èÒ¡ÑºÈÙ¹Âì «Öè§¨Ðä´é Characteristic equation ´Ñ§ÊÁ¡ÒÃ PD-8

(PD-8)

áµè¨Ò¡ÊÁ¡ÒÃ PD-7 àÃÒÂÑ§äÁèÊÒÁÒÃ¶¹ÓÁÒÇÔà¤ÃÒÐËìËÒ¾ÄµÔ¡ÃÃÁ(Charactoristic)¢Í§ÃÐººä´é à¹×èÍ§¨Ò¡àÃÒµéÍ§·ÓãËéà»ç¹ÊÁ¡ÒÃ·ÕèÍÂÙèã¹ÃÙ» ¾ËØ¹ÒÁ(Polynomail)àÊÕÂ¡èÍ¹ «Öè§µÒÁËÅÑ¡¤³ÔµÈÒÊµÃìáÅéÇàÃÒÊÒÁÒÃ¶·ÓãËéÊÁ¡ÒÃ PD-7 ÍÂÙèã¹ÃÙ»¢Í§¾ËØ¹ÒÁä´éà»ç¹´Ñ§ÊÁ¡ÒÃ PD-9 «Öè§à»ç¹ÊÁ¡ÒÃ Transfer Function ·ÑèÇä»·Õèãªéã¹¡ÒÃÇÔà¤ÃÒÐËìÃÐºº¤Çº¤ØÁ

(PD-9)

z₁, z₂, ... , z_m = ¤èÒ·Õè·ÓãËé Transfer Function ÁÕ¤èÒà·èÒ¡ÑºÈÙ¹Âì àÃÕÂ¡ÇèÒ Zero
p₁, p₂, ... , p_n = ¤èÒ·Õè·ÓãËé Tranfer Function ËÒ¤èÒäÁèä´é ËÃ×ÍÁÕ¤èÒà»ç¹Í¹Ñ¹µì àÃÕÂ¡ÇèÒ Pole «Öè§¨Ðà»ç¹¤ÓµÍº¢Í§ Characteristic equation
M(s) = Transfer Function «Öè§¨Ò¡ÊÁ¡ÒÃ PD-8 ¨ÐàËç¹ÇèÒ M(s) ÊÒÁÒÃ¶à»ç¹ä´é·Ñé§àÅ¢¨Ó¹Ç¹¨ÃÔ§ áÅÐ¨Ó¹Ç¹àªÔ§«éÍ¹ä´é «Öè§ÊÒÁÒÃ¶á·¹ä´é´éÇÂÊÁ¡ÒÃ PD-10

(PD-10)

â´Â·Õè

áÊ´§¶Ö§ ÊèÇ¹¢Í§ Pole ·Õèà»ç¹¨Ó¹Ç¹¨ÃÔ§

áÊ´§¶Ö§ ÊèÇ¹¢Í§ Pole ·Õèà»ç¹¨Ó¹Ç¹àªÔ§«éÍ¹

áÊ´§¶Ö§ ¼Å¤Ù³¢Í§ ...

àÃÒÊÒÁÒÃ¶·Õè¨ÐÇÔà¤ÃÒÐËì¾ÄµÔ¡ÃÃÁ ËÃ×Í·Ó¹ÒÂ¤èÒàÍÒ·ì¾Øµ¢Í§ÃÐºº·ÑèÇä» ä´é¨Ò¡ÊÁ¡ÒÃ¾×é¹°Ò¹¢Í§ Transfer Function (PD-10) â´ÂàÍÒ·ì¾Øµ¢Í§ÃÐºº,C(t) ¨Ð¤Ó¹Ç³ä´éµÒÁÊÁ¡ÒÃ PD-10 â´Â·ÕèàÃÒ¨ÐµéÍ§ÃÙé ¿Ñ§¡ìªÑ¹ÍÔ¹¾Øµ, Transfer Function áÅéÇ·Ó¡ÒÃá»Å§àÍÒ·ì¾Øµ,C(s) «Öè§à»ç¹¿Ñ§¡ìªé¹¢Í§¤ÇÒÁ¶ÕèãËéà»ç¹¿Ñ§¡ìªÑ¹¢Í§àÇÅÒ â´Â¡ÒÃ·Ó Invert Laplace Transform ´Ñ§ÊÁ¡ÒÃ PD-11

(PD-11)

ÊÁ¡ÒÃ Transfer Function áÅÐ Characteristic equation ãªéã¹¡ÒÃÇÔà¤ÃÒÐËì¾ÄµÔ¡ÃÃÁ¢Í§ÃÐºº ËÃ×ÍàÍÒ·ì¾Øµä´éÍÂèÒ§äÃ¨Ð¡ÅèÒÇã¹ ËÑÇ¢éÍ µÑÇÍÂèÒ§¡ÒÃÇÔà¤ÃÒÐËìÃÐºº¤Çº¤ØÁ ´éÇÂ Characteristic equation

µÑÇÍÂèÒ§¡ÒÃÇÔà¤ÃÒÐËìÃÐºº¤Çº¤ØÁ ´éÇÂ Characteristic equation

ã¹ËéÇ¢éÍ·ÕèáÅéÇä´é¡ÅèÒÇ¶Ö§·ÕèÁÒ¢Í§ÊÁ¡ÒÃ Characteristic equation áÅéÇ ã¹ËéÇ¢éÍ¹Õé¨Ð¡ÅèÒÇ¶Ö§ÇÔ¸Õ¡ÒÃãªéÊÁ¡ÒÃ Characteristic equation à¾×èÍÇÔà¤ÃÒÐËì¾ÄµÔ¡ÃÃÁ¢Í§ÃÐºº, àÍÒ·ì¾Øµ â´Â·Ó¡ÒÃ»éÍ¹ÍÔ¹¾Øµ,r(t) à»ç¹¿Ñ§¡ìªÑ¹áºº Unit Step áÅÐ Transfer Function,M(s) à»ç¹´Ñ§ÊÁ¡ÒÃ PD-10 â´ÂàÍÒ·ì¾Øµ,c(t) ¨Ðà»ç¹´Ñ§ÊÁ¡ÒÃ PD-12 â´Â¾¨¹ì 1/s ·Õèà¾ÔèÁ¢Öé¹ÁÒ à¹×èÍ§ÁÒ¨Ò¡¡ÒÃá»Å§ÍÔ¹¾Øµ·Õèà»ç¹¿Ñ§¡ìªÑ¹ Unit Step ·Õè¢Öé¹¡ÑºàÇÅÒ à»ç¹¿Ñ§¡ìªÑ¹·Õè¢Öé¹¡Ñº¤ÇÒÁ¶Õè â´ÂÇÔ¸Õ Laplace Transform

(PD-12)

ÊÁ¡ÒÃ PD-12 ÊÒÁÒÃ¶ãªéÇÔ¸ÕàÈÉÊèÇ¹ÂèÍÂã¹·Ò§¤³ÔµÈÒÊµÃì à¾×èÍáÂ¡ÍÍ¡à»ç¹ÊèÇ¹ÂèÍÂæ´Ñ§ÊÁ¡ÒÃ PD-13 áÅéÇ¹ÓÊèÇ¹ËÒÃ¢Í§áµèÅÐÊèÇÂÂèÍÂ à¾×èÍ¹ÓÁÒËÒ Pole ÊÓËÃÑºãªéã¹¡ÒÃÇÔà¤ÃÒÐËìËÒ¾ÄµÔ¡ÃÃÁ¢Í§ÃÐºº áÅÐàÍÒ·ì¾Øµ

(PD-13)

â´Â·Õè¤èÒ¤§·Õè A, B_i, C_j áÅÐ D_j ¨Ð¢Öé¹ÍÂÙè¡ÑºáµèÅÐ Pole áÅÐ Zero ¢Í§ Transfer Function,M(s) â´Â·ÕèÊÁÁµÔÇèÒ¤èÒ¢Í§ Pole ¨ÐÁÕ¤èÒäÁè«éÓ¡Ñ¹àÅÂ ¼ÅÅÑ¾¸ì¢Í§¡ÒÃ·Ó Invert Laplace Transform àÃÒ¨Ðä´éàÍÒ·ì¾Øµ¢Í§áµèÅÐ¾¨¹ìà»ç¹ÍÔÊÃÐµèÍ¡Ñ¹ â´Â¼ÅÅÑ¾¸ì·Õèä´é ¨Ðà»ç¹´Ñ§ÊÁ¡ÒÃ PD-14 ¶Ö§ PD-18 áÅÐ·ÓãËéä´éàÍÒ·ì¾Øµ¢Í§ÃÐººà»ç¹´Ñ§ÊÁ¡ÒÃ PD-19

(PD-14)

(PD-15)

(PD-16)

(PD-17)

(PD-18)

(PD-19)

ÊÑ§à¡µàÍÒ·ì¾Øµ¢Í§ÃÐºº â´Â·Õè¾¨¹ì Au(t) à»ç¹¼ÅÅÑ¾¸ìà¹×èÍ§ÁÒ¨Ò¡ÍÔ¹¾Øµ·Õèà»ç¹¿Ñ§¡ìªÑ¹ Unit Step ÊèÇ¹¾¨¹ì·Õè 2 áÅÐ 3 ¨Ðà»ç¹¼ÅÅÑ¾¸ì¢Í§ Transient Response ¨ÐºÍ¡¾ÄµÔ¡ÃÃÁ¢Í§àÍÒ·ì¾Øµ¢³Ðã´¢³ÐË¹Öè§ â´Â¶éÒ¤èÒ

áÅÐ

à»ç¹¨Ó¹Ç¹¨ÃÔ§·ÕèÁÕ¤èÒà»ç¹ºÇ¡·Ñé§¤Ùè ¨Ð·ÓãËé¤èÒ¢Í§¾¨¹ì Exponential ÁÕ¤èÒÅ´Å§àÁ×èÍàÇÅÒà¾ÔèÁ¢Öé¹ ¼Å¤×Í Transient Response ¢Í§ÃÐºº¨ÐÁÕ¤èÒà»ç¹ÈÙ¹ÂìàÁ×èÍàÇÅÒà¾ÔèÁ¢Öé¹ ÃÐºº¨Ðà¢éÒÊÙèÊÀÒÇÐ Stable ä´éã¹·ÕèÊØ´ áÅÐ¾¨¹ì Au(t) ¨Ðà»ç¹àÍÒ·ì¾Øµ·ÕèáÊ´§¶Ö§ Steady State Response ÍÂèÒ§äÃ¡çµÒÁËÒ¡¤èÒã´¤èÒË¹Öè§¢Í§

áÅÐ

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áÅÐ

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ÃÙ»·Õè 5 ÅÑ¡É³ÐàÍÒ·ì¾ØµàÁ×èÍ Pole ÁÕ¤èÒµèÒ§æ

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ÃÙ»·Õè 6 (a) Step Respone , (b)Error Signal , (c)Time rate of change of error signal

ÃÙ»·Õè 7 ÃÐºº¤Çº¤ØÁª¹Ô´»éÍ¹¡ÅÑº PD

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Overshoot ã¹ÃÐºº¤Çº¤ØÁª¹Ô´»éÍ¹¡ÅÑºáºº Propotional ¤èÒ Overshoot ÁÕ¤èÒÊÙ§à»ç¹¼Åà¹×èÍ§ÁÒ¨Ò¡·ÍÃì¡(Torque) ·ÕèÁÕ¤èÒà»ç¹ºÇ¡·ÕèÍÂÙèã¹ªèÇ§àÇÅÒ 0 < t < t1 ÁÕ¤èÒÁÒ¡à¡Ô¹ä» áÅÐáÃ§µéÒ¹(ÁÕ¤èÒà»ç¹ -)¡ÒÃà¡Ô´·ÍÃì¡à¡Ô¹·Õèà»ç¹ºÇ¡ ã¹ªèÇ§àÇÅÒ t1 < t < t2 ÁÕ¤èÒ¹éÍÂà¡Ô¹ä»(à»ç¹Åº¹éÍÂà¡Ô¹ä»)
Undershoot ¤ÇÒÁ¤ÅÒ´à¤Å×èÍ¹·Õèà¡Ô´¢Öé¹ã¹ªèÇ§ t3 < t < t4 à»ç¹¼Åà¹×èÍ§ÁÒ¨Ò¡·ÍÃì¡·ÕèÁÕ¤èÒà»ç¹Åº ·Õè¶Ù¡ãËéá¡èÃÐººã¹ªèÇ§àÇÅÒ 0 < t < t1 à¾×èÍµéÒ¹¡ÒÃà¡Ô´ Overshoot ÁÕ¤èÒÁÒ¡à¡Ô¹ä» áÅÐáÃ§µéÒ¹(ÁÕ¤èÒà»ç¹ +)¡ÒÃà¡Ô´·ÍÃì¡à¡Ô¹·Õèà»ç¹Åº ã¹ªèÇ§àÇÅÒ t3 < t < t4 ÁÕ¤èÒ¹éÍÂà¡Ô¹ä»
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º·ÊÃØ»

àÍ¡ÊÒÃÍé§ÍÔ§

Ronald P. Hunter "Automated Process Control System" Printice Hall,1987
David M. Ausiander and Paul Saques "Microprocessor for Measurement and Control" Osborn/McGrawhill 1981

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