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Proportional Action (P)
Integral Action (I)
Derivative Action (D)
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ÍØ»¡Ã³ìÇÑ´ (sensor) ãªéÇÑ´ÊÑÒ³ ÍÍ¡¢Í§ ¡ÃÐºÇ¹¡ÒÃ ã¹·Ò§ »¯ÔºÑµÔ ¢Í§ ÃÐºº ÍØµÊÒË¡ÃÃÁ ÍØ»¡Ã³ì ÇÑ´¨Ð ¶Ù¡¼¹Ç¡ äÇé´éÇÂ transmitter à¾×èÍá»Å§ÊÑÒ³ ÍÍ¡ ¢Í§ ÍØ»¡Ã³ì·ÕèÇÑ´ãËéÍÂÙèã¹ÃÙ»¢Í§ÊÑÒ³ÁÒµÃ°Ò¹·Ò§ÍØµÊÒË¡ÃÃÁ
µÑÇ¤Çº¤ØÁ (controller) ÁÕË¹éÒ·Õèà»ÅÕèÂ¹ÊÒÃÊ¹à·È·Õèä´é¨Ò¡ÍØ»¡Ã³ìÇÑ´à»ç¹ÊÑÒ³¤Çº¤ØÁ
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Proportional Action (P)
à»ç¹à·¤¹Ô¤àÃÕÂº§èÒÂ·ÕèÊØ´ËÅÑ¡¡ÒÃ¡ç¤×ÍÊÑÒ³¤Çº¤ØÁ¨Ò¡µÑÇ¤Çº¤ØÁ·ÕèÊè§ ä»ÃÑº¡ÃÐºÇ¹¡ÒÃ ÁÕ¤èÒà»ç¹ÊÑ´ÊèÇ¹¡Ñº¤ÇÒÁ¼Ô´¾ÅÒ´ (error = setpoint - output) ·Õèà¡Ô´¢Öé¹ ËÃ×Í¡ÅèÒÇÍÂèÒ§§èÒÂ¡ç¤×Íà»ç¹ÍÑµÃÒ¢ÂÒÂÐÃÃÁ´Ò (gain ,K) ¹Ñè¹àÍ§ µÑÇ¤Çº¤ØÁºÒ§µÑÇ ÊÑÒ³à¢éÒáÅÐÊÑÒ³ÍÍ¡ÍÒ¨ÁÕË¹èÇÂµèÒ§¡Ñ¹ àªè¹¡ÒÃà»ÅÕèÂ¹á»Å§¢Í§ÍØ³ËÀÙÁÔ ·Õè·ÓãËéà¡Ô´¡ÒÃà»ÅÕèÂ¹á»Å§¤ÇÒÁ´Ñ¹ à¾×èÍËÅÕ¡àÅÕèÂ§¡ÒÃá»Å§Ë¹èÇÂ ¤ÇÒÁÊÑÁ¾Ñ¹¸ìÃÐËÇèÒ§ÊÑÒ³ÍÍ¡ áÅÐ ÊÑÒ³à¢éÒ¢Í§µÑÇ¤Çº¤ØÁ ÍÒ¨áÊ´§à»ç¹á¶ºÊÑ´ÊèÇ¹ (Proportional Band, PB) â´Â·Õèá¶ºÊÑ´ÊèÇ¹¤×Í¾ÔÊÑÂ¢Í§ÊÑÒ³à¢éÒ·Õè¨Ð·ÓãËéµÑÇ¤Çº¤ØÁ»¯ÔºÑµÔ§Ò¹àµçÁ¾ÔÊÑÂ»¯ÔºÑµÔ§Ò¹¢Í§ÁÑ¹ â´ÂáÊ´§à»ç¹à»ÍÃìà«¹µì¢Í§¾ÔÊÑ¨¢Í§Ê¶Ò¹Ð¤Çº¤ØÁ «Öè§ÍØ»¡Ã³ì¨ÐÇÑ´ä´é ¤ÇÒÁÊÑÁ¾Ñ¹¸ìÃÐËÇèÒ§ÍÑµÃÒ¢ÂÒÂáÅÐà»ÍÃìà«ç¹µìá¶ºÊÑ´ÊèÇ¹¤×Í K = 100 % PB ÊÓËÃÑºÅÑ¡É³ÐÊÁºÑµÔ¢Í§ Proportional Control ¹ÕéáÊ´§äÇéã¹ÃÙ»·Õè 4

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                                    ÊÑÒ³ÍÍ¡ = (¤ÇÒÁ¤ÅÒ´à¤Å×èÍ¹ % / % PB) + 50 %
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            ¡ÒÃ¤Çº¤ØÁàªÔ§ ÊÑ´ÊèÇ¹¹ÕéÊÒÁÒÃ¶·Õè ¨Ð¤Çº¤ØÁ ÃÐºº ä´é´Õ¾ÍÊÁ¤ÇÃ àËÁÒÐ¡Ñº ¡ÃÐºÇ¹ ¡ÒÃ ·ÕèµéÍ§ ¡ÒÃ ¼ÅµÍº Ê¹Í§ÃÇ´àÃçÇ áÅÐã¹¢³Ðà´ÕÂÇ¡Ñ¹ÂÍÁãËéà¡Ô´¤ÇÒÁ¤ÅÒ´à¤Å×èÍ¹¢¹Ò´¤§·Õè¢¹Ò´Ë¹Öè§ áµèÍÂèÒ§äÃ¡çµÒÁ ËÒ¡ã¹¡ÃÐºÇ¹¡ÒÃà¡Ô´ÁÕ¡ÒÃà»ÅÕèÂ¹á»Å§¾ÒÃÒÁÔàµÍÃìºÒ§µÑÇ¡ç¨Ð·ÓãËéà¡Ô´»ÑËÒ¢Öé¹ä´é à¹×èÍ§¨Ò¡ÍÒ¨à¡Ô´¤ÇÒÁ¤ÅÒ´à¤Å×èÍ¹ã¹ÊÀÒÇÐÍÂÙèµÑÇ (steady state error) ËÃ×Í·ÕèàÃÕÂ¡ÇèÒ "ÍÍ¿à«µ" ¢Öé¹ «Öè§µÑÇ¤Çº¤ØÁáºº P äÁèÊÒÁÒÃ¶á¡éä¢ãËéËÁ´ä»ä´é µÑÇÍÂèÒ§ã¹¡Ã³Õ¹Õé¡çä´éá¡èÃÐººã¹ÃÙ»·Õè 5

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Integral Action (I)
¼ÅµÍº¢Í§ proportional-plus-integral action ÊÒÁÒÃ¶Í¸ÔºÒÂä´éã¹ÊÁ¡ÒÃ

o = output % PB = Proportional Band %
e = error % Ti = Integral time (ÇÔ¹Ò·Õ)

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¤Ø³ÊÁºÑµÔ¢Í§ integral action ã¹¡ÒÃ¡Ó¨Ñ´ÍÍ¿à«µà»ç¹¢éÍ´ÕÍÂèÒ§ÁÒ¡ ´Ñ§¹Ñé¹ integral action ¨Ö§à»ç¹·Õè¹ÔÂÁã¹¡ÒÃãªé¡ÑºÃÐºº¤Çº¤ØÁ»éÍ¹¡ÅÑº ÍÂèÒ§äÃ¡çµÒÁ integral action ¡çÁÕ¢éÍàÊÕÂÍÂÙèºéÒ§ à¾ÃÒÐ ·ÓãËéà¡Ô´ capacity-like lag ¤ÃèÍÁµÑÇ¤Çº¤Á áÅÐ·ÓãËéªèÇ§àÇÅÒ¢Í§¡ÒÃá¡Çè§ÂÒÇ¹Ò¹¢Öé¹ â´Â·ÑèÇ æ ä»áÅéÇ ÃÐºº proportional-plus-integral ¨ÐÁÕªèÇ§àÇÅÒ¢Í§¡ÒÃá¡Çè§¹Ò¹¡ÇèÒÃÐººàªÔ§ÊÑ´ÊèÇ¹ÍÂèÒ§à´ÕÂÇ 50 % ËÃ×Í

T_PI = 1.5T_P                ÍÂèÒ§äÃ¡çµÒÁ ÊÓËÃÑºÃÐºº·ÕèÁÕ time constant àÃçÇ (àªè¹ ÃÐºº¤Çº¤ØÁÍÑµÃÒ¡ÒÃäËÅ) »ÑËÒ¹Õé ¨ÐäÁèÁÕ¼ÅÁÒ¡¹Ñ¡ áµèÊÓËÃÑºÃÐºº·ÕèÁÕ time constant ªéÒ »ÑËÒ¹Õé¨ÐãËèÁÒ¡áÅÐÍÒ¨·ÓãËéÃÐººà¢éÒÊÙè ¨Ø´ÇÔ¡ÄµÔ·ÕèäÁèÊÒÁÒÃ¶ÂÍÁÃÑºä´é (àªè¹ ÃÐºº¤Çº¤ØÁÃÐ´Ñº)
                Integral action ¡çàªè¹à´ÕÂÇ¡Ñº proportional action ¤×Í¨ÐàÔèÁÍÑµÃÒ¢ÂÒÂ¢Í§µÑÇ¤Çº¤ØÁ «Öè§ËÒ¡ ÁÒ¡à¡Ô¹ä»¨Ð·ÓãËéÃÐººà¡Ô´¡ÒÃá¡Çè§ â´Â·ÑèÇ æ ä» integral time ( Ti = 1/Ki sec Ffpmuj Ki = repeats/sec) ¨Ðà»ç¹µÑÇáÊ´§ÇèÒ¡ÃÐºÇ¹¡ÒÃÁÕ¡ÒÃµÍºÊ¹Í§µèÍ¡ÒÃ¤Çº¤ØÁàÃçÇá¤èäË¹ ¶éÒàÇÅÒÁÕ ¤èÒ¹éÍÂÁÑ¹¨ÐãËé¤èÒ äºáÍÊ¶Ö§¤èÒ ·ÕèµéÍ§ ¡ÒÃ¤Çº¤ØÁ àÃçÇ¡ÇèÒ¤èÒ·ÕèÇÑ´ä´é áµè¤ÇÒÁ¤ÅÒ´à¤Å×èÍ¹ÂÑ§à»ç¹ ¤èÒºÇ¡ÍÂÙè ´Ñ§¹Ñé¹¡ÇèÒ¤ÇÒÁ ¤ÅÒ´à¤Å×èÍ¹ ¨Ðà»ç¹ÈÙ¹Âì («Öè§·ÓãËéà·ÍÁ   e dt ËÂØ´·Ó§Ò¹) à·ÍÁäºáÍÊ¡ç¨ÐÁÕ¤èÒÊÙ§¡ÇèÒà·ÍÁ·ÕèµéÍ§¡ÒÃ ´Ñ§¹Ñé¹¨Ö§à¡Ô´¡ÒÃ¾Øè§à¡Ô¹ (over shoot) àË¹×Í¤èÒ·Õè¡ÓË¹´¢Öé¹ä» à¾×èÍãËéà¡Ô´¡ÒÃÍÔ¹·Ô¡ÃÑÅ¤ÇÒÁ¤ÅÒ´à¤Å×èÍ¹¤èÒÅºÅ§ÁÒ
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                2. ÊÑÒ³ÍÍ¡¢Í§¡ÃÐºÇ¹¡ÒÃ¶Ù¡ÊØèÁµÑÇÍÂèÒ§´éÇÂ A/D converter à¾×èÍá»Å§ÊÑÒ³µèÍà¹×èÍ§à»ç¹ÊÑÒ³àªÔ§àÅ¢
                3. äÁâ¤Ãâ»Ãà«Êà«ÍÃìÃÑº¤èÒÊÑÒ³àªÔ§àÅ¢¨Ò¡ A/D converter ÁÒãªéã¹¡ÒÃ¤Ó¹Ç³µÒÁ¢Ñé¹µÍ¹ÇÔ¸Õ (algorithm) ·Õè¡ÓË¹´äÇé áÅéÇÊè§¤èÒ·Õèä´é¨Ò¡¡ÒÃ¤Ó¹Ç³ä»ãËé D/A converter
                4. D/A converter á»Å§ÊÑÒ³àªÔ§àÅ¢·Õèä´éÃÑº¨Ò¡äÁâ¤Ãâ»Ãà«Êà«ÍÃìä»à»ç¹
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µÑÇ¤Çº¤ØÁàªÔ§àÅ¢ PID
µÑÇ¤Çº¤ØÁÍ¹ÒÅçÍ¡ PID ·Õèà»ç¹ä»µÒÁ·ÄÉ®ÕÊÒÁÒÃ¶à¢ÕÂ¹à»ç¹ÊÁ¡ÒÃä´é´Ñ§¹Õé

                    e(t) = error signal                                K_p = proportional gain
                    u(t) = control output                             T_i   =   integral time
                                                                                   T_d = derivative time

áµè¨Ò¡¤Ø³ÊÁºÑµÔáÅÐ»ÑËÒ¢Í§ control action áµèÅÐáºº´Ñ§·Õè¡ÅèÒÇä»áÅéÇ ·ÓãËéäÁèÊÒÁÒÃ¶ ¹ÓÃÙ»µÒÁ·ÄÉ®Õä»ãªéä´éâ´ÂµÃ§ áµè¨ÐÁÕ¡ÒÃ´Ñ´á»Å§ãËéàËÁÒÐÊÁ¡èÍ¹ àªè¹¡ÒÃ´Ñ´á»Å§à¾×èÍÅ´¤ÇÒÁäÇ¢Í§ÊèÇ¹Í¹Ø¾Ñ¹¸ì´éÇÂ¡ÒÃ¡ÃÍ§¤ÇÒÁ¶ÕèµèÓ¼èÒ¹

µÑÇ¤Çº¤ØÁ PID ·Õè¹ÓÁÒãªé§Ò¹¨ÃÔ§ÊÒÁÒÃ¶à¢ÕÂ¹ÊÁ¡ÒÃä´é´Ñ§¹Õé

            â´Â·Õè     r(t) ¤×Í setpoint ËÃ×ÍÊÑÒ³ÍéÒ§ÍÔ§
                         y(t) ¤×Í ÊÑÒ³ÍÍ¡
                         v(t) ¤×Í ÊÑÒ³ÍÍ¡¢Í§ satuation actuator
                          T_t ¤×Í time constant for tracking action à»ç¹àÈÉÊèÇ¹¢Í§ Tt
                          N    = 10 (»ÃÐÁÒ³ 3-20)
            «Öè§µÑÇ¤Çº¤ØÁàªÔ§àÅ¢·Õè·ÓË¹éÒ·Õèä´éàªè¹à´ÕÂÇ¡ÑºµÑÇ¤Çº¤ØÁÍ¹ÒÅçÍ¡ PID ¨ÃÔ§ à¢ÕÂ¹ä´éà»ç¹

â´Â·Õè h ¤×Í ¤Òº¡ÒÃÊØèÁµÑÇÍÂèÒ§ (sampling period)
ËÒ¡¤Òº¡ÒÃÊØèÁµÑÇÍÂèÒ§ÊÑé¹¾ÍµÑÇ¤Çº¤ØÁàªÔ§àÅ¢·ÕèáÊ´§¢éÒ§µé¹¡ç¨ÐÊÒÁÒÃ¶·Ó§Ò¹ä´é´Õ àªè¹à´ÕÂÇ¡ÑºµÑÇ¤Çº¤ØÁÍ¹ÒÅçÍ¡ ¤èÒ¾ÒÃÒÁÔàµÍÃìã¹¡ÒÃ¨Ù¹µÑÇ¤Çº¤ØÁ¤×Í K, T_i áÅÐ T_d¡çÊÒÁÒÃ¶»ÃÑºä´éâ´ÂÍÒÈÑÂÇÔ¸Õ¡ÒÃàªè¹à´ÕÂÇ¡ÑºµÑÇ¤Çº¤ØÁÍ¹ÒÅçÍ¡

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ã¹»Ñ¨¨ØºÑ¹¹Õé à·¤â¹âÅÂÕµèÒ§æ ä´éà¢éÒÁÒÁÕº·ºÒ· ¡ÑºªÕÇÔµ»ÃÐ¨ÓÇÑ¹¢Í§àÃÒÁÒ¡¢Öé¹ ÍØ»¡Ã³ìàËÅèÒ¹ÕéÂÑ§ »ÃÐ¡Íºä»´éÇÂÊèÇ¹µèÒ§æËÅÒÂÊèÇ¹ ÊèÇ¹ÊÓ¤ÑÊèÇ¹Ë¹Öè§·Õè¢Ò´àÊÕÂÁÔä´é¹Ñè¹¡ç¤×Í ÊèÇ¹¢Í§µÑÇ¤Çº¤ØÁ«Öè§à»ç¹µÑÇ·Õè¨ÐªèÇÂãËé¡ÒÃ ·Ó§Ò¹¢Í§ÍØ»¡Ã³ìàËÅèÒ¹Ñé¹ÁÕ»ÃÐÊÔ·¸ÔÀÒ¾ÁÒ¡¢Öé¹
PID(Propotional Integral Derivative) à»ç¹¡ÒÃÃÇÁàÍÒà·¤¹Ô¤·Ñé§ 3 áººà¢éÒ´éÇÂ¡Ñ¹
· ÓãËé¡ÒÃ¤Çº¤ØÁä´é¼Å´ÕÁÒ¡¢Öé¹¡ÇèÒ¡ÒÃãªé à·¤¹Ô¤ÍÂèÒ§ã´ÍÂèÒ§Ë¹Öè§à¾ÕÂ§µÑÇà´ÕÂÇ

àÍ¡ÊÒÃÍéÒ§ÍÔ§

K.OGATA , Modern Control Engineering , 3rd Edition Prentice-Hall , Englewood Cliffs , 1997
B.C. Kuo , Automatic Control Systems , 6th Edition , Prentice-Hall Anglewood ,1991
D.E. Seborg , T.F. Edgar & D.A. Mellichamp , Process Dynamics and Control , John Wiley , NewYork , 1989
G. Stephenapoulos , Chemical Process Control , Prentice Hall , Englewood Cliffs , 1984

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