which the tuning of PID controllers can be done. These methods include the trial and error, in which the PID parameters are obtained using hit and trial method.
6WDELOL]DWLRQRI0RELOH,QYHUWHG3HQGXOXP8VLQJ )X]]\3,'&RQWUROOHUV 6DQNDOS3DOLZDO
9LNUDP&KRSUD6XQLO.XPDU6LQJOD
(OHFWULFDODQG,QVWUXPHQWDWLRQ(QJLQHHULQJ'HSDUWPHQW 7KDSDU8QLYHUVLW\ 3DWLDOD,QGLD HPDLO SDOLVDQ#JPDLOFRP
(OHFWULFDODQG,QVWUXPHQWDWLRQ(QJLQHHULQJ'HSDUWPHQW 7KDSDU8QLYHUVLW\ 3DWLDOD,QGLD HPDLO YLNUDPFKRSUD#WKDSDUHGXVVLQJOD#WKDSDUHGX
$EVWUDFW²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²PRELOHLQYHUWHGSHQGXOXP VWDELOL]DWLRQ IX]]\3,' SROHSODFHPHQW
, ,1752'8&7,21
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
)LJ6WUXFWXUHRIIX]]\FRQWUROOHU 7KH RXWSXW JDLQV DUH VFDOHG GRZQ EHWZHHQ DQG 7KH PLQLPXPDQGWKHPD[LPXPYDOXHVRIYDULRXVJDLQVKDYHEHHQ REWDLQHG E\ DQDO\]LQJ WKH VWHS UHVSRQVH RI WKH JLYHQ SURFHVV ZLWK WKH FRQYHQWLRQDO 3,' FRQWUROOHU 7KH PHPEHUVKLS IXQFWLRQV IRU ERWK HUURU H DQG GH DUH VKRZQ LQ )LJXUH GW DQG)LJXUHIRUDQJOHFRQWURO7KHPHPEHUVKLSIXQFWLRQVIRU WKHRXWSXWYDULDEOHVDUHUHSUHVHQWHGLQ)LJXUH
)LJ7ZRORRS3,'FRQWUROOHUIRU0,3V\VWHP 6LQFH WKHUH DUH WZR RXWSXWV WR FRQWURO WKHUHIRUH WZR 3,' FRQWUROOHUVDUHUHTXLUHG
)LJ0HPEHUVKLSIXQFWLRQVWUXFWXUHRIHUURU
7ULDODQGHUURU SROHSODFHPHQW IX]]\ORJLF
3RVLWLRQ
)LJ0HPEHUVKLSIXQFWLRQVWUXFWXUHRIHUURU
7LPH 6HF
)LJ3RVLWLRQYV7LPHJUDSK
7ULDODQGHUURU 3ROHSODFHPHQW )X]]\ORJLF
)LJ0HPEHUVKLSIXQFWLRQIRURXWSXWVHWV 7KHXQLYHUVHRIGLVFRXUVHRIWKHLQSXWDQGWKHRXWSXWYDULDEOHV KDYH EHHQ REWDLQHG E\ WXQLQJ WKH 3,' FRQWUROOHU XVLQJ WULDO DQGHUURUPHWKRG 7DEOH)X]]\UXOHEDVHIRUIX]]\FRQWUROOHU H 1% 16 = 36 3% GHGW 1%
1%
1%
16
16
=
16
1%
16
16
=
36
=
16
16
=
36
36
36
16
=
36
36
3%
3%
=
36
36
3%
3%
$QJOH UDGLDQ
7LPH 6HF
)LJ $QJOHYV7LPHJUDSK 7KH3,'SDUDPHWHUVXVLQJWULDODQGHUURUDQGSROHSODFHPHQW WHFKQLTXHDUHJLYHQLQ7DEOHDQG7DEOH 7DEOH3,'SDUDPHWHUVXVLQJSROHSODFHPHQW &RQWUROOHU
N S NL N G
3,'
3,'
7DEOH3,'SDUDPHWHUVXVLQJSROHSODFHPHQW
6LPLODUO\ IX]]\ EDVHG 3,' FRQWUROOHU IRU FRQWUROOLQJ WKH SRVLWLRQ FDQ EH GHVLJQHG ZLWK WKH VDPH UXOH EDVH 7KH FRQWUROOHUVDUHLPSOHPHQWHGLQPDWODEVLPXOLQNDQGWKHUHVXOWV DUHFRPSDUHGZLWKWKHFRQYHQWLRQDO3,'WXQLQJPHWKRGV ,,, 5(68/76$1'',6&866,21 7KH VLPXODWLRQ UHVXOWV IRU SRVLWLRQ DQG DQJOH FRQWURO DUH JLYHQLQ)LJXUHDQG)LJXUH XVLQJGLIIHUHQWWXQLQJPHWKRGV )RUSRVLWLRQFRQWUROWKHUHIHUHQFHLVDXQLWVWHSVLJQDOZKLOHIRU DQJOHFRQWUROWKHUHIHUHQFHLVUDGLDQ
&RQWUROOHU
NL
NS
3,'
3,'
NG
$ FRPSDUDWLYH DQDO\VLV RI GLIIHUHQW WXQLQJ PHWKRGV LV JLYHQLQ7DEOHDQG7DEOHIRUSRVLWLRQDQGDQJOHFRQWURO
7DEOH3HUIRUPDQFHSDUDPHWHUVIRUSRVLWLRQFXUYH 3DUDPHWHUV
)X]]\ 3,'
3ROH SODFHPHQW
7ULDO DQG HUURU
5LVHWLPH W U VHF 6HWWOLQJWLPH W V VHF
0D[RYHUVKRRW 0 S
0D[XQGHUVKRRW 0 X
6WHDG\VWDWHHUURU HVV
7DEOH3HUIRUPDQFHSDUDPHWHUVIRUDQJOHFXUYH 3DUDPHWHUV
)X]]\ 3,'
7ULDODQG HUURU
3ROH SODFHPHQW
6HWWOLQJWLPH W V
VHF 0D[RYHUVKRRW 0 S
0D[XQGHUVKRRW 0 X
6WHDG\VWDWHHUURU HVV
5LVHWLPH W U VHF
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
>@ :HLJXR :@ /XSLDQ / ) $YLOD 5 6WDELOL]DWLRQ RI D ZKHHOHGLQYHUWHGSHQGXOXPE\ D FRQWLQXRXVWLPH LQILQLWH KRUL]RQ/4*RSWLPDO FRQWUROOHU 5RERWLF 6\PSRVLXP ,((( /DWLQ$PHULFDQ± >@ .DQJ 079R +'.LP +. .LP 6% &RQWUROV\VWHP GHVLJQ IRU DPRELOHLQYHUWHGSHQGXOXPYLDVOLGLQJPRGH WHFKQLTXH ,((( ,QWHUQDWLRQDO&RQIHUHQFHRQ0HFKDWURQLFV± >@&KRSUD96LQJOD6. 'HZDQ/ 6WDELOL]DWLRQ RI DQ ;
