Predictor based Self tuning Control of Pressure Plants
Transcription
Predictor based Self tuning Control of Pressure Plants
,661±;SULQW,661±;RQOLQH,1)250$7,217(&+12/2*<$1'&21752/71U 3UHGLFWRUEDVHG6HOIWXQLQJ&RQWURORI3UHVVXUH3ODQWV 9\WDXWDV.DPLQVNDV*HGLPLQDV/LDXþLXV 9\WDXWDV0DJQXV8QLYHUVLW\'HSDUWPHQWRI6\VWHPV$QDO\VLV 9LOHLNRVVW-/7-.DXQDV/LWKXDQLD H-PDLOYNDPLQVNDV#LIYGXOWJOLDXFLXV#LIYGXOW http://dx.doi.org/10.5755/j01.itc.43.4.8742 Abstract. A digital predictor-based self-tuning control with constraints for the pressure plants, which is able to cope with minimum-phase and nonminimum-phase plant models is presented in this paper. We determined that applying polynomial factorization for such models the characteristic polynomials of closed-loops are changed. Therefore, the on-OLQHLGHQWLILFDWLRQRIWKHPRGHOV¶SDUDPHWHUVLVSHUIRUPHGLQDZD\WKDWHQVXUHVVWDEOHFORVHG-loops. A choice of the sampling period in digital control typically impacts a control quality of the plant, thus we propose a method for optimization of a sampling period in the digital predictor-based self-tuning control system. The impact of the selection of the sampling period and input signalV¶constraints ± amplitude boundaries and the change rate - on the control quality of the pressure plant is experimentally analysed. Keywords: predictor-based self-tuning control, minimum-phase and nonminimum-phase model, factorization, online identification, closed-loop stability, sampling period optimization, pressure plant. 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Scheme of predictor-based self-tuning controller with constraints for the ith tube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o min , T0 J T T0 1 N ¦ ^y N (1)* t y t(1) y 2 ( 2 )* t y t( 2) t 1 `, 2 ZKHUH N LVWKHQXPEHURIREVHUYDWLRQV ,Q RUGHU WR ILQG DQ RSWLPDO YDOXH T0* RI VDPSOLQJ SHULRGLQWHUPVRIRSWLPL]DWLRQSUREOHP-WKH JROGHQVHFWLRQDOJRULWKPKDVEHHQXVHG> @ 7KH VFKHPH RI WKH GLJLWDO SUHGLFWRU-EDVHG VHOI-WXQLQJFRQWURORIWKHSUHVVXUHSODQWLVGHSLFWHGLQ)LJ Figure 3. 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Search process of the optimal sampling period T0 in the digital predictor-based self-tuning control system with various input signal constraints for the pressure plant 9.DPLQVNDV*/LDXþLXV 7DEOH &RQWUROTXDOLW\FULWHULRQGHSHQGHQF\RQVDPSOLQJSHULRG T0 DQGYDULRXVLQSXWVLJQDOVFRQVWUDLQWV Input signals constraints T0 , s JT 0.005 - - - 199.41 0.01 - 194.014 133.55 130.97 0.02 311.96 146.29 105.03 150.77 0.04 294.83 163.28 130.34 212.41 0.08 325.38 262.13 164.90 240.12 0.1 522.21 281.78 186.02 272.15 0.2 819.51 309.42 209.09 286.45 0.5 879.27 447.16 283.08 396.70 1.0 918.63 595.54 333.16 407.71 VDPSOLQJ SHULRG VLJQLILFDQWO\ LPSDFWV WKH FRQWURO TXDOLW\RIWKHSUHVVXUHSODQW &RQWURO SHUIRUPDQFHV RI WKH GLJLWDO SUHGLFWRUEDVHG VHOI-WXQLQJ FRQWURO ZLWK LQSXW VLJQDOV FRQVWUDLQWV IRU WKH SUHVVXUH SODQW RQ YDULRXV VDPSOLQJ SHULRGV - T0 0.02s, 0.08s, 0.2s, 1.0s - DUH LOOXVWUDWHGLQ)LJXUH 1RWLFHWKDWDKLJKYDULDWLRQRI WKH LQSXW VLJQDOV RFFXU LQ DOO RI WKH FDVHV )LJXUH DQG)LJXUH 7KH GHSHQGHQF\ RI FRQWURO TXDOLW\ FULWHULRQ RQ GLIIHUHQW VDPSOLQJ SHULRGV DQG YDULRXV LQSXW VLJQDOVFRQVWUDLQWVLVSUHVHQWHGLQ7DEOH &RQWURO SHUIRUPDQFHV RI WKH GLJLWDO SUHGLFWRUEDVHG VHOI-WXQLQJ FRQWURO ZLWK LQSXW VLJQDOV FRQVWUDLQWV IRU WKH SUHVVXUH SODQW RQ YDULRXV VDPSOLQJ SHULRGV - T0 0.02s, 0.08s, 0.2s, 1.0s - DUH LOOXVWUDWHGLQ)LJXUH ,WLVVHHQWKDWWKHVHOHFWLRQRI T0* 0.02s, JT* 146.29 T0 (a) T0 0.08s, JT 0.2s, JT 309.42 (c) 262.13 T0 1.0s, JT (b) 595.54 (d) Figure 5. Control performance of predictor-based self-tuning control with input signals constraints (33) for the pressure plant 3UHGLFWRU EDVHG6HOIWXQLQJ&RQWURORI3UHVVXUH3ODQWV T0* 0.02s, JT* 105.03 T0 0.2s, J T 164.90 T0 1.0s, JT (a) T0 0.08s, JT 209.09 (c) 333.16 (d) (b) Figure 6. Control performance of predictor-based self-tuning control with input signal constraints (34) for the pressure plant T0* 0.02s T0 (a) T0 0.08s (b) 0.2s T0 (c) 1.0s (d) Figure 7. On-line identification of modelV¶ parameters of predictor-based self-tuning control with input signals constraints (34) 9.DPLQVNDV*/LDXþLXV [3] &RQVLGHULQJWKH YDOXHVRIFRQWUROTXDOLW\FULWHULRQ LW FDQ EH VHHQ WKDW ZLWK VHOHFWHG LQSXW VLJQDOV FRQVWUDLQWV)LJXUH WKRVHYDOXHVDUHXSWR- WLPHV VPDOOHU EHWWHU DV FRPSDUHG WR FULWHULRQ YDOXHV ZLWKVHOHFWHGLQSXWVLJQDOVFRQVWUDLQWV)LJXUH 2Q-OLQH LGHQWLILFDWLRQ RI PRGHOV¶ SDUDPHWHUV RI SUHGLFWRU-EDVHG VHOI-WXQLQJ FRQWURO ZLWK LQSXW VLJQDOV FRQVWUDLQWV DQG YDULRXV VDPSOLQJ SHULRGV T0 0.02s, 0.08s, 0.2s, 1.0s LVGHPRQVWUDWHGLQ)LJXUH 1RWLFH WKDW WKH FKRLFH RI VDPSOLQJ SHULRG DOVR VLJQLILFDQWO\ LPSDFWV WKH HVWLPDWHV RI PRGHOV [4] [5] SDUDPHWHUVHVSHFLDOO\ bÖ1(ti ) , bÖ2(it) [6] &RQFOXVLRQV [7] $ GLJLWDO SUHGLFWRU-EDVHG VHOI-WXQLQJ FRQWURO ZLWK FRQVWUDLQWV V\VWHP IRU SUHVVXUH SODQW KDV EHHQ GHYHORSHG ZKHUH RQ-OLQH LGHQWLILHG PRGHO RI HDFK SODQW¶V WXEH FDQ IHDWXUH ERWK - PLQLPXP-SKDVH DQG QRQPLQLPXP-SKDVH :HVKRZHGWKDWDSSO\LQJSRO\QRPLDOIDFWRUL]DWLRQ IRU PLQLPXP-SKDVH DQG QRQPLQLPXP-SKDVH SODQW PRGHOV WKH FORVHG-ORRSV RI WKH FRQWURO V\VWHP DUH FKDQJHG DQG H[SUHVVLRQV RI WKH WUDQVIHU IXQFWLRQV RI FORVHG-ORRSVKDYHEHHQREWDLQHG ,Q RUGHU WR HQVXUH WKH VWDELOLWLHV RI FORVHG-ORRS V\VWHPV ZKLFK PRGHOV¶ SDUDPHWHUV DUH REWDLQHG YLD RQ-OLQH LGHQWLILFDWLRQ ZKHWKHU DOO WKH URRWV RI FKDUDFWHULVWLF SRO\QRPLDOV RI FORVHG-ORRSV DUH LQVLGH WKH XQLW GLVF DW HDFK FRQWURO VWHS DUH QHFHVVDU\ WR WUDFN :H KDYH SURSRVHG D PHWKRG IRU RSWLPL]DWLRQ RI VDPSOLQJ SHULRG LQ WKH GLJLWDO SUHGLFWRU-EDVHG VHOIWXQLQJFRQWUROV\VWHPRIWKHSUHVVXUHSODQW 7KHLPSDFWRIWKHVHOHFWLRQRIWKHVDPSOLQJSHULRG DQG LQSXW VLJQDOV FRQVWUDLQWV ± DPSOLWXGH ERXQGDULHV DQG WKH FKDQJH UDWH - RQ WKH FRQWURO TXDOLW\ RI WKH SUHVVXUH SODQW KDV EHHQ DQDO\VHG :H GHPRQVWUDWHG WKDW WKH SUHGLFWRU-EDVHG FRQWUROOHU LV SDUWLFXODUO\ VHQVLWLYH WR WKH OLPLWDWLRQ RI WKH FKDQJH UDWH RI WKH LQSXW VLJQDOV 2SWLPL]DWLRQ RI VDPSOLQJ SHULRG VLJQLILFDQWO\ LPSURYHV WKH FRQWURO TXDOLW\ RI WKH SUHVVXUHSODQW [8] [9] [10] [11] [12] [13] [14] [15] 5HIHUHQFHV [1] [2] K. J. Åström, B. Wittenmark. Self-tuning controller based on pole-zero placement. In: IEE Proceedings D, 1980, Vol. 127, pp. 120-130. K. J. Åström, B. Wittenmark. Computer-Controlled Systems: Theory and Design. New Jersey: Prentice Hall, Third Edition, 1997. [16] V. Bobál, J. Böhm, J. Fessl, J. 0DFKiþHN Digital Self-tuning Controllers. London: Springer-Verlag, 2005. C. Caro, N. Quijano. Low Cost Experiment for Control System. IEEE IX Latin American and IEEE Colombian Conference on Automatic Control and Industry Applications (LARC), Robotics Symposium, 2011, pp. 1-6. S. L.Coelho, W. M. Pessôa. Nonlinear Model Identification of an Experimental Ball-and-Tube System using a Genetic Programming Approach. Mechanical Systems and Signal Processing, 2009, Vol. 23, No. 5, 1434-1446. R. Isermann. Digital Control Systems: Volume 2: Stochastic Control, Multivariable Control, Adaptive Control, Applications. London: Springer-Verlag, 2nd edition, 1991. V. Kaminskas. 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