Improvement of Accuracy for Continuous Mass Measurement in Checkweighers with an Adaptive Notch Filter
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1 Vol.47, No.10, 477/ Improvement of Accuracy for Continuous Mass Measurement in Checkweighers with an Adaptive Notch Filter Processing in Measurement Time Toshitaka Umemoto, Morihito Kamon and Yoichiro Kagawa As manufacturing processes are steadily automatized, quick and accurate mass measurement systems are in great demand. In this respect, recently, active belt conveyer checkweigher is used by many enterprises. This system possesses a serious technical problem, in which three types of mechanical noises, that is, proper vibration, motor vibration, and belt pulley vibration, are included in detection signals. The noises should be removed to increase the accuracy. In the current mass measurement system, moving average method is applied for the aim. However, it is not enough to realize the quick and accurate measurement. Very recently, we applied frequency analysis method using the complex LMS algorithm for this problem. Only a signal in the stable time had to be used for real-time processing with this method. In this study, therefore, we decreased the moving average filters and increased the adjustment notch filters. Key Words: adaptive algorithm, dynamic mass measurement, frequency analysis 1. 1), 2) Osaka Prefecture University College of Technology, Saiwai-cho, Neyagawa Yamato Scale Co., Ltd., 5-22 Saenba-cho, Akashi Received December 27, 2010 Revised October 3, FIR Finite Impulse Response 3), 4) 3) FIR TR 0010/11/ c 2010 SICE
2 478 T. SICE Vol.47 No.10 October ) 5) IIR Infinite Impulse Response IIR FIR 6) LMS 7) 9) CHS22L 5) Table 1 Fig. 1 Our checkweigher Specifications of checkweigher Specification Weighing Range Weighing Speed (Max) Sampling Period Weigh Conveyer Length Product Dimensions of Length Performance g 220 packs/min 2ms 435 mm 300 mm Fig. 1 2 Table 1 WS: Weighing Speed 1 v c v c = WS L L 0
3 v c f p vc f p = 2 πd p d p f m M p M m f m = Mm f p 3 M p 2. 3 τ τ τ = L0 L τ AD 4 v c L τ AD AD Fig. 2 Spectra analysis system with the LMS algorithm LMS 7), 8) 9) 9) Fig. 2 G(k) kt T X(k) Ḡ(k) X(k) G(k) X(k) X(k) X(k) =exp(j2πf akt) 5 f a d(k) f a ε(k) d(k) y(k) ε(k) =d(k) y(k) = d(k) {G(k)X(k)+Ḡ(k) X(k)} 6 B. Widrow LMS 10) ε 2 (k) 7) G(k) Ḡ(k) G(k +1)=G(k)+4με(k) X(k) Ḡ(k +1)=Ḡ(k)+4με(k)X(k) 7 8 μ 9) 0 <μ< τ sys = T 8μ 10
4 480 T. SICE Vol.47 No.10 October 2011 Fig. 3 Block diagram of transfer function A(z) 3. 2 Fig. 2 6 d(k) ε(k) G(k)X(k) ε(k) 7 X(k +1) X(k) G(k +1)X(k +1) Fig. 4 Block diagram of adaptive notch filter with the LMS algorithm Table 2 Relation between weighing speed and frequency of noise Weighing Natural Oscillation Oscillation speed Oscillation by Motor by Pulley (packs/min) (Hz) (Hz) (Hz) = G(k)X(k +1)+4με(k) X(k)X(k +1) = G(k)X(k)X(1) + 4με(k)X(1) 11 G(k)X(k) W (k) 11 W (k +1)=W (k)x(1) + 4με(k)X(1) 12 z Fig. 3 A(z) A(z) = W (z) E(z) = 4μX(1) 13 z X(1) Ḡ(k) X(k) ε(k) Ā(z) = W (z) E(z) = 4μ X(1) z X(1) 14 2 d(k) ε(k) Fig. 4 H(z) H(z) = E(z) D(z) = 1 1+A(z)+Ā(z) = z 2 {X(1) + X(1)}z +1 z 2 (1 4μ){X(1) + X(1)}z +1 8μ 15 X(1) X(1) 1 z = X(1) z = X(1) H(z) =0 f a H(z) Fig. 5 Current system used in checkweigher 30.2 Hz (2) (3) d p 27 mm 2:1 Table 2 (4) Fig. 5 1 Fig. 5 1 Table mm 350 mm Table 3 Table 2
5 Table 3 Length of filter calculated from checkweigher Weighing Speed Measurement Length of Filter (packs/min) Time (ms) Table 4 Relation between weighing speed and length of filter Weighing Natural Oscillation Oscillation speed Oscillation by Motor by Pulley (packs/min) Table 2 Table 4 2ms Table 4 Table Fig mm 3 A B C (10) 20 Table Table Table 5 Table IIR IIR Fig. 7 AD Fig. 6 Table 5 Proposed system used in checkweigher Length of filter with proposed system Weighing Speed Length of Filter Amount of data (packs/min) Filter A Fileter B for Notch Filter s s N x(k) (k =1,,N) N Fig. 6 A x 1(k) (k =1,,N) x 1(k) =x(k) x(1) k =1,,N 16 A x 1(N) C ε 3(N) x(1)
6 482 T. SICE Vol.47 No.10 October 2011 Fig. 7 Data obtained from checkweigher Table 6 Relation between optimum value of step-sizeparameter and weighing speed Weighing Step-size-parameter Speed Natural Oscillation Oscillation (packs/min) Oscillation by Motor by Pulley ms Table 3 Table 5 40 ms (10) ) ε(k) σ σ g Table Table 2 Fig. 8 Identification results of step-size-parameter Table 6 Table 6 Fig. 8 3 (μ Natural μ Motor μ P ulley ) 1 μ Natural = WS μ Motor = WS μ P ulley = WS WS 5. 2 Table 7 5 Table
7 Table 8 Result of comparative experiment Weighing Amount of weight Three times standard deviation (g) Speed input Current Proposed Warranty (packs/min) data (g) Method Method max. values Table 7 Length and weight of measurement objects used to experiment Length (mm) Weight (g) (Table 3) Table 5 2 Table σ Table 8 Table mm Fig ms g 57 packs/min 300 mm 300 mm 51 packs/min 71 packs/min 300 mm 83 packs/min 1600 g 300 mm 94 packs/min 1000 g 2.0 g 106 packs/min 4 6. FIR Finit Impulus Response 3), 4)
8 484 T. SICE Vol.47 No.10 October mm g 57 packs/min 300 mm 300 mm 57 packs/min 71 packs/min 300 mm 83 packs/min 1600 g 300 mm 94 packs/min 1000 g 2.0 g 10 B. Widrow and S.D. Stearns: Adaptive Signal Processing, New Jersey, Prentice-Hall, Inc. (1985) /44 (1999) , 489/495 (2003) , 759/764 (2002) , 1205/1201 (2004) 5 C , 2122/2128 (2008) 6 FIR , SIP , 7/12 (2010) , 619/625 (1992) , 1257/1262 (1992) , 959/965 (1994)
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