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November 9th, 2017, 03:51 AM  #1 
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Program low pass first order
We have to program a low pass first order filter in Siemens S7.
From an engineering company we got following transfer function : ��(��)=(1/��)/(��+1/��) ��=50 I found following on this forum as implementation : Y0 = (Y1 * Kf) + (X * (1  Kf)) where: Y0 is the filtered output Y1 is the filtered output from the previous scan X is the input to be filtered Kf is the first order filter constant Kf = et/T where" t is the time between scans T is the first order time constant Can I use the above formula : Y0 = (Y1 * Kf) + (X * (1  Kf)) where I can set T (Kf = et/T) to 50? Or is this the wrong approach? 
November 9th, 2017, 07:23 AM  #2 
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November 9th, 2017, 09:01 AM  #3 
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The equation you show is an easy way to approximate a 1storder lowpass filter. It is variously termed "running average" or "exponential filter". The later is from Management Science and Industrial Engineering. It is simple to implement because you need store only one past value. In the classification of digital filters, it falls into "infinite impulse response" (IIR) because any spike or such will affect the output forever (slowly decaying). The contrast is FIR filters which average a block of input readings (must store all of them), a useful one being a "window average" such as averaging over exactly 1 period (or n) of 60 Hz (or 50 Hz) to eliminate AC noise.
I usually write the running average as: yout = w*yin + (1w)yout where y is the filter output (i sample on left, i1 sample on right). yin is the raw signal (i sample), and w is the weighting factor, which approximates a 1storder filter w/ time constant tau: w = 1  (T/tau) where T = sampling period (sec). For the common RC lowpass circuit in textbooks, tau = R*C. In terms of cutoff frequency (3 dB attenuation point), fco = 1/(2*pi*tau). Of course, a faster sampling rate better approximates an analog filter. Last edited by RocketTester; November 9th, 2017 at 09:15 AM. 
November 9th, 2017, 12:56 PM  #4 
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T has units of what? Minutes? Seconds?
You need to set T on initialization as well as calculate Kf. However, you could set T= 50 each scan and calculate Kf each scan it just wouldn't be as efficient. BTW, don't get sloppy with your equations y(n) = Kf*y(n1)+(1Kf)*x(n)
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November 9th, 2017, 02:39 PM  #5 
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Peter,
I clearly said T has units of sec. But, not necessary since the equations work in any consistent set of units. If T <> sec, then fco <> Hz. Yes, one must assign values to the constants before using them. In PLC world that doesn't have to be done in PLC code. In Beckhoff's TwinCAT, one can download a value for w from a Visual Basic HMI program (I recall similar for AB ControlLogix). T is best set from a function call which polls the PLC OS for the current value of cycle time. In Structured Text, the equation should be: yout := w*yin + (1w)*yout; One doesn't need to distinguish which yout goes with which calculation cycle, since implicit in the way the code flows. As in most computer languages, variables on the left side are assigned, thus "new value", while variables on the right side are inputs, thus "last value". That is why many languages use ":=" instead of math's "=". I just noticed a mistake. Should be w = T/tau. I grabbed this from an email I sent to a young engineer here years ago, and made the mistake then. I related the weighting to an equivalent time constant long ago when at Westinghouse. I recall seeing the same in a textbook after that, but forgot where (if someone finds, please post). For those who care, look at the simple mathematical derivation below and compare to the runningaverage equation to equate w to equivalent tau. Exact Integration The time derivative is a function of the input (yin) and current output value (yout): dyout/dt = (yin – yout)/tau As a numerical approximation, one recalculates the slope at intervals T, projecting to a new yout, each time: yout = yout + (dyout/dt)T = yout + (T/tau)(yin – yout) or yout = (1T/tau)yout + (T/tau) yin 
November 9th, 2017, 02:46 PM  #6 
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What are they talking about?

November 9th, 2017, 05:25 PM  #7 
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Ronnie,
aand74 needs to smooth a signal by numerical averaging. A running average is a simple method. It approximates an analog lowpass filter. 
November 9th, 2017, 07:40 PM  #8 
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I'm leaning towards Kalman filtering for analog signals that may have unwanted noise, but I've yet to find a simple explanation as to how it works.
I've used it in Arduino projects with great success, you can addin a kalman library function quite easily, it's all prebuilt, but have no knowledge of the nuts and bolts of it. Perhaps I haven't looked long and hard enough, but I've yet to see a Kalman filtering method applied in the PLC world.
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November 9th, 2017, 09:11 PM  #9  
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Quote:
FV=FV+C(NVFV) Where: FV= Filtered value C= constant (range 0.99) The smaller the number the more dampening. NV= New Value Filtered Value= Filtered Value+Constant*(New ValueFiltered Value) New Value = Unfiltered Value Constant= 0.00.99 The smaller the number the more damping.
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November 10th, 2017, 12:53 AM  #10 
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Two Pole Butterworth filter and comparison with single pole low pass filter.
http://deltamotion.com/peter/Mathcad...worth%20NG.pdf
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November 10th, 2017, 07:42 AM  #11  
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Quote:
It is suitable for applications where the noise is more constant, such as noise induced by mainsborne interference, or where the "noise" is relatively constant and largely predictable. Large transients will still propagate through the maths, and produce noticeable shifts in the output until it is "shiftedout" of the equations. So, I've been reading up on Kalman filtering, and the description of how it operates seems to suit my needs better. My application is a tracking receiving antenna system for FPV flying R/C aircraft, helis etc., and my findings are such that you can get large, short term, deviations in Received Signal Strength as the model moves around, mainly due to multiple signal paths being created and disappearing. The Kalman filter assigns a "weighting" to each successive reading, based on the probability of its "correctness". The larger the deviation, the smaller the probability. The subsequent averaging includes the weighting factor, so large transients have much less effect on the final filtered value. My initial tests when I first adopted Kalman were extremely encouraging. If anyone is interested in the math involved, I have attached the Arduino "Kalman.h" library file FYI. I'm relatively new to Arduino programming, and don't yet undersyand some of the syntax, but it may be useful if anyone wants to try translating into PLC code.
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___________________________ ControlLogix & SLC Training ab train ltd. abtrain@tiscali.co.uk www.abtrain.co.uk tel: 07506 73 9999 nil illegitimi carborundem Last edited by daba; November 10th, 2017 at 08:01 AM. 

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