revisi - application of kalman filter for estimated elevation water

8/10/2019 Revisi - Application of Kalman Filter for Estimated Elevation Water

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APPLICATION OF KALMANFILTER FOR ESTIMATED

ELEVATION WATER IN TANK

Nur Hasanah Ahniar 2414201003Singgih Yudya Setiawan 2414201004Sisca Dina N N 2414201006Sefi Novendra Patrialova 2414201007Nur Fitriyani 2414201010Iftihatur Rohmah 2414201015


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INTRODUCTION Fluid level control is a basic control in all

industries. Inaccuracies of the measurementdata and the presence of noise in themeasurement can be harmful in a complexprocess. Kalman filtering technique is a type of

filter to reduce measurement noise. Thisapplication of Kalman Filter in control of the water level is expected to reduce the risk of dataacquisition errors.


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The problems definition of this Kalman Filterapplication are as follows:

How to estimate the fluid level using KalmanFilter How to represent measurement data which is

filtered by Kalman Filter How to simulate Kalman Filter in fluid levelcontrol using MATLAB


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STUDY LITERATUREOverview of Kalman Filter Kalman filtering, also known as linear quadratic

estimation (LQE), is an algorithm that uses a series ofmeasurements observed over time, containing noise (random variations) and other inaccuracies, and produces estimates ofunknown variables that tend to be more precise than those based on a single measurement alone

The Kalman filter has numerous applications in technology

The algorithm works in a two-step process is a common misconception that the Kalman filter assumesthat all error terms and measurements are Gaussiandistributed
http://en.wikipedia.org/wiki/Algorithmhttp://en.wikipedia.org/wiki/Statistical_noisehttp://en.wikipedia.org/wiki/Kalman_filterhttp://en.wikipedia.org/wiki/Kalman_filterhttp://en.wikipedia.org/wiki/Statistical_noisehttp://en.wikipedia.org/wiki/Algorithm


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Kalman Filter Algoritm

Kalman Filter algoritm is used to estimate the dynamic linearprocess such given following equation: x k = Ax k-1 + Bu k-1 + w k-1

And measurement equation as following equation: Z k= Hx k + v k

For which w k and vk : random variable represent the process noise and

measurement noise. This kind of noise is assumed as white noise. Covariance Q and R are assumed constant. A : matrix which shows previous time state and current time state.

B : matrix shows control signal or input and current state time. H : matrix shows current state time and picking measurement.


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State of The Kalman Filter

Kalman filter is widely used in many applications.Many applications of Kalman Filter can be appliedto various systems

In 2003, John Valasek and Wei Chen used an observerof Kalman Filter to identified airplane online system

In 2004, Pratap R has done a research about EKF which is used to filter noise into the biological reactor

In 2005, Kalman Filter has been used to estimateinternal temperature of linear hybrid system by L.Boillereaux, H. Fibrianto and J. M Flaus

Mickael Hilairet, Francois Auger, dan Eric Berthelot

have modified Kalman Filter in 2007


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MODELLING PROCESS A process will be observed is

simple process, it is ameasurement height of waterin tank by using floating ball. At this process, there are somepossibles:

Filling process, emptying, orstatic, that is when the heightof tank increased, decreased,or unchanged.

Mixing process or stagnant isthe relative height from buoysat average height of tankchange to time or static.


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The tank by the water height constant(L = c) State processing model

The level of water in the constant tank, L=c

Process model measurementThere are level of float that can be represented with y=y

Noise model

we assume the noise comes from measurement, i.e. R=r Filtering testing

Filter was defined. Accordingly, for first measurement we set the level of tank L=c=1


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The tank by increasing water height

constant ( dL/dt = c ) The tank is filled with constant debit. It causes

changing of water level constantly.That Lt = L t-1 + c.t . By assumption c = 0,1/s. With the assumption r = 0,1 and variation 0,001 q0,1


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q = 0,001


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q = 0,01


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Filling Model State Process Model

for the best results, Kalman Filter Model from Lt = Lt-1 + c.t will be converted into a continous processtransition x = (x 1,x f )t

Measurement Process Modelstill used the assumption that there is noise H = (1,0)

y (y,0)T


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Noise Model

Also still get the noise R = r

Filtering Testingassumed that the noise r = 0,1 and the accuracyof the noise process q f = 0,00001


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Obtained result


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The Constant Height


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Mixing models L = c.sin(2 .r. t)+l By c =0.5 ; r = 0.05 ; l = 1 By using filters kalman get :


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Matlab Program For Case 3.2 Constan clc; clear; L0 = 1; c = 0; x0 = [0; 0]; r = 0.1; qf = 0.00001; tmax = 30; H = [1 0]; Ft = [1 1; 0 1]; Q = qf*[1/3 1/2; 1/2 1]; P0 = [1000 0; 0 1000];

fprintf(' | L | x1 | y | x2 '); for t=1:tmax if (t==1) L = L0; x1 = Ft*x0; P1 = Ft*P0*Ft' + Q; else

L = L + c; x1 = Ft*x2; P1 = Ft*P2*Ft' + Q; end y = (L - r + 2*r*rand()); if (y


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CONCLUSION Kalman Filtration technique was introduced as a

reliable technique to diminish noise signal and was succeed to improve data convergence.

Well preliminary initiation will also enhancefiltration data converging.

In linier system assumption and short time step,linier modeling was quite enough.

revisi - application of kalman filter for estimated elevation water

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