# Kalman filter

Kalman filter Kalrez [c.539]

Other chemometrics methods to improve caUbration have been advanced. The method of partial least squares has been usehil in multicomponent cahbration (48—51). In this approach the concentrations are related to latent variables in the block of observed instmment responses. Thus PLS regression can solve the colinearity problem and provide all of the advantages discussed earlier. Principal components analysis coupled with multiple regression, often called Principal Component Regression (PCR), is another cahbration approach that has been compared and contrasted to PLS (52—54). Cahbration problems can also be approached using the Kalman filter as discussed (43). [c.429]

The Kalman filter single variable estimation problem [c.285]

The Kalman filter is a eomplementary form of the Weiner filter. Let be a measurement of a parameter x and let its varianee Pa be given by [c.285]

The Kalman filter multivariable state estimation problem [c.286]

Equations (9.71)-(9.76) are illustrated in Figure 9.7 whieh shows the bloek diagram of the Kalman filter. [c.287]

A control system that contains a LQ Regulator/Tracking controller together with a Kalman filter state estimator as shown in Figure 9.8 is called a Linear Quadratic Gaussian (LQG) control system. [c.288]

The full LQG system, eomprising of the LQ optimal eontroller and Kalman filter was then eonstrueted. Figure 9.17 shows a set of moisture eontent measurements z ikT) together with the estimated moisture eontent x ikT). [c.299]

If the forward velocity of the ship is the state variable u, a best estimate of which is given by the Kalman filter, the gain scheduling controller can be expressed as [c.300]

The plant deseribed in Example 9.8 by equations (9.185) and (9.186) is to be eontrolled by a Linear Quadratie Gaussian (LQG) eontrol seheme that eonsists of a LQ Regulator eombined with the Kalman filter designed in Example 9.8. The [c.322]

This tutorial uses the MATLAB Control System Toolbox for linear quadratie regulator, linear quadratie estimator (Kalman filter) and linear quadratie Gaussian eontrol system design. The tutorial also employs the Robust Control Toolbox for multivariable robust eontrol system design. Problems in Chapter 9 are used as design examples. [c.408]

Continuous Linear Quadratic Estimator (Kalman Filter] [c.411]

Discrete Linear Quadratic Estimator (Kalman Filter) [c.411]

Rotary Kiln Incinerators. The rotary kiln has been used to incinerate a large variety of Hquid and soHd industrial wastes. Any Hquid capable of being atomized by steam or air can be incinerated, as well as heavy tars, sludges, pallets, and filter cakes. This abiUty to accept diverse feeds is the outstanding feature of the rotary kiln and, therefore, this type of incinerator is often selected by the chemical and waste treatment industries. [c.46]

The average dust loading in rotary kilns is 10% of the kiln feed or approximately 20 kg/t of lime, allowing for a ratio of limestone to lime of 2 on a weight basis. Primary collection of particulates is accompHshed with multiple cyclones that entrap about 85% of the dust loading. A secondary system is necessary to abate most of the remaining dust. Of the secondary systems in use, the baghouse is the predominant type, followed by the wet scmbber, electrostatic precipitator, and gravel bed filter (see Airpollution control methods). [c.172]

The white Hquor is separated from the calcium carbonate by decantation in a clarifier and is then available for a new cooking cycle. The underflow from the clarifier, which contains the calcium carbonate and is referred to as lime mud, is diluted with water and passed to a second clarifier known as the lime mud washer. The clarified weak white Hquor (weak wash) goes to storage and then enters the dissolving tank. The lime mud residue from the lime mud washer is passed to a rotary filter and subsequently to the lime kiln where calcium carbonate is converted back to calcium oxide, thus completing the lime cycle. [c.270]

LIME KILN PRECOAT FILTER ESTIMATION [c.491]

A lime kiln is a common piece of equipment used in the chemical process industry for decomposing calcium carbonate into calcium oxide and carbon dioxide. In the pulp and paper industry the slurry, which consists of a mixture of calcium carbonate, water and some inert materials, is filtered to remove a portion of the water. The filter that is employed is a rotary drum filter, commonly called the precoat filter. The fuel consumption in the kiln depends upon the amount of water entering the kiln. A useful calculation that is often made is aimed at determining the fuel savings when the mud solids to the kiln are increased incrementally. The calculation method outlined below is derived on the basis of one minute of operation, and using the mass balance diagram given in Figure 1. [c.491]

At the first eonferenee of the International Federation of Automatie Control (IFAC), Kalman (1960) introdueed the dual eoneept of eontrollability and observability. At the same time Kalman demonstrated that when the system dynamie equations are linear and the performanee eriterion is quadratie (LQ eontrol), then the mathematieal problem has an explieit solution whieh provides an optimal eontrol law. Also Kalman and Buey (1961) developed the idea of an optimal filter (Kalman filter) whieh, when eombined with an optimal eontroller, produeed linear-quadratie-Gaussian (LQG) eontrol. [c.3]

This work was extended by Kalman and Buey (1961) who designed a state estimation proeess based upon an optimal minimum varianee filter, generally referred to as a Kalman filter. [c.285]

The general form of the Kalman filter usually eontains a diserete model of the system together with a set of reeursive equations that eontinuously update the Kalman gain matrix K and the system eovarianee matrix P. [c.286]

The reeursive equations (9.74)-(9.76) that ealeulate the Kalman gain matrix and eovarianee matrix for a Kalman filter are similar to equations (9.29) and (9.30) that [c.287]

Kalman filter design If the three stages of the eovarianee matrix P are written as P(/c//c) = Pi P(/c + 1 jk) = P2 and P(/c + 1 //c + 1) = P3, then reeursive equations (9.74), (9.75) and (9.76) beeome [c.295]

The disturbanee and measurement noise is taken into aeeount by the Kalman filter. In the following example, undertaken by the author (1984), a non-linear simulation of a ship of length 161m and displaeement 17 000 tonnes was given a series of step ehanges in demanded rudder-angle at forward speeds of 2.572 m/s (5 knots), 5.145 m/s (10 knots) and 7.717 m/s (15 knots). At eaeh forward speed a linear model was eonstrueted and the Q and R matriees in an LQG implementation seleeted to return the elosed-loop eigenvalues baek to some desired value (Aekermann s formula eould not be used sinee y(t) and u(t) were veetor, not sealar quantities). [c.299]

The reverse-time process is shown in Figure 9.3. The discrete-time steady-state feedback matrix could also have been found using Iqrd, but this would not have generated the command vector v. The forward-time tracking process is shown in Figure 9.4 using Kf/cT) and vf/cT) to generate Uopif/cT) in equation (9.55). The script file kalfilc.m uses the MATLAB command Iqe to solve the continuous linear quadratic estimator, or Kalman filter problem. [c.410]

The script file kalfild.m solves, in forward-time, the discrete solution of the Kalman filter equations, using equations (9.74), (9.75) and (9.76) in a recursive process. The MATLAB command Iqed gives the same result. [c.411]

Discrete solution of Kalman filter equations %Init ialize [c.412]

Pearson, A.R., Sutton, R., Burns, R.S. and Robinson, P. (2000) A Kalman Filter Approach to Fault Tolerance Control in Autonomous Underwater Vehicles. In Proc. 14th International Conference on Systems Engineering, Coventry, 12-14 September, 2, pp. 458 63. [c.431]

Because the energy going iato the agitation converts mostly iato heat, the extmded cake may be quite hot, from 50 to 80°C ia some cases. High torque is needed to drive the agitators and most, if not all, of the energy saved by reduciag the cake thickness may go back iato the agitation. Little information exists about the actual power requirements but a favorable comparison has been made with a soHd bowl centrifuge operated with the same calcium carbonate slurry (35). It is iadisputable, however, that higher productivity is obtained per unit area of the filter surface than with conventional pressure filters, ie, the soHds dry cake yield varies from 20 to 1000 kg/m h for slurries such as pigments, calcium carbonate, magnesium hydroxide, and kaolin. Other materials handled by this filter iaclude dyestuffs, polymer slurries, clays, pharmaceuticals, and metal oxides. [c.412]

Tabular alumina also offers advantages over other materials as an aggregate in castables made from calcium aluminate cement as the binder and in phosphate-bonded monolithic furnace linings in all thermal processing industries. Other appHcations include their use in electrical insulators, electronic components, and kiln furniture. AppHcations other than refractories and high AI2O2 ceramics include molten metal filter media (116), ground filler for epoxy and polyester resins (see Eillers), inert supporting beds for adsorbents or catalysts, and heat exchange media, among others. [c.163]

Argillaceous, siliceous, and ferriferous raw mix components are added to the cmsher product. At the grinding mills, the constituents are fed into the mill separately, using weigh feeders or volumetric measurements. Ball mills are used for wet and dry processes to grind the material to a fineness such that only 15—30 wt % is retained on a 74 ]lni (200 mesh) sieve. In the wet process the raw materials are ground with about 30—40% water, producing a well-bomogenized mixture called slurry. Low concentrations of slurry thinners may be added, such as sodium carbonates, silicates, and phosphates, as well as lignosulfonates and modified petrochemicals. Filter presses or other devices remove water from slurries before feeding into the kiln. [c.292]

During the burning process, the high temperatures cause vaporization of alkahes, sulfur, and haUdes. These materials are carried by the combustion gases iato the cooler portions of the kiln system where they condense, or they may be carried out to the kiln dust collector, usually a fabric filter or electrostatic precipitator, together with partially calciaed feed and unprocessed raw feed. This kiln dust is reusable. However, ASTM specifications limit the total SO content of the finished cement to 2.3—4.5%, depending on the cement type and C A content. Similarly, an optional ASTM C150 specifications limits the total alkah content of the cement to 0.60%, expressed as equivalent Na20. Other potential and actual uses of dust iaclude fertilizer supplements (see Fertilizers), acid mine waste neutralization (see Wastes, industrial), boiler SO2 control, and soil stabilization (qv). [c.293]

FIG. 18-132 Sectional view of the Cuno Flo-Klean backwashing edge filter. Fluid pumped through the nozzle loosens solids from the filter surface and clears the filtering area. The pump draws filtered fluid from the filter discharge and returns it to the system through the nozzle. Thus, there is no loss of backwash fluid. (Cuno Division, AMF, Inc.) [c.1720]

See pages that mention the term

**Kalman filter**:

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Advanced control engineering (2001) -- [ c.3 , c.285 , c.287 ]