Classifications

• • G—PHYSICS
  • G05—CONTROLLING; REGULATING
  • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
  • G05D11/00—Control of flow ratio
  • G05D11/02—Controlling ratio of two or more flows of fluid or fluent material
  • G05D11/13—Controlling ratio of two or more flows of fluid or fluent material characterised by the use of electric means
  • G05D11/131—Controlling ratio of two or more flows of fluid or fluent material characterised by the use of electric means by measuring the values related to the quantity of the individual components
  • G05D11/132—Controlling ratio of two or more flows of fluid or fluent material characterised by the use of electric means by measuring the values related to the quantity of the individual components by controlling the flow of the individual components
• • B—PERFORMING OPERATIONS; TRANSPORTING
  • B01—PHYSICAL OR CHEMICAL PROCESSES OR APPARATUS IN GENERAL
  • B01F—MIXING, e.g. DISSOLVING, EMULSIFYING OR DISPERSING
  • B01F33/00—Other mixers; Mixing plants; Combinations of mixers
  • B01F33/80—Mixing plants; Combinations of mixers
  • B01F33/834—Mixing in several steps, e.g. successive steps
• • B—PERFORMING OPERATIONS; TRANSPORTING
  • B01—PHYSICAL OR CHEMICAL PROCESSES OR APPARATUS IN GENERAL
  • B01F—MIXING, e.g. DISSOLVING, EMULSIFYING OR DISPERSING
  • B01F35/00—Accessories for mixers; Auxiliary operations or auxiliary devices; Parts or details of general application
  • B01F35/20—Measuring; Control or regulation
  • B01F35/21—Measuring
  • B01F35/213—Measuring of the properties of the mixtures, e.g. temperature, density or colour
• • B—PERFORMING OPERATIONS; TRANSPORTING
  • B01—PHYSICAL OR CHEMICAL PROCESSES OR APPARATUS IN GENERAL
  • B01F—MIXING, e.g. DISSOLVING, EMULSIFYING OR DISPERSING
  • B01F35/00—Accessories for mixers; Auxiliary operations or auxiliary devices; Parts or details of general application
  • B01F35/20—Measuring; Control or regulation
  • B01F35/21—Measuring
  • B01F35/2132—Concentration, pH, pOH, p(ION) or oxygen-demand
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
  • G01N9/00—Investigating density or specific gravity of materials; Analysing materials by determining density or specific gravity
  • G01N9/36—Analysing materials by measuring the density or specific gravity, e.g. determining quantity of moisture
• • B—PERFORMING OPERATIONS; TRANSPORTING
  • B01—PHYSICAL OR CHEMICAL PROCESSES OR APPARATUS IN GENERAL
  • B01F—MIXING, e.g. DISSOLVING, EMULSIFYING OR DISPERSING
  • B01F33/00—Other mixers; Mixing plants; Combinations of mixers
  • B01F33/80—Mixing plants; Combinations of mixers
  • B01F33/81—Combinations of similar mixers, e.g. with rotary stirring devices in two or more receptacles

Definitions

• the present invention generally relates to process control, and more particularly to systems and methods of estimating the volumetric ratio of a material to the total materials in a mixing vessel.
• Control systems are currently being employed to control processes for mixing together multiple components in a mixing vessel.
• An example of such a process is mixing together dry cement and water to form a cement slurry for use in
• Well cementing is a process in which wells that penetrate
• subterranean formations are formed in the earth, allowing natural resources such as
• Well cementing is a process used
• a wellbore is drilled while a drilling fluid is circulated through the wellbore.
• a string of pipe e.g., casing
• the drilling fluid in the well bore is conditioned by circulating
• cementing operation is squeeze cementing whereby a cement slurry is forced under
• a Proportional-Integral- Derivative (PID) controller may be used to calculate the commanded input water flowrate based on the total commanded input flowrate and the commanded slurry density. It may also be used to calculate the output water flowrate based on the total measured output flowrate and the measured slurry density. Further, a PID controller may be used to calculate the commanded input cement flowrate based on the commanded total input flowrate and the commanded slurry density. Moreover, it may be used to calculate the output cement flowrate based on the total measured output flowrate and the measured slurry density.
• this type of control system has a major drawback in that the response of the water and cement control loops are time lagged. Thus, a change in the water flowrate usually is not observed and corrected for by the cement control loop for some time and vice versa. As a
• the output slurry density, or the output slurry density is ill-conditioned to be used as a control variable (Le., the value of the density of one component being mixed is very close to the value of the density of the other component being mixed in a two-
• Such disturbances include oscillations in the height of the fluid in the
• mixing vessel particularly when the mixing vessel is in motion such as in a ship-
• the dry cement may become plugged in the pipe being fed to the
• the fluid in the mixing vessel may contain unaccounted for air.
• the estimated volume of a material to total materials in a mixing vessel may be determined using a volumetric ratio observer comprising a feedback loop.
• the volumetric ratio observer advantageously provides for filtered, zero-lag estimations of the actual volumetric ratios within the mixing vessel in a manner that accounts for unwanted disturbances in the system.
• the materials being combined in the mixing vessel may be dry cement and water, and the slurry formed therein may be pumped down a. wellbore during a well cementing process. Knowing the relative volumes inside the mixing vessel at any time and thus the relative volumes of the cement and water being pumped downhole may be very useful.
• volumetric ratio observer may also be employed to estimate the volumetric ratios of the components in two or more mixing vessels in series that are
• the volumetric ratio observer desirably may be used in a control system of such a mixing process where the density of the slurry mixture is unavailable. It may also be employed to control the mixing process even if the densities of the materials being mixed are near the same value such that a . densitometer cannot clearly differentiate between them.
• the volumetric ratio desirably may be used in a control system of such a mixing process where the density of the slurry mixture is unavailable. It may also be employed to control the mixing process even if the densities of the materials being mixed are near the same value such that a . densitometer cannot clearly differentiate between them.
• the mixing process may be controlled volumetrically, providing for tighter control over the relative volumes of the materials in the mixing vessels.
• the process may be optimized such that the overall cost of the process is minimized.
• FIG. 1 depicts a mixing apparatus comprising two mixing vessels
• FIG. 2 is a state block diagram of an embodiment of a physical system and a flow modulator being used to volumetrically mix components in the
• FIG. 3 A is a state block diagram of an embodiment of a portion of a volumetric ratio observer for use with a single mixing vessel.
• FIG. 3B is a state block diagram of another embodiment of a portion of volumetric ratio observer for use with two mixing vessels.
• FIG. 4 is a state block diagram of an embodiment of a control system for controlling the mixing apparatus depicted in FIG. 1.
• FIG. 5 is a state block diagram of another embodiment of. a control system for controlling the mixing apparatus depicted in FIG. 1.
• FIG. 6 is a state block diagram of yet another embodiment of a
• control system for controlling the mixing apparatus depicted in FIG. 1.
• FIG. 7 is a state block diagram of yet another embodiment of a portion of a volumetric ratio observer for use with mixing three components
• FIG. 8 is a state block diagram of still another embodiment of a volumetric ratio observer . for use with mixing three, components utilizing a two-
• FIG. 9 shows how a process for mixing multiple components in a mixing
• apparatus comprising a single vessel or tank can be controlled using a volumetric ratio mixing
• FIG. 10 shows results obtained from systems according to Figures 2-9.
• FIG. 11 shows yet another embodiment, with a different implementation of the
• the physical system considered here is a mixing apparatus comprising two mixing vessels 10 and 12, e.g., tanks, separated, by a weir 14 as shown in FIG. 1. It is understood that weir 14 may be replaced by other forms of
• the mixing process may be carried out through the action of rotating paddles 16 and 18 in respective mixing vessels 10 and 12.
• Two different materials may be separately added to mixing vessel 10 through pipes 20 and 24.
• Valves 22 and 26 may be disposed in respective pipes 20 and 24 for controlling the flow of the materials into mixing vessel 10.
• the mixing vessel 10 Within mixing vessel 10, the two materials are mixed together using rotating paddle 16.
• the mixture formed in mixing vessel 10 may then flow over weir 14 into mixing vessel 12 where the mixing process continues with second rotating paddle 18.
• the mixture in mixing vessel 12 is finally pumped out of the mixing apparatus through an output pipe 28 in which a pump 30 is disposed.
• the mixing system depicted in FIG. 1 may reside on the ground, on an oil platform, or on a ship.
• water and dry cement are the same
• liquids other than water and dry additives other than cement could be
• the volumetric flowrates of the water and the dry cement supplied to mixing vessel 10 are represented in FIG. 1 as V w and V c> respectively.
• the mixing apparatus may be capable of mixing the dry cement and the water to a desired density at a desired volumetric flowrate as required for use in oil well cementing applications. Additional parameters shown in FIG. 1 include the volumetric slurry flowrate V 12 over the weir from mixing vessel 10 to mixing vessel 12, the slurry height hi in mixing vessel 10, the output slurry rate V s from mixing vessel 12, and the slurry height h 2 in mixing vessel 12.
• the approximate values for these parameters of the actual physical system are as follows:
• V 5 ranges from about 1 bbl/min (barrels per minute) to about 15 bbl/min;
• V w /V s ranges from about 03 to about 0.90; hi is approximately 4 ft. as defined by the weir height; h 2 is approximately controlled to 3.5 ft.; h] A 1 is approximately 220 gallons; and h 2 A 2 is approximately controlled to 175 gallons.
• the mixing apparatus may be designed to run at a V s of up to 100 bbl/min.
• AvVw + A v c - A2V12 + m D pn h] A 1 + p 12 HjAi (1)
• p w is the density of water
• p c is the dry cement density
• p n is the density of the slurry flowing over the weir
• Ai is the cross-sectional area of mixing vessel 10.
• the parameter rn D represents the sum of all disturbances accounting for unknown mass rate inputs into the system such as the input mass rate of air.
• Equation 1 assumes instantaneous mixing such that any change in the relative proportions of V w and V c is instantaneously realized in the resulting value of the slurry density in mixing vessel 10.
• simplification p l2 now represents the density of all the slurry in mixing vessel 10 at any given moment.
• the conservation of mass equation for mixing vessel 12 is given as follows:
• Equation 2 also assumes instantaneous mixing such that p s represents the density of all the slurry in mixing vessel 12 at any given moment.
• the physical system can also be modeled mathematically by volume conservation assuming that both the water and the cement added to the system are incompressible. This model is represented for mixing vessel 10 and
• V w + V C - V 12 + V 0 H 1 A 1 (3)
• V 12 - V 5 Ii 2 A 2 (4)
• V D in Equation 3 represents the "volumetric disturbance flowrate,” which is herein defined as the sum of the flowrates of inputs, e.g., air, into the. mixing process other than the primary materials being mixed.
• V 12 which represents the volumetric flowrate over the weir, is a non-linear function of the weir shape, fluid rheology and the height of fluid in mixing vessel 10. If the weir shape and the fluid rheology are assumed to be constant, V 12 is predominantly a function of hi as indicated by the following equation:
• V 12 FQx 1 ) (5)
• Equation 5 could also define the volumetric flow rate through other forms of channeling devices besides a weir.
• FIG. 2 depicts the Laplace frequency domain state block diagram of the physical system 34 modeled by Equations 1 through 5, which will be described in more detail later. The inputs of water and dry cement to the system are shown to
• valves 38 and 48 are the control point for both slurry
• valves 38 and 48 also represent
• valves 38 and 48 The positions of valves 38 and 48 directly
• the resulting input volumetric rate and input mass rate may be represented by the following
• V in V w + V c (6)
• fl n is the combined instantaneous density of both input water and dry cement.
• V in and rh in may be
• the desired input volumetric rate V in and the desired input mass rate m m can be
• V* V* + v! • • (9)
• V w and V c represent the desired commanded rates of water and dry cement to each valve, respectively.
• the parameters /> w and ⁇ c represent the predetermined estimated values of water density and dry cement density.
• Equations 14 and 15 verify that the volumetric input rate is completely independent
• a mixing system in which the input water rate V w into the first mixing vessel, the fluid height h 2 in the second mixing vessel, and the output slurry rate V 5 from the second mixing vessel are available for measurement may be controlled using a so-called volumetric ratio mixing control approach. That is, the mixing process may be controlled volumetrically, and the chosen control variables may be the overall total flowrate of the slurry through, the system and the percentage
• a Flow Modulator 32 is shown that incorporates Equations 6 through 13 by modulating from commanded volumetric flowrates to actual volumetric flow and mass rates through water and cement valves 38 and 48. . .
• the Flow Modulator 32 may send V w directly to water valve 38 via signal 36. Further, it may send the overall commanded input rate V in via signal 40 and the commanded input water rate V w via signal 42 to a summation block 44
• V w is subtracted from V i ⁇ to obtain the commanded input cement rate V c , which may then be sent to cement valve 48 via signal 46.
• the positions of valves 38 and 48 may be set according to those commanded input rates. [0030]
• the resulting water flowrate V w exiting water valve 38 and the resulting cement flowrate V c exiting cement valve 48 may be measured.
• the total input mass flowrate m in to the mixing process is the result of the summation (summation block 60) of the water mass flow rate V w (signal 50) multiplied by p w (gain element 52) and the cement mass flow rate V c (signal 56) multiplied by p c (gain element 58) as described in Equation 7.
• riii n may be sent to another summation block 67 to which the mass disturbance flowrate m D , the total mass flowrate out of the first mixing vessel,
• total mass flowrate within the first mixing vessel may be subtracted from the sum of
• total mass rate of change may then be sent via signal 72 to an Integral controller comprising gain element 74 for multiplying the total mass rate of change by 1/hiAj
• controller also comprises an integral element 76 for multiplying the total density rate
• controller may then feed p n back to summation block. 67 via signals 78 and 82.
• signal 78 On its way to summation block 67, signal 78 may pass through gain element 80 where it
• signal 80 may pass through gain element 84 where it is multiplied by Vi 2 to obtain the total mass fiowrate out of the first mixing vessel, i.e., over the weir.
• Integral controller may dynamically recompute /T 12 - After being sent to integral element 76, signal 72 further may be sent to gain element 86 where it
• mixing vessel (a measured value), indicated by signal 88, may be subtracted from
• the Integral controller may then be sent via signal 90 to an Integral controller comprising gain element 92 for multiplying the total mass rate of change by IZh 2 A 2 to obtain the total density rate of change in the first mixing vessel.
• the Integral controller also comprises an integral element 94 for determining the density of the slurry flowing out of the second mixing vessel, p s . The Integral controller may then
• signal 96 may pass through gain element 98 where it is multiplied by h 2 A 2 to
• Integral controller may dynamically recompute p s .
• valve 48 and the water flowrate V w exiting water valve 38 may be sent via signals 54
• V 1n and a total volumetric disturbance flowrate V D may be sent to summation block 100 via signals 65 and 102, respectively.
• the volumetric flowrate within the first mixing vessel may also be fed back to summation block 100 where it
• the volumetric mass rate of change may then be
• the Integral, controller also comprises an
• integral element 108 for determining the height of the mixture in the second mixing
• the Integral controller may then feed hi back to summation block 100
• signal 110 On its way to summation block 100, signal 110 may pass through gain element 112 where it is multiplied by F(Ia 1 ) to obtain the total volumetric flowrate out of the first mixing vessel Vi 2 . In this manner, the Integral controller, may dynamically recompute hj .
• signal 104 may be sent to a gain element 114 for multiplying hj by FQa 1 ) to determine Vj 2 before it is sent to yet another summation block 115.
• the total flowrate of the slurry exiting the second mixing vessel, V s is also sent via signal 116 to summation block 115 where it is subtracted from V 12 to obtain the total volumetric rate of change in the second mixing vessel.
• the output of summation block 115 is further sent to gain elements 120 and 122 for multiplying the total volumetric rate of change by 1/A 2 and 1/s, respectively, to thereby determine the height of the slurry in the second mixing vessel, h 2 .
• volumetric ratio of one material relative to the total materials in one of the mixing vessels may be determined using a Volumetric Ratio Observer. This observer is based on the same physical dynamics described above and may be derived in a way that does not include density parameters. That is, a single mixing
• the parameter ⁇ represents the sum of all disturbances accounting for unknown mass rate inputs into the system and is given as follows:
• ni D /J 1 (V D ) 1 + /? 2 (V D ) 2 + ... + /? N (V D ) N (18)
• V D represents the unknown volumetric flowrate disturbance of the Nth component.
• the total volumetric flowrate disturbance V D is given as the sum of all the component disturbances as follows:
• V D (V D ) 1 + (V D ) 2 + ... + (V D ) N (19)
• the density p out may be represented by the following equation:
• V T represents the volume of the Nth component currently in the mixing vessel.
• V ⁇ represents the total volume of the mixture in the mixing vessel.
• V 7 (VT) 1 + (V T ) 2 + ... + (V T ) N (21)
• volumetric ratio of the Nth component with respect to the overall volume of the mixture is riven as
• Equation 21 gives the relationship between all the component volumetric ratios as follows:
• VRO's Ratio Observers
• FIG. 3A and FIG. 3B respectively. Using the same notation from earlier,
• setpoint inputs for the VRO's represent the commanded rates to the actual physical system and are signified by the symbol (*).
• the VRO may be implemented using various arrangements of closed loops, as will be detailed later in particular embodiments of the Volumetric Mixing Control approach.
• the VRO may serve to decouple the effects of disturbances in the system.
• the VRO for the Nth component being fed to a single mixing vessel may include a summation block 55 for subtracting an estimated output fiowrate of the Nth component (V 0Ut ) N from the sum of a volumetric disturbance fiowrate of the Nth component, (V D ) N , and a commanded
• the (V 0Ut ) N may be fed to summation block 55 via signal 65
• the (V D ) N may be fed to summation block 55 via signal 51
• the output of summation block 55 may represent an estimated volumetric rate of change of the Nth component in the mixing vessel.
• the estimated volumetric rate of change of the Nth component may be fed to an Integral controller comprising an integral element 59 for computing the estimated volume of the Nth component in the mixing vessel.
• the Integral controller may also include a gain element 61 for multiplying the estimated volume of the Nth component in the mixing vessel by l/(the estimated volume of the total materials in the mixing vessel)
• the Integral controller dynamically recomputes (V out ) N , [0039] As illustrated in FIG. 3B,. the Volumetric Ratio Observer may be
• V 12 ) N is the estimated flowrate of the Nth component out of the first mixing vessel and into the second mixing vessel.
• the total estimated flowrate between the two mixing vessels, i.e., over the weir, may be represented by
• V 12 (V 12 ), + (V 12 ) 2 + ... + (V 12 ) N (25)
• the volumes of the mixture in the first mixing vessel and the second mixing vessel are given by V 1 and V 2 , respectively.
• the portion of the state block diagram depicted in FlG. 3B that dynamically recomputes (V 12 ) N using a first Integral controller is the same as the state block diagram shown in FIG. 3A with the exception that gain, element 61 multiplies by 1/V 1 and gain element 63 multiplies by V 12 .
• the (V 12 ) N computed by the first Integral controller may be sent to a summation block 67 via signal 79 where an estimated value of the output flowrate
• controller comprises an integral element 71 for determining the total volume of the
• Nth component in the second, mixing vessel, (V 2 ) N also comprises gain element
• VRO is not limited to one or two mixing vessels but may be used for any number of mixing vessels by the addition of an Integral controller for each additional mixing vessel. Further, control schemes like those shown in FIGS. 3A and 3B may be implemented for any component being mixed in the one or more mixing vessels. There is no limit to the number of components that may be mixed together using the control system described herein.
• HG. 4 illustrates one embodiment of the volumetric ratio mixing control scheme mentioned earlier.
• the process being controlled comprises mixing cement and water together in a mixing apparatus containing two mixing vessels separated by a weir as shown in FIG. 1.
• FIG. 4 depicts a control system 130 that includes two Height Observers 132 and 134, a State Feedback Controller 136, a
• the Flow Modulator 32 and the state block diagram of the physical system 34 that are depicted in FIG. 2 are
• the first Height Observer 132 depicted in FIG. 4 takes as input the measured height h 2 of fluid in the second mixing vessel, the measured output flowrate of the slurry V s exiting the second mixing vessel, and the overall
• This Height Observer 132 then estimates the fluid height in the second mixing vessel, which is used as feedback in State Feedback Controller 136. It further estimates the overall volumetric disturbance flowrate V D , which is used for disturbance input decoupling in How Regulator 138.
• h 2 may be fed from
• the estimated height of the fluid h 2 in the second mixing vessel may also be sent via signal 144 to summation block 146 where it is subtracted from h 2 to determine an estimation of a height error for the second mixing vessel.
• This estimation of height error may then be fed via signal 148 to a Proportional-Integral controller 152 comprising an integral element 154, an integral gain element 156 for multiplying it by a constant N io i, and a proportional gain element 150 for multiplying it by a constant N o i.
• the second mixing vessel may be set to remove the noise and oscillations of the second mixing vessel from the
• summation block 158 may then be summed at a summation block 158 to estimate the total volumetric disturbance flowrate V D .
• the V D may be sent via signal 160 to another summation block 166.
• both the V in and the V s as measured by a sensor may be fed to summation- block 166 via signals 162 and 164, respectively.
• the Y s may be subtracted from the sum of V in and V D to obtain the volumetric rate of change in the second mixing vessel.
• the output of summation block 166 may be sent to an Integral controller comprising a gain
• the Height Observer 132 may continue to dynamically recompute h 2 in this manner.
• the Weir Flow Observer 134 may be very similar to the Height Observer 132. That is, it may also include a summation block 178 to which h 2 is fed via signal 142 and h 2 is negatively fed via signal 176. The output of summation block 178, i.e., an estimation of a height error for the second mixing vessel, may then be fed via signal 148 to a Proportional-Integral controller 184 comprising an integral element 186, an integral gain element 188 for
• proportional gain element 182 may then be summed, at a summation block 190 to
• the V 12 may then be used to estimate the total output flowrate Vi 2 from the first mixing vessel. The V 12 may then be used to estimate the total output flowrate Vi 2 from the first mixing vessel. The V 12 may then be used to estimate the total output flowrate Vi 2 from the first mixing vessel. The V 12 may then be used to estimate the total output flowrate Vi 2 from the first mixing vessel. The V 12 may then be used to estimate the total output flowrate Vi 2 from the first mixing vessel. The V 12 may then be used
• summation block 166 the V 5 may be subtracted from the V 12 to obtain the volumetric rate of change in the second mixing vessel.
• the output of summation block 194 may be sent to an Integral controller comprising a gain element 198 where it is multiplied by l/(the estimated cross-sectional area of the second mixing vessel) to convert the volumetric rate of change to the rate of height change in the second mixing vessel.
• This rate of height change may be sent to an integral element 200 to compute h 2 .
• the Height Observer 134 may continue to dynamically recompute h 2 in this manner. Additional information related to height observers may be found in U.S. Patent Application Serial No. 11/029,072, entitled “Methods And Systems for Estimating a Nominal Height or Quantity of a Fluid in a Mixing Tank While Reducing Noise," filed on January 4, 2005, which is incorporated by reference herein in its entirety.
• a State Feedback Controller 136 may be implemented where h 2 is the state feedback.
• the h 2 determined by Height Observer 132 may be sent via signal 204 to a summation block 206 where it is subtracted from the commanded height of the fluid h 2 in the second mixing vessel, indicated by signal 202, to estimate the height error
• summation block 206 may be sent to a proportional gain element 210 via signal 216 where it is multiplied by the constant
• State Feedback Controller 136 computes a commanded output flowrate Vi 2 of the total
• This volumetric disturbance flowrate estimation may be negatively fed back
• V 12 may be fed back
• summation block 220 via signal 216.
• the output of summation block 220 may then be sent to a proportional gain element 224 where it may be multiplied by a constant K v before being sent to another summation block 230.
• the V D may be fed back to summation block 230 via signal 226, and V 12 may also be fed to summation block 230 via signal 228 such that V D is subtracted from the sum of the output of gain element 224 and
• the output of summation block 230 is the total commanded input flowrate V in to the mixing process, which may be fed to Flow Modulator 32 via signal 232. As described previously, Flow Modulator 32 may modulate from, the commanded
• the Volumetric Ratio Observer 140 shown in FIG. 4 may be implemented to estimate the ratio of water to total materials in the first mixing vessel in accordance with the following equation:
• the inputs to Volumetric Ratio Observer 140 may include the commanded input
• This disturbance may be used for disturbance
• a comparator 240 is employed, to determine the estimated volumetric disturbance flowrate of the water (V D ) W by comparing V w to V w , which are fed to comparator 240 via signals 236 and 238, respectively.
• the (V D ) W may then be fed to
• the output of summation block 266 may be fed via signal 268 to an Integral controller comprising an integral element 270 and a gain element 272 for multiplying it by 1/V 1 , thereby determining the estimated volumetric ratio (R ⁇ 2 ) w of the water to the total materials in the first mixing vessel.
• the Integral Controller further comprises another gain element 274 for multiplying (R 12 ) w by the total estimated output flowrate V 12 from the first
• the Volumetric Ratio Observer 140 may also determine the volumetric Ratio Observer 140 .
• volumetric disturbance flowrate of the cement (V D ) C through the use of another summation block 244 for subtracting the volumetric disturbance flowrate of the water (V D ) W from the total input volumetric disturbance flowrate V D determined by Height Observer 132,
• the (V D ) W may be fed from, the output of comparator 240 to summation block 244 via signal 242, and the V D may be fed to summation block
• V D volumetric disturbance flowrate of the cement (V D ) C may then be sent to yet another summation block 252 via signal 246. Further, a
• the output of summation block 252 may be fed. via signal 254 to an Integral controller comprising an integral element 256 ? a gain element 258 for multiplying it by l/Vj, and another gain element 260 for multiplying it by the total estimated output flowrate Vi 2 from the first mixing vessel.
• an Integral controller comprising an integral element 256 ? a gain element 258 for multiplying it by l/Vj, and another gain element 260 for multiplying it by the total estimated output flowrate Vi 2 from the first mixing vessel.
• the estimated volumetric rate of change of the cement in the first mixing vessel may be converted to the estimated output flowrate
• the cement (Vi 2 ) c may then be fed back to summation block 252 via signal 250.
• Integral controller continues to dynamically recompute the estimated rate (V I2 ) C in this manner.
• the estimated water ratio (&i 2 ) w in the first mixing vessel may be fed back and compared to the desired water ratio (Ri*) w in a Proportional controller within a lower portion of Flow Regulator 138. That is, the (&i 2 ) w may be fed via signal 278 from Volumetric Ratio Observer 140 to a comparator .279 of How Regulator. Further, the (R 12 ) w may be fed via signal 276 to comparator 279. The output of comparator 279 may then be fed via signal 280 to a proportional gain element 282 for multiplying it by K m before being sent to a summation block 288 of
• the estimated output flowrate of the water (V 12 ) w exiting me first mixing vessel also may be fed back to the Flow Regulator for decoupling purposes. That is, the (Vi 2 ) w may be fed via signal 286 to summation block 288.
• the estimated volumetric disturbance flowrate of the water (V D ) W may be fed to summation block 288.
• the (V D ) W rnay be subtracted from the summation of the output of gain element 282 and (Y 12 ) W5 thereby computing the commanded input flowrate of the water V w .
• the V w may be fed to
• volumetric Ratio Observer 140 with state feedback allows control system 130 to be fully enhanced.
• the VRO provides for filtered, zero-lag estimations of actual signals.
• FIG. 5 illustrates another embodiment of the volumetric ratio mixing control scheme in which the process being controlled comprises mixing cement and water together in a mixing apparatus containing two mixing vessels separated by a weir as shown in HG. 1.
• FIG. 5 depicts a control system 291 that. is the same as control system 130 of FIG.4 except for some changes in the Volumetric Ratio Observer, the State Feedback Controller, and the Flow Regulator.
• this embodiment extends the VRO in FIG. 4 from a one vessel implementation .to a two vessel implementation for estimating the ratio of water to total materials in the second mixing vessel rather than the first mixing vessel.
• This embodiment also provides for water ratio control within the State Feedback Controller.
• the estimated output flowrate of the water (Vi 2 ) w from the first mixing vessel may be further passed to another summation block 292.
• an estimated output flowrate of the water (V s ) w from the second mixing vessel may be subtracted from (V 12 )W to determine the volumetric rate of change in the second mixing vessel.
• the output of summation block 292 may then be sent via signal 294 to an Integral
• the Integral controller comprising an integral element 296 and a gain element 298 for multiplying it by 1/V 2 to determine the estimated volumetric ratio of the water to total materials R w in the second mixing vessel.
• the Integral controller may further include a gain element 300 for multiplying & w by the total output flowrate V s from the second mixing vessel, which may be measured, to determine the estimated total output flowrate (V s ) w of the water.
• the (V s ) w may be fed back to summation block 292 via signal 302, allowing it to be dynamically recomputed. .
• (Vi 2 ) c from the second mixing vessel may be further passed to another summation block 303.
• an estimated output flowrate of the cement (V s )c from the second mixing vessel may be subtracted from (Vi 2 ) c to determine the volumetric rate of change in the second mixing vessel.
• the output of summation block 303 may then be sent via signal 304 to an Integral controller comprising an integral element 306 and a gain element 308 for multiplying it by 1/V 2 to determine the estimated volumetric ratio of the cement to total materials R c in the second mixing vessel.
• the Integral controller may further include a gain element 310 for multiplying RV by the total output flowrate V 5 from the second mixing vessel, which
• V s ⁇ may be measured, to determine the estimated total output flowrate (V s ) c of the cement. Further, the (V s ) c may be fed back to summation block 303 via signal 312, allowing it to be dynamically recomputed.
• State Feedback Controller 137 may be different
• R w may be calculated using the following equation:
• the R w and the R w may be fed to comparator 318 via signals 314 and 316 respectively.
• the output of comparator 318 may be fed to a proportional gain element 322 for multiplying it by a constant K p and a gain element 324 for multiplying it by the desired total output flowrate V 12 from the first mixing vessel before being positively sent to a summation
• the R w may also pass through a gain element 328 for multiplying it by
• This desired output flowrate of the water may be positively fed forward to summation block 330 via signal 326 to decouple the effect of the water exiting the second mixing vessel.
• the output of State Feedback Controller 137 and the estimated flowrate of water (V ]2 ) w out of the first mixing vessel, as determined by Volumetric Ratio Observer 141, may be fed via respective signals 276 and 278 to a summation block 279 of Flow Regulator 139 where they may be compared.
• Regulator 193 is implemented in the same way as Flow Regulator 138 in FIG. 4 with the exception that the proportional control compares the estimated flowrate of
• the output of summation block 279 may be sent via signal 280 to a proportional gain element 282 for multiplying it by a constant K m before sending it to another summation block 288, where the estimated volumetric disturbance fiowrate of the water (V D ) W may be subtracted from it and from the estimated output fiowrate of the water (V 12 ) w from the first mixing vessel.
• the (V D ) W determined by Volumetric Ratio Observer 141 may be sent to summation block 288 via signal 284. Further, the estimated output
• a fiowrate of the water (V ]2 ) w from the first mixing vessel may be sent to summation block 288.
• the output of summation block 288 may be the commanded input water
• FIG. 6 depicts yet another embodiment of the volumetric ratio mixing control scheme in which the process being controlled comprises mixing cement and water together in a mixing apparatus containing two mixing vessels separated by a weir as shown in FIG. 1.
• FIG. 6 depicts a control system 331 that is similar to control system 130 of FIG. 4. Notably, control system 331 does not contain a Weir Flow Observer. Further, this embodiment extends the VRO in FIG. 4 from a one vessel implementation to a two vessel implementation for estimating the ratio of water to total materials in the second mixing vessel rather than the first mixing vessel. This two vessel VRO may also be used to estimate the total
• volumetric disturbance fiowrate by applying an internal PI controller to the fluid height in the second mixing vessel. Moreover, within the VRO the commanded
• a PI control loop may act directly on the water
• the water valve thus may be driven to produce the desired input water flowrate
• VRO may determine this disturbance by closing a loop on the estimated height of fluid in the second
• the estimated height of fluid h 2 in the second mixing vessel may be
• valve errors in both valves are
• control system 331 in FIG. 6 The differences between control system 331 in FIG. 6 and control system 130 in FIG. 4 are described in more ⁇ detail below.
• the volumetric disturbance flowrate of trie cement being fed to summation block 248 via signal 246 may be determined by first feeding the height of the fluid h 2 in the second mixing
• the PI controller may comprise an integral element 334, an integral gain element 336 for multiplying the height error by N io i, and a proportional gain element 340 for multiplying it by N 01 before sending it to summation block 342.
• summation block 342 is the estimated volumetric disturbance flowrate of the cement, which is equivalent to the estimated total volumetric disturbance flowrate V D as represented by signal 344. Also, no estimated volumetric disturbance flowrate of the water is fed to summation block 266 nor to summation
• elements 274 and 260 may be replaced by respective gain elements 275 and 261,
• the estimated output flowrate of the water (V 12 ) w from the first mixing vessel may be farther passed to another summation block 292.
• an estimated output flowrate of the water (V s ) w from the second mixing vessel may be subtracted from (Vi 2 ) w to determine the volumetric rate of change in the second mixing vessel.
• the output of summation block 292 may then be sent via signal 294 to an Integral controller comprising an integral
• the Integral controller may further include a gain element 301 for multiplying (n 2 ) w by l/h 2 and a gain element 300 for multiplying (fi 2 ) w by the measured total output flowrate V s
• the (V s ) w may be fed back to summation block 292 via signal 302, allowing it to be dynamically recomputed.
• volumetric Ratio Observer 140 is that the estimated output flowrate of the cement (Vi 2 ) c from the second mixing vessel may be further passed to another summation block 303. At summation block 303, an estimated output flowrate of the cement (V s ) c from, the second, mixing vessel may be subtracted from (Vi 2 ) c to determine the
• the Integral controller may further include a gain element 311 for multiplying by IZh 2 and a gain element 310 for multiplying (fi 2 ) c by the measured total output flowrate V s from
• the second mixing- vessel to determine the estimated total output flowrate (V s ) c of the water. Further, the (V s ) c may be fed back to summation block 303 via signal 312, allowing it to be dynamically recomputed.
• the (Ii 2 ) w and (fi 2 ) c may be fed to and added together at summation block 326 before being fed to comparator 330 via signal 328.
• the total estimated volumetric disturbance flowrate V 0 determined by Volumetric Ratio Observer 145 may be negatively fed to a summation block 230 of Flow Regulator 143, which does not contain a proportional controller for the volumetric flowrate exiting the first mixing vessel as in FIG. 4.
• V 0 may be subtracted from the commanded total output flowrate V 12 from the first mixing vessel, which may be fed to summation block 230 via signal
• the output of summation block 230 is the total commanded input
• FIG. 6 also depicts V in being fed via signal 162 from How Regulator
• the measured parameters include the input water flowrate V w into the first mixing vessel, the slurry density pyi in the first
• any of the embodiments discussed previously may be employed to control the system.
• one of the inherent problems with the mixing system depicted, in FIG. 1 is the introduction of air into the mixture. Air entrained in the mixture may cause the overall slurry volume in the mixing vessels to be larger than expected, resulting in an increased h 2 value. Additionally, air entrained in the mixture may cause the measured density of the mixture to be lower than expected. For most applications it is ideal to be able to mix the water and the cement to a density and. a volume that does not reflect the entrainment of air.
• the Volumetric Ratio Observer may be implemented to predict the ratio of not only the water and cement in the mixture but also the amount of air entrained therein. As such, the system can be controlled to mix exactly the desired proportions of water and cement.
• FIG. 7 illustrates an embodiment of the primary components of a two vessel Volumetric Ratio Observer 350 for modeling a system in which three components, i.e., water, cement, and air, are mixed through the system.
• the Volumetric Ratio Observer 350 includes control schemes 352, 354, and 356 for the water, the cement, and the air, respectively. Those control schemes are very similar
• 1/s by the estimated total output flowrate V 12 from the first mixing vessel is replaced by a gain element for multiplying 1/s by a. commanded total output fiowrate from the first mixing vessel V 12 .
• the commanded input water fiowrate V w and the measured input water fiowrate V w are also known, allowing the disturbance in water fiowrate to be calculated directly. That is, the V w and the V w may be fed via respective signals 364 and 366 to a comparator 368 for comparing the two and thus determining the estimated, volumetric disturbance fiowrate of the
• Disturbances due to the cement delivery and due to the entrained air may be provided from external observers controllers that may be implemented via hardware or software modules.
• the total mass disturbance fiowrate m D may be
• the (V D ) W computed by comparator 368 may be multiplied by the estimated density of water by passing it to a gain element 372 before sending it to another comparator 376 via signal 370.
• Gain element 372 determines the estimated mass flowrate of the water.
• the i ⁇ D is . also sent to comparator 376 via signal 374 where it may be compared to the estimated mass flowrate of the water to determine the estimated mass flowrate of the cement
• This estimated mass flowrate of the cement may be sent via signal 360 to gain element
• Both (V D ) W and (V D ) C may be fed to a summation block 384 via respective signals 380 and 382 where they may be subtracted from V D , which is sent to element 384 via signal 364, to determine (V D ) a .
• the disturbance fiowrates (V D ) W , (V D ) C , and (V D ) a for each component may then be sent to controllers via respective signals 358, 360, and 362 to implement respective control schemes 352, 354, and 356.
• the components may be separated and the densities of the water and cement mixture excluding entrained air for the first mixing vessel and the second mixing vessel may be calculated from estimated parameters within the VRO in accordance with the following equations:
• HG. 8 illustrates another embodiment of the primary components of
• volumetric Ratio Observer 386 for modeling a system in which water, cement, and air are mixed in a two-vessel mixing apparatus.
• the Volumetric Ratio Observer 386 includes control schemes 388, 390, and 392 for the water, the cement, and the air, respectively. Those control schemes are very similar to the control scheme shown in FIG. 3B except that the V 12 gain element may be replaced by a V 12 gain element.
• the disturbance in water flowrate may be calculated directly. That is, the V w and the V w may be fed via respective signals 400 and 402 to a comparator 404 for comparing the two and thus determining the estimated
• disturbances due to cement delivery and due to entrained air are provided from internal PI feedback loops on the slurry density in the first mixing vessel and the fluid height in the second mixing vessel as shown.
• the mass disturbance flowrate rh D may be calculated through a PI controller that compares the measured slurry density in the first mixing vessel to the estimated density calculated from the combined water, cement, and air mixture in the first mixing vessel. More specifically, the volumetric ratio of each component to the total materials in the first mixing vessel may be calculated by the PI controller of
• Those volumetric ratios may then be sent via respective signals 410, 412, and 414 to respective gain elements 416, 418, and 420 for
• estimated slurry density ⁇ n may be sent to a comparator 428 for calculating the
• the estimated mass flowrate of the cement thus may be the estimated mass flowrate of the cement.
• flowrate of the cement may be passed through gain element 434 where it may be
• the total volumetric disturbance flowrate V D may be calculated
• n 2 may be calculated by sending the volumes of water
• the total volume may then be sent to a gain element 444 for multiplying it by l/(the estimated cross-sectional area of the second mixing vessel) to determine h 2 before being sent to comparator 450.
• the comparator 450 may determine the difference between h 2 and n 2 , and that difference may be sent to a PI controller 452 via signal 451.
• the outputs of the integral portion and the proportional portion of PI controller 452 may then be
• Equations 28 and 29 may be implemented to estimate the mixture densities in the first and second mixing vessels due to water and cement but excluding entrained air.
• FIG. 9 depicts a control system 500 that includes a Flow Regulator 502, a Height Observers 506, and a Volumetric Ratio Observer 530.
• the Flow Regulator 502 includes a How Modulator 32, shown in detail in FIG. 2, a State Feedback Controller 510, and a model of a physical system 508 similar to the physical, system 34 shown in- FIG.- 2.
• the physical system 508 is different from physical system 34 of FIG. 2 in that it only models a single mixing vessel with the height and density of the mixture in. the single mixing vessel given as outputs. That is, the volumetric rate of change in the mixing vessel of physical system 508 is converted to the rate of change of height in the mixing vessel, which when integrated results in the height h of the slurry in the mixing vessel. Further, the mass rate of change in the mixing vessel of physical system 508 is converted to the rate of change of the density in the mixing vessel, which when integrated results in the density p of the slurry in the mixing vessel.
• the measured height h of the slurry in the mixing vessel as given by the model of physical system 508 may be sent, to Height Observer 506, which contains the same components as Height Observer 132 in FIG. 6.
• the Height Observer 506 may estimate the height h of the fluid in the mixing vessel and feed that to Flow Regulator 502.
• the measured height h may also be fed to Volumetric
• Ratio Observer 530 which is similar to the Volumetric Ratio Observer 145 shown in FIG. 6 except that it only contains one feedback loop for estimating the volumetric
• V s flowrate
• volumetric flowrate (V s ) c The Volumetric Ratio Observer 530 may estimate the total volumetric disturbance flowrate V 0 in the same manner as does Volumetric Ratio. Observer 145.. ..• . . .. •.., • ⁇ •
• Regulator. 502 its upper portion • includes a comparator 514 to which h may be sent via signal 510 and a commanded height h may be sent via signal 512.
• the comparator 514 may subtract h from h .
• the output of comparator 514 may then be sent to a proportional gain element 518 via signal 516 where it may be multiplied by a constant Ky before being sent to another comparator 524.
• ⁇ mixing vessel and V D as determined by Volumetric Ratio Observer 530 may be also be fed to comparator 524 via signals 520 and 522, respectively.
• ⁇ * may subtract V D from the sum of the output of gain element 518 and V s to determine the total commanded input flowrate V in to the mixing vessel, which may be fed to How Modulator 32 via signal 526.
• the lower portion of Flow Regulator 502 may include a comparator
• control schemes may be implemented by hardware or by software via a computerized system.
• a person of ordinary skill in the art. would know how to create and use such hardware or software to implement the control schemes.
• FIG. 1 The mixing apparatus shown in FIG. 1 was assembled and operated using the embodiment of the control scheme shown in FIG. 6.
• Various parameters of the mixing process were determined and plotted as a function of time in FIG. 10. More specifically, line 550, labeled as the slurry recirculation density, represents the change in the measured slurry density in the first vessel.
• Line 552, labeled as the Ve_ density represents the change in the density as given by the volumetric ratio observer with active disturbance decoupling.
• Line 554, labeled as the tub level represents the change in the height of the slurry in the second vessel.
• Line 556 labeled as the cement valve position, represents the change in the position of the valve for controlling the flowrate of the cement into the mixing apparatus.
• Line 55S labeled as h2_hat s represents the change in the estimated height of the slurry in the second vessel as determined by the height, observer, which filters the height sensor- without zero lag.
• Line 560 labeled as the water valve position, represents the change in the position of the valve for controlling the flowrate of the cement into the
• FIG. 11 shows yet another embodiment, with a different implementation of the
• .methods of determining an estimated volumetric ratio of a material to total materials in a mixing vessel comprise: summing a commanded input flowrate of the material and a volumetric disturbance flowrate of the material being fed to the mixing vessel; estimating the output flowrate of the material exiting the mixing vessel; negatively feeding back the estimated output flowrate of the material to obtain an estimated volumetric rate of change of the material in the mixing vessel; and integrating the estimated volumetric rate of change of the material to compute the estimated volumetric ratio of the material to the total materials in the mixing vessel.
• methods of determining an estimated volumetric ratio of a material to total materials in a second mixing vessel that is partially separated from a first mixing vessel comprise: summing a commanded input flowrate of the material and a volumetric disturbance flowrate of the material being fed to the first mixing vessel; estimating an output flowrate of the material exiting the first mixing vessel; negatively feeding back the estimated output flowrate of the material to obtain an estimated volumetric rate of change of the material in the first mixing vessel; integrating the estimated volumetric rate of change of the material in the first mixing vessel to dynamically recompute the estimated output flowrate of the material exiting the first mixing vessel; estimating an output flowrate of the ' material exiting the second mixing vessel; negatively feeding back the estimated output flowrate of the material exiting the second mixing vessel and summing it with the estimated output flowrate of the material exiting the first mixing vessel, thereby obtaining an estimation of a volumetric rate of change of the material in the second mixing vessel; and integrating the estimated volumetric rate of change of the material in the second mixing
• methods of determining an estimated volumetric ratio of a second material to total materials in a first mixing vessel that is partially separated from a second mixing vessel comprise: measuring a height of the total materials in the second mixing vessel; comparing the height of the total materials in the second mixing vessel to a summation of an estimated height of a first material in the second mixing vessel and an estimated height of the second material in the second mixing vessel to obtain an estimation of a height error for the second mixing vessel; feeding the estimation of the height error to a controller to
• systems for determining an estimated volumetric ratio of a material to total materials in a mixing vessel are also possible.
• a summation block for determining an estimated volumetric rate of change of the material in the mixing vessel; an integration element for determining an estimated volume of the material in the mixing vessel based on the estimated volumetric rate of change of the material in the mixing vessel; a first gain element for converting the estimated volume of the material in the mixing vessel to the estimated volumetric ratio of the material to the total materials; and. a second gain element for converting the estimated volumetric ratio of the material to the total materials to the output flowrate of the material from the mixing vessel.
• systems for determining an estimated volumetric ratio of a material to total materials in a second mixing vessel that is
• volume of the material in the first mixing vessel a first gain element for converting the estimated volume of the material in the first mixing vessel to the estimated volumetric ratio of the material to the total materials in the first mixing vessel; a ⁇ second gain element for converting the estimated. volumetric ratio of the material to the total materials in the first mixing vessel to the output flowrate of.
• a second summation block for determining an estimated volumetric rate of change of the material in the second mixing vessel based on the output flowrate of the material from the first mixing vessel; a second integration element for integrating the estimated volumetric rate of change of the material in the second mixing vessel to determine the estimated volume of the material in the second mixing vessel; a third gain element for converting the estimated volume of the material in the second mixing vessel to the estimated volumetric ratio of the material to the total materials in the second mixing vessel; and a fourth gain element for converting the estimated volumetric ratio of the material to the total materials in the second mixing vessel to the output flowrate of the material from the second mixing vessel.
• systems for determining an estimated volumetric ratio of a second material to total materials in a first mixing vessel that is partially separated from a second mixing vessel comprise: a sensor for measuring a height of the total materials in the second mixing vessel; a first summation block for determining an estimation of a height error for the second mixing vessel by
• methods of controlling a volumetric ratio of a material to total materials in a mixing vessel comprise: estimating the volumetric ratio of the material to the total materials in the mixing vessel and an output fiowrate of the material from the mixing vessel using a volumetric ratio observer; dynamically recomputing the commanded input fiowrate of the material based on outputs of the volumetric ratio observer using a flow regulator; and adjusting an input valve of the material based on the commanded input fiowrate of the material using a flow modulator.
• the mixing vessel comprises a first mixing vessel partially separated from a second mixing vessel.
• a height observer may be used to estimate the height of the total materials in the second mixing vessel
• the volumetric ratio observer may be used to estimate the volumetric ratio of the material to the total materials in the first mixing vessel and an output flowrate of the material from the first mixing vessel
• methods of controlling a volumetric ratio of a material to total materials in a first mixing vessel that is partially separated from a second mixing vessel comprise: estimating the volumetric ratio of the material to the total materials in the second mixing vessel, an output flowrate of the material from the first mixing vessel, and a volumetric disturbance flowrate of the material using a volumetric ratio observer having the following inputs: a commanded input flowrate of the material and a measured input flowrate of the material; computing a commanded output flowrate of the material from the first mixing vessel using a state feedback controller having the following inputs: a commanded volumetric ratio of the material to the total materials in the second mixing vessel and the estimated volumetric ratio of the material to the total materials
• methods of controlling a volumetric ratio of a material ' to total materials in a first mixing vessel that is partially separated from, a second mixing vessel comprise: estimating a total volumetric disturbance flowrate, the volumetric ratio of the material to the total materials in the first mixing vessel, and an output flowrate of the material from the first mixing vessel using a volumetric ratio observer having the following inputs: a measured height of the total materials in the second mixing vessel; a commanded input flowrate of the material; and a commanded input flowrate of a second material that is also being fed to the first mixing vessel; dynamically recomputing the commanded input flowrate of the material using a flow regulator having the following inputs: a commanded volumetric ratio of the material to the total materials in the first mixing vessel; an estimated volumetric ratio of the material to the total materials in the first mixing- vessel; and the estimated
• systems for controlling a volumetric ratio of a material to total materials in a mixing vessel comprise: a volumetric ratio observer for estimating the volumetric ratio of the material to the total materials in the mixing vessel and an output flowrate of the material from the mixing vessel; a flow regulator coupled to the volumetric ratio observer for dynamically recomputing a commanded input flowrate of the material based on outputs of the volumetric ratio observer; and a flow modulator coupled to the flow regulator for adjusting an input valve of the material based on the commanded input flowrate of the material.
• the mixing vessel comprises a first mixing vessel partially separated from a second mixing vessel.
• a height observer may be used to estimate the height of the total materials in the second mixing vessel, and the volumetric ratio observer may be capable of estimating the volumetric ratio of the material to the total materials in the first mixing vessel and an output flowrate of the material from the first mixing vessel.
• systems for controlling a volumetric ratio of a material to total materials in a first mixing vessel that is partially separated from a second mixing vessel comprise: a volumetric ratio observer for estimating the volumetric ratio of the material to the total materials in the second mixing vessel, an output flowrate of the material from the first mixing vessel, and a volumetric disturbance flowrate of the material, the volumetric ratio observer having the following inputs: an estimated total volumetric disturbance flowrate and a commanded input flowrate of the material; a state feedback controller for computing a commanded output flowrate of the material from the first mixing vessel, the state
• a flow regulator coupled to the state feedback controller and to the volumetric ratio observer for dynamically recomputing the commanded input fiowrate of the material, the flow regulator having the following inputs: the estimated volumetric disturbance flowrate of the material and the estimated output flowrate of the material from the first mixing vessel; and a flow modulator coupled to the flow regulator for adjusting an input valve of the material based on the commanded input flowrate of
• vessel comprise: a volumetric ratio observer for estimating a total volumetric disturbance flowrate,
• a flow regulator coupled to the volumetric ratio
• flow modulator coupled to the flow regulator for adjusting an input valve of the material based on
• the present application also discloses A system comprising: multiple open loop volumetric estimators for multiple respective components; and a closed loop feedback block which uses at least one physical measurement of mixed product and which is combined with said open loop estimators to provide a closed loop system.

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