# Патент USA US3088673

код для вставкиMay 7, 1963 M. W. OGLESBY, JR., ET AL 3,088,664 METHOD OF AND APPARATUS FOR PROCESS DEAD TIME SIMULATION Filed March 15, 1961 ‘an I v u! w E ISL, _’ gm %M4/7"M ATZORNEVS Jnited States Patent O?hce 3,088,664 Patented May 7, 1963 1 2 3,088,664 time. Further, we have discovered a method of and apparatus for simulating a long dead time in a process METHOD OF AND APPARATUS FOR PROCES§ DEAD TIME SIMULATION Minor W. Oglesby, Jr., and Roy T. Brashear, Bartlesville, Okla, assignors to Phillips Petroleum Company, a cor poration of Delaware Filed Mar. 13, 1961, Ser. No. 95,089 6 Claims. (Cl. 235-61) control system with said simulated dead time responding as a pure dead time at higher frequencies. FIGURE 1 is a diagrammatic representation of the inventive pneumatic circuit for a simulated dead time of a second order approximation. FIGURE 2 is a portion of the diagrammatic pneumatic circuit of FIGURE 1. FIGURE 3 is another portion of the diagrammatic cir This invention relates to a method of and apparatus 10 cuit of FIGURE 1. for simulating process dead time. In one speci?c aspect, Referring to FIGURE 1, there is illustrated a conduit this invention relates to a method of and apparatus for pneumatically simulating process dead time. Dead time in a process can be de?ned as the time means 10 for transmitting a pressure P1 to a conventional pneumatic force balance computing relay 11, such as a elapsing between the initiation of a change in the process 15 Foxboro M58-1 computing relay illustrated in bulletin 13-19 distributed by Foxboro. The relay employed must and the detection of the effect of the change upon the be capable of solving the equation, process. In some instances, a process or a part of a process can X (Output) =g (A-C) be characterized dynamically as a pure dead time. A where A and C are variables and g is the adjustable gain pure dead time process is one which will pass all input of the relay. A conduit means 12 transmits a pressure P2 from computing relay 11 to a ?ow restriction means an amount equal to the dead time. Pure dead time 13 having a resistance R1. Conduit means 14 transmits processes or processes with long dead times as compared a reduced pressure from restriction means 13 to a capac with their largest time constants are difficult to control with the conventional three~mode controller. In order 25 itor 15 having a capacitance C1. A restriction means and a capacitor connected as illustrated produces a ?rst order for a process control loop containing dead time to be lag. A conduit means 16 transmits a pneumatic pres stable, the controller gain and reset action must be de sure from capacitor 15 to a conventional 1:1 repeating creased from those values that could be used if the dead relay 17. As hereinafter noted, under speci?ed condi time was not present. This results in large deviations tions repeating relay 17 can be removed from the pneu of the control variable from the set point and longer signals unattenuated in amplitude but delayed in time by recovery time. Procedures exist for compensating for dead time in process control, but to employ these procedures it is matic circuit. A conduit means 18 transmits a pneu matic pressure P3 from repeating relay 17 to a restriction means 19 having a resistance R2. Measuring the pres necessary to simulate the dead time in the process. The sure drop across restriction means 13 and 19, and divid time models, a device dynamically equivalent to the con trol system which is being analyzed, are not available for through each said restriction means is the method where di?iculty with this approach is that good reliable dead 35 ing each said pressure drop by the quantity of ?ow plant operations. by values for R1 and R2 are obtained. A pnuematic pressure P3 is transmitted from repeating relay 17 via conduit means 18 and 25 to a conventional force balance When all variations or frequencies of a controlling variable are relayed, merely delaying the passage of said 40 computing relay 23. A reduced value of penumatic pressure P3 is trans frequencies, said delay then is identi?ed as pure dead mitted from restriction means 19 via conduit means 20 time. With the unavailability of reliable and inexpen to a capacitor 21 having a capacitance C2. Conduit sive dead time models, it is necessary to obtain an eifec means 22 transmits a pneumatic pressure R, from capac tive approximation of pure dead time for use in process 45 itor 21 to a conventional pneumatic force balance com— control. puting relay 23 such as a Foxboro M58~1 computing re The prior art discloses several methods of obtaining a lay. The computing relay employed must be capable of perfect dead time model such as employing an electro magnetic delay, a magnetic tape, magnetic drums or solving the equation X (Output) =g (A—-C)+B, where A, B, and C are variables and g is the adjustable gain discs, punch tape, etc. However, these are all very eX pensive and are not commercially available or adaptable 50 of the relay. A conduit means 24 transmits an output to plant operation. pressure F5 from computing relay 23. A pneumatic pres Accordingly, an object of this invention is to provide an improved method and apparatus for simulating proc sure P4 is transmitted via conduits 22 and 27 from capac itor 21 to said conventional force balance computing re lay 11. A pneumatic pressure P1 is transmitted via con Another object of this invention is to provide an im 55 duit means 26 to said conventional force balance com ess dead time. proved method of and apparatus for pneumatically simu puting relay 23. lating a second order dead time approximation. It is well known in the art that the transfer function Other objects, advantages, and features of our inven for a second order dead time approximation is of the tion will be readily apparent to those skilled in the art form: 60 from the above description and the appended claims. A process control system based on approximate dead time is limited in the frequencies it can relay without alteration. The phase shift of an approximate dead where T is the dead time and S is the Laplace operator. time operation will be the same as for a pure dead time A second order dead time will perform as a pure dead operation up to a maximum frequency and then will be 65 time up to a frequency where: gin to deviate. By increasing the order of the approxi W:1.7/T mation, the maximum frequency at which the phase shift of an approximate dead time operation and a pure dead W is radians per minute and T is the dead time in min time operation will be the same is increased. Broadly, we have discovered a method of and ap 70 utes. In the derivation of the transfer function of the pneu~ paratus for simulating a second order dead time approxi matic circuit of FIGURE 1, it is noted that the general mation for a process control system having a long dead 3,088,664 35 form of the equation expressing the second order dead time approximation is: where T is the dead time being simulated. For any desired value of dead time, T1, one of the four parameters (T1, T2, g1 or g2), can be assumed. The other three parameters can then be determined by the above equation. Input _(T»S')2+6TS+l2 By dividing the numerator by the denominator the follow ing equation is obtained: 7 Output__ Input * __E!: T 2 S 6_S By employing the disclosed inventive pnuematic circuit simulating a second order dead time approximation in series with a ?rst order pneumatic dead time approxima 1_2 tion circuit and/or other pneumatic second order dead time approximation circuits, higher order dead time ap~ Referring to FIGURE 2, there is illustrated a portion of FIGURE 1. The equation that relay 11 solves can proximations can be simulated. be written as: An advantage of the inventive pneumatic circuit em 15 ployed to simulate a second order dead time over an electronic circuit employed to simulate a second order where the subscript (S) denotes the Laplace form and dead time is the simplicity and low cost of the pneumatic P2(s>=g1(P1<s)—P/.(s)) g1 is the gain in relay 11. The 121 relay 17 is used for isolation purposes only. Having relay 17 in this circuit circuit. Electronic circuits employed to simulate second and higher order dead time lags are extremely complex. prevents the loading of one penumatic RC by another. Relay 17 can be removed from the pneumatic circuit in Also, electronic circuits are not as compatible with pres ent plant control systems as the pneumatic circuit, since those special instances where the capacitance C1 is rel atively large when compared to the Capacitance C2. In most plant control systems are pneumatic. As a result, an electronic circuit requires a power supply and EMF to pneumatic transducers in addition to the ‘basic circuit. this manner, the loading e?ect previously noted can be prevented. 25 This increases the complexity and cost of the electronic From FIGURE 2 it can be seen that: dead time approximation and reduces its reliability. Although an electronic circuit can be employed to simulate a second order dead time approximation, it is not economically feasible to utilize the electronic circuit 30 to simulate a relatively long dead time. For example, the capacitance of the electronic circuit is very limited for practical purposes while the capacitance of the pneumatic circuit can be readily expanded. As previously noted, where S is the Laplace operator, time constant T1 equals RlCl, and time constant T2 equals RZCZ. the results ‘obtained when an electronic circuit is em Substituting the values for P2, P3 and P4, obtained 35 ployed to simulate a relatively long dead time approxima tion are not as reliable and the equipment required is far above in the equation for relay 11, there is obtained: more expensive when compared to a penumatic circuit. As will be evident to those skilled in the art, various modifications of this invention can be made, or followed, 40 in the light of the foregoing disclosure and discussion without departing from the spirit or scope thereof. We claim: 1. A method of pneumatically simulating a second order dead time approximation which comprises passing Referring to FIGURE 3, the equation that relay 23 a ?rst pneumatic pressure P1 representative of a meas solves can be written as: ured condition toa ?rst pneumatic computing zone and a second computing zone, passing a second pneumatic pressure P2 hereinafter ‘described to said ?rst computing zone, said ?rst computing zone solving the equation Pats)=92(P4<s)—Pa(s>)-l-P1<s) where g2 is the gain of relay 23. Substituting previously obtained values of P3 and P4 into the above equation, there is obtained the overall transfer function P5/P1 of the pneumatic circuit of FIGURE 1. where g1 is the adjustable gain of said ?rst computing zone, passing a third pneumatic pressure P3 from said ?rst computing zone and through a ?rst pressure reduc~ 55 ing zone having a resistance R1 to a ?rst storage zone having a capacitance C1, passing a pressure P4 from said ?rst storage zone to a second pressure reducing zone hav ing a resistance R2 and to said second pneumatic com puting zone, passing a pressure from said second pressure reducing zone to a second storage zone having a capaci tance C2, passing said second pneumatic pressure P2 from 82+ T1112 T1 T2 said second storage zone to said ?rst and second com 1 puting zones, said second computing zone solving the equation Comparing the above equation with the conventional equation written for a second order dead time approxi P5=g2(P2-P4) +131 mation establishes that the two equations are of the same form. If T1, T2, g1, g2 are adjusted so that the following where g2 is the adjustable gain of said second computing zone, and passing a ?fth output pneumatic pressure P5 equalities are satis?ed, then the pneumatic circuit shown from said second computing zone in response to said in FIGURE 1 will provide a second order dead time ap proximation ?rst input pressure P1 representative of said ?rst pressure 70 P1 with a dead time of the second order. 2. The method of claim 1 wherein the pneumatic cir cuit is adjusted so that 9192 75 R101 3,088,664. 5 6 fecting an adjustable ?rst order lag, a third conduit means communicating between said ?rst means of pneumatical ly effecting a ?rst order lag and a second means of pneu matically effecting an adjustable ?rst order lag, a fourth conduit means communicating between said second means of pneumatically effecting a ?rst order lag and a where T is the dead time being simulated. second pneumatic computing means, said second pneu matic computing means capable of solving the equation 3. A method of pneumatically simulating a second order dead time approximation which comprises passing a ?rst pneumatic pressure P1 representative of a meas 10 ured condition to a ?rst pneumatic computing zone and where A, B and C are variables and g2 is the adjustable a second computing zone, passing a second pneumatic gain of said second pneumatic computing means, a ?fth pressure P2 hereinafter described to said ?rst computing conduit means communicating between said third con zone, said ?rst computing zone solving the equation duit means and said second pneumatic computing means, 15 a sixth conduit means communicating between said fourth conduit means and said ?rst pneumatic comput Where g1 is the adjustable gain of said ?rst computing ing means, a seventh conduit means communicating be zone, passing a third pneumatic pressure P3 from said tween said ?rst conduit means and said second pneumatic ?rst computing zone and through a ?rst pressure reduc computing means, and an eighth conduit outlet means ing zone having a resistance R1 to a ?rst storage zone communicating with said second pneumatic computing having a capacitance C1, passing a pressure R, from said 20 ?rst storage zone and through a lz'l relay zone to a sec sure from said second pressure reducing zone to a second storage zone having a capacitance C2, passing said sec ond pneumatic pressure P2 from said second storage zone means. 6. Apparatus comprising a ?rst conduit means com ond pressure reducing zone having a resistance R2 and to said second pneumatic computing zone, passing a pres municating with a ?rst pneumatic computing means, said ?rst pneumatic computing means capable of solving the 25 equation where A and C are variables and g1 is the adjustable gain of said ?rst pneumatic computing means, a second conduit means communicating between said ?rst pneu 30 matic computing means and a ?rst means of pneumati where g2 is the adjustable gain of said second computing cally effecting an adjustable ?rst order lag, a third con zone, and passing an output pneumatic pressure P5 from duit means communicating between said ?rst means of said second computing zone in response to said input ?rst pneumatically effecting an adjustable ?rst order lag and pressure P1 representative of said ?rst pressure P1 with a pneumatic 1:1 relay means, a fourth conduit means to said ?rst and second computing zone, said second com puting zone solving the equation 35 a dead time of the second order. communicating between said pneumatic 1:1 relay means 4. The method of claim 3 wherein the pneumatic cir and a second means of pneumatically effecting an ad cuit is adjusted so that justable ?rst order lag, a ?fth conduit means communi cating between said second means of pneumatically ef fecting an adjustable ?rst order lag and a second pneu matic computing means, said second pneumatic comput ing means capable of solving the equation g1+1 _1_2 (R1C1)(RzC2)_T2 where T is the dead time being simulated. 5. Apparatus comprising a ?rst conduit means com municating with a ?rst pneumatic computing means, said 45 where A, B and C are variables and g2 is the adjustable gain of said second pneumatic computing means, a sixth conduit means communicating between said fourth con duit means and said second pneumatic computing means, a seventh conduit means communicating between said ?fth conduit means and said ?rst pneumatic computing ?rst pneumatic computing means capable of solving the 50 means, an eighth conduit means communicating between equation X(Output) =g1(A-.C) said ?rst conduit means and said second pneumatic com puting means, and a ninth outlet conduit means com municating with said second pneumatic computing where A and C are variables and g1 is the adjustable gain of said ?rst pneumatic computing means, a second con 55 means. duit means communicating between said ?rst pneumatic computing means and a ?rst means of pneumatically ef No references cited.

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