HD1963MM2SI

CONTROLLED EXPENDITURE

of

SECONDARY INJECTANT FLUID

by

D. W. Landau

20 September 1963

Pub. No. 550-A-83

New 10/63

Contents

		Title	page
I.		Secondary Injection Control	3
	A.	Definition of Secondary Injection	3
	B.	The Problem Involved With Secondary Injection	4
	C.	Why a Dump System Was Needed to Solve the Problem.	5
II.		Various Dump Systems and the One Finally Chosen by Autonetics	5
	A	Dump System Comparisons	5
	B	Basic Types of Dump Systems	6
	C	The Dump System Chosen by Autonetics	9
III		Dump System Design Problems and Their Solution	10
	A	Modifying the Basic Control System	10
	B	Dual Feedback Loop Circuit Description	11
IV		Dump System Design Error Analysis	14
	A	The Root Sum Square Method of Error Combination	14
	B	Error Equations	14
	C	Total Error Tabulation	17
	D	Evaluation of Systems when Installed	17
	E	Summation	18

Illustrations

Fig	Title	page
1	The Secondary Injection Process	3
2	Injector Location for Secondary Injection (View Looking Into Nozzle Exit Plane)	3
3	Thrust Alignment Correction Angle	4
4	Injectant Flow us Time	4
5	"Good" Vehicle and "Poor" Vehicle Flight Performance	5
6	Relationship of Dump Error to Weight or Range	5
7	Cost per Pound vs Time	6
8	Method of Dump Control	7
9	Possible Flow Meter Systems	8
10	Flow per Injector us Time	8
11	Total Injectant Consumption us Time	9
12	Injectant Control and Feedback Loops (Inset: Typical Amplifier Module)	10
13	Flow per Injector us Time	11
14	Region of Flow Registered by Each Feedback Leg	11
15	Servo Injector Assembly	12
16	Secondary Injectant Hardware and Location	12
17	Checkout Feedback Circuit Used for Part of Dump Monitor	13
18	Freon Utilization Monitor and Associated Hardware	13
19	Computer Dump Monitor and Command Functions	14
20	Definition of Injector Error as a Function of Position	16
21	Flow vs Volts Near Closed Position	16

Tables

Table	Title	page
1	Comparison of Dump Systems With Respect to a Perfect Dump System	6
2	Extremes of Flow Meter Range	8
3	Extremes of Flow Distribution Between Injectors Where Any Combination May Exist for 90 % of Total Usage	9
4	Total Dump System Relative Error	17

I. SECONDARY INJECTION CONTROL

A. DEFINITION OF SECONDARY INJECTION

Secondary injection attitude control is the process of injecting a control fluid into a thrust nozzle so that a buildup of pressure occurs on one side of the nozzle; i.e., the net pressure becomes greater on one side of the nozzle than on the opposite side (see Figure 1). This produces a force imbalance which cause s a turning moment with respect to the vehicle's center of gravity. By changing either the rate and/or the location of the jnjection, the vehicle turning moment can be regulated (Figure 2).

Figure 1 The Secondary Injection Process

Figure 2. Injector Location for Secondary Injection

(View Looking Into Nozzle Exit Plane)

For flight control applications, secondary injection has a basic appeal; however, it also has its Achilles' heel. A control system which employs a tilting nozzle corrects for thrust offset, bias misalignment, etc, by expending energy only once to realign the nozzle. The secondary injection process requires that this energy be continually expended during the entire duty cycle. It follows then that a well-aligned vehicle is the most desirable. Or is it ?

B. THE PROBLEM INVOLVED WITH SECONDARY INJECTION

Vehicle control by secondary injection, however, poses a problem wherein the "best" vehicle actually performs the poorest. The poor vehicle is defined as one whose aerodynamic or thrust alignment diverges from the vehicle neutral line of thrust (see Figure 3); i.e., its thrust vector does not pass through the combined effective center of gravity (CG) and center of pressure (CP). When the thrust vector is offset, and while there is primary thrust, the injectant must be consumed continually to correct for this misalignment.

Figure 3. Thrust Alignment Correction Angle

The sizing of the injectant quantity is based on the volume of fluid required to handle the launch misalignment, desired change s in vehicle attitude, and maximum thrust misalignment. It is interesting to note that control activity does not necessarily cost injectant fluid. Figure 4 illustrates this point. The result is that no fluid is required for control activity so long as the average quantity consumed does not exceed that required to overcome the thrust offset. Because this is true in most designs, one can generalize by saying that aside from exceptional activity periods such as staging, pitch-over, etc, the thrust offset magnitude determines the tankage quantity needed.

Figure 4. Injectant Flow us Time

The "good" vehicle is defined as one whose design and fabrication is nearly perfect and does not require continuous injection to correct alignment. After performing a mission consisting of the ordinary vehicle maneuver vs, the "good" vehicle will retain a large percent of the injectant on board. This is ironic because the "good" vehicle carries extra weight throughout the mission (Figure 5). Conversely, the "poor" vehicle consumes its injectant and will travel farther or carry more weight for the same distance,

Figure 5 "Good" Vehicle and "Poor" Vehicle Flight Performance

C. WHY A DUMP SYSTEM WAS NEEDED TO SOLVE THE PROBLEM

Secondary injection would have faded into relative obscurity except for a satisfactory technique of solving this problem. The solution to the problem was the incorporation of a "dump" system to control the expenditure of fluid throughout the vehicle mission and retain only that fluid necessary to complete the mission.

II. VARIOUS DUMP SYSTEMS AND THE ONE FINALLY CHOSEN BY AUTONETICS

A. DUMP SYSTEM COMPARISONS

The actual magnitude of the dump system problem depends upon the type of vehicle and its mission duty cycle. The penalty for carrying an extra pound of injectant varies with time (Figure 6). The injectant error is converted to an equivalent fixed weight, then added to the real fixed weight of the dump system, and, in turn, converted to an effective loss in range. This permits a comparison in terms of payload or range for different dump system mechanizations.

Figure 6 Relationship of Dump Error to Weight or Range

There is no best way to mechanize a dump system. In the case of the MINUTEMAN vehicle, Autonetics reviewed many different design approaches to a dump system. The best criteria found for comparison of the various methods was an expression of pounds of dump system error with respect to a perfect dump system (Figure 7).

Figure 7 Cost per Pound vs Time

The dump systems were further compared in terms of delivery cost to the customer, and effect on vehicle performance, accuracy, and reliability (refer to Table 1). The relative value of these parameters was scaled in accordance with the customer's expression of their relative worth when:

Dump system error, (pounds of injectant) = W_i

Conversion factors, (fixed weight pounds / injectant pounds) = K

Equivalent injectant fixed weight = W_fi

Fixed weight of additional hardware = W_fh

Then: W_i x K = W_fi and W_fi + W_fh, = W_ft(total fixed weight) in comparison of dump systems with respect to a perfect dump system.

Table 1. Dump System Value Analysis

Item	Worth Factor Value ($/Item)	Value ($)
Vehicle weight change Wft	K1 *	V1
Cost per vehicle system		V2
Vehicle accuracy	K2	V3
Reliability	K3	V4
Total		Vt**

* This value may be based on weight, range, or both.

** The desirable system is the one with the least cost.

B. BASIC TYPES OF DUMP SYSTEMS

Figure 8 illustrates a typical secondary injection system to which a dump function would be added. It consists of a gas generator for fluid expulsion, a tankage-manifold system, and a servo injector for controlling the actual fluid injection.

Figure 8 Method of Dump Control

In general, five basic types of dump systems were considered by Autonetics. The needs and capabilities of associate and supporting contractors were solicited to lend objectivity to the respective studies. The following techniques were studied:

1. Expulsion Regulation Method. Programmed rate of total injectant flow versus time by regulating the gas generator output versus time. In this case, the control is achieved by unbalancing the opposing injectors.

2. Tankage Measurement System. Direct measurement of the tank quantity versus time, and programming the injectors to achieve a desired tank quantity reduction rate.

3. Flow Meter Dump System. Measurement of actual flow versus time by use of flow meters and programming the injector s to achieve the desired expulsion rate.

4. Command Monitor System. Use of vehicle control commands as an indication of consumption and modifying the commands to achieve the desired expulsion rate.

5. Injector Monitor System. Use of the metering injectors as flow meters and reprogramming them to achieve the desired expulsion rate.

In all five cases, it was intended that the dumping of injectant would be through the injectors. This is practicable since the expulsion of injectant when expanded into the main motor nozzle adds to the vehicle thrust. No turning moment is produced when the injectant is dumped through all injectors equally and simultaneously.

All of the methods except one, Type 1, required a computing function. This was fortunate because Autonetics has used a digital computer for control computations in its flight control systems since 1948. One of the least obvious advantages of this computer operation is its versatility. A design freeze in an early phase of development can be corrected or optimized by changing the computer program after the inherent characteristics of the system it controls have been determined. This can save costly resizing and modification of system hardware by the simple process of making a new computer tape for an otherwise completed vehicle. The computer cannot work miracles, but its versatility helps solve control system design problems.

Two approaches were made to Type 1, the Expulsion Regulation Method. One method was to provide a servo loop which would regulate gas expulsion versus time, and the other was to preshape a solid propellant to provide a given expulsion gas flow versus time. The first method became too complex and involved, and the second did not offer the development versatility or the accuracy's of the other proposed methods.

The Tankage Measurement System, Type 2, was dropped because of the difficulty in achieving a direct fluid measurement due to the tankage configuration required.

Single Meter System Dual Meter Systems Four Meter System

Figure 9 Possible Flow Meter Systems

Four types of the Flow Meter Dump System, Type 3, were studied. These are shown in Figure 9, and are:

1, A four-flow meter system with one meter serving each injector.

2. A two-flow meter system, with one meter serving the two pitch injectors and the other serving the two yaw injectors

3. A two-flow meter system with each meter serving one pitch and one yaw injector

4. A one-flow meter system serving all four injectors.

The relative demands per flow meter are shown in Table 2.

Table 2. Extremes of Flow Meter Range

Type System	% Usage Range, 90 % of Time	Max Flow, %	Size Ratio
Single meter	3 to 3.5	100	2
Dual meter (P+Y and P+Y)	0 to 2.0	100	2
Dual meter (P+P and Y+Y)	0.3 to 3.5	100	1
Four meter	0 to 2.0	100	1

With respect to dump system accuracy, the single flow meter looked good; however, when combined with the practical packaging problems and the added fixed weight, its accuracy advantage was discounted.

The multi-flow meter systems, which reduced packaging problems, posed extremely formidable problems for the flow meter (Table 2). Here, the meters had to measure from zero to maximum injectant flow with 95 percent of the activity expected at less than 3.5 percent of the maximum flow rate. The problem can be appreciated by looking at Figure 10, a simplified plot of flow extremes per injector, and Figure 11, which is a plot of the net flow through all injectors. The maximum error for any of the flow combinations given in Table 3 is the one which must be used for an error analysis.

Figure 10 Flow per Injector vs Time

Figure 11 Total Injectant Consumed vs Time

Table 3. Extremes of Flow Distribution Between Injectors Where Any

Combination May Exist for 90 Percent of Total Usage

	Case A, %	Case B, %	Case C, %
Injector No. 1	25	50	79
Injector No. 2	25	50	7
Injector No. 3	25		7
Injector No. 4	25		7
	100 *	100	100

* Represents approximately 2 percent of an injector's maximum flow capability.

C. THE DUMP SYSTEM FINALLY CHOSEN BY AUTONETICS

Finally the drawbacks to the other four injection methods resulted in the selection of the Feedback Monitoring System, Type 5. Both Types 4 and 5 have appeal in that few change s are required to the basic control system; however, the feedback monitor, Type 5, was selected over the command monitor, Type 4, due to its inherent accuracy. The accuracy of a servo loop is more dependent on the feedback loop than on the forward loop. In fact, forward loops often are quite inaccurate.

Figure 12 Injectant Control and Feedback Loops (Inset: Typical Amplifier Module)

The selected feedback circuit is shown in Figure 12. The encoder module is the only component added to the original system. In order to describe the circuitry, it is best to show how it evolved.

III. DUMP SYSTEM DESIGN PROBLEMS AND THEIR SOLUTION

A. MODIFYING THE BASIC CONTROL SYSTEM

From the beginning, the problem was viewed as one of adding an injectant monitor system to a control system design. The selected technique, Type 5, was studied further to determine if the combined functions of control and dump could be improved by modifying the basic control system.

The basic element serving both control and monitoring functions is the injector pintle. The simplest pintle is one with a straight profile providing semi-linear flew as a function of position (Figure 13, line a). If control commands are in terms of position, then ideally, the position should be linearly translated into side force. This require s a contoured pintle to compensate for the fact that more injectant is required propound of side force as the side force is increased (Figure 13, line b).

Knowing the most desirable pintle characteristics from the monitoring standpoint require s a knowledge of the critical flow regions. The accuracy's in region A and point B of Figure 1 3 determine the cue rail accuracy of the monitor system. Figure 10 indicate s that most of the injection time will be spent in region A, but for short time periods, the flow may extend to point B. If point B, full flow, represents the maximum error, and if the error diminishes as the flow is reduced, then region A and point B characteristics determine the error magnitude.

The flow error at point B can be held to a minimum by adjusting the pintle stroke to achieve a specified flow. The accuracy in region A can be improved if there is more stroke required or more volts monitored per pound of metered injectant. Such a curve is shown in Figure 13, line c.

Figure 13 Flow per Injector vs Position

During this research, Autonetics ran computer studies which predicted vehicle performance as a function of various injector flow shapes. As a result, these studies produced a two-slope injector flow design which satisfied both the monitor and control objective s. (See Figure 13, line d.)

B. DUAL FEEDBACK LOOP CIRCUIT DESCRIPTION

Figure 14. Region of Flow Registered By Each Feedback Leg

The two-slope pintle posed a monitoring problem at first, as each injector could be at a different position and the feedback (volts per pound of injectant) change s at the break point. Studies also indicated that conventional electrical feedback technique s would not be sufficiently accurate, especially if each injector's output were independently transmitted to the computer. Consequently, a dual feedback method was evolved, accounting for the two feedback types of fluid monitor circuits shown in Figure 12.

The output of each injector position transducer is summed and fed back through the encode r module to the computer. This feedback leg transmits flow information from all the injectors represented by area X in Figure 14. An independent feedback leg, also used for checkout, transmits the flow information represented by area Y of Figure 14.

Figure 15 Servo Injector Assembly

Figure 16 Secondary Injection Hardware and Location

The injectors, shown in Figures 15 and 16, are located so that only one pitch or one yaw injector is used for control purposes at any given time. This means that only two of the independent checkout legs are active at a given time, and that the maximum flow rate information transmitted through the encoder leg is the maximum output of two injectors based on the low slope rate. It also means that except for activity such as staging or pitch over, the nominal operative level of the encoder leg is that established as the injectant expenditure rate for any given time.

The following paragraphs give a description of each of the flow monitor circuits shown in Figure 12.

The checkout feedback circuit is shown in Figure 17. The position transducers are of the induction transformer type; the transducer output is converted to a d-c voltage by the use of a demodulator for each transducer. The demodulator outputs are connected to an analog-to-digital converter, which is time shared as a digital-to-analog converter in the command leg. The computer periodically checks the signal level from the checkout leg and either ignores or processes the information, depending on the signal level.

Figure 17 Checkout Feedback Circuit used for part of Dump Monitor

Figure 18 Freon Utilization Monitor and Associated Hardware

The encoder module feedback leg is shown in Figure 18. The outputs of all the transducers are summed at one point and then passed through a single demodulator. The encoder amplifier takes the demodulator output, amplifies it, and in so doing, charges an integrating capacitor. When the capacitor is charged to a given voltage level, the level detector sends a True ON signal to the computer. Whenever the capacitor is below the trip level, the level detector sends a False OFF signal to the computer.

When the input to the computer is True, the computer stores a count in its storage register and issues a True ON command to the precision pulser. The precision pulser then sends a controlled pulse quantity to the encoder amplifier which discharges the integrating capacitor by a specified amount. Thus, the integrating capacitor voltage level fluctuates with respect to a given value.

The accuracy of the encoder feedback leg is due, in part, to the fact that the sampling errors average out. In comparison, the check out leg technique samples injector position at periodic intervals and has a conversion error which accumulates rather than averages out.

Voltage drift with time is compensated for by using the same power supply for the encoder module and the position transducers. Thus, if power supply drift causes the transducer outputs to increase, the precision pulser output also increases, causing the counted computer pulses to remain the same.

Figure 19 Computer Dump Monitor and Command Functions

The computer (Figure 19) multiplies the input pulses from the encoder feedback leg by a conversion constant, and stores the information in an accumulator register. The input from the checkout feedback is read

as a digital number. A value equivalent to the voltage at the flow break point is subtracted from this sampled feedback and all negative answers are disregarded. All positive values are then multiplied by another conversion constant, and these results are stored as an addition to the encoder feedback accumulation. The total accumulated number in this memory register represents the total quantity of injectant consumed.

A reference value, (desired injectant quantity versus time) is preprogrammed into the computer, and the actual accumulated quantity is compared with it at discrete intervals of time. The difference between the two quantities is then issued as an equal dump command signal (either increase or decrease) to all injectors, and is superimposed on any attitude control signals.

IV. DUMP SYSTEM DESIGN ERROR ANALYSIS

A. THE ROOT SUM SQUARE METHOD OF ERROR COMBINATION

The quality of the injectant monitor circuitry is directly dependent on a good error analysis of the system. For this design, the root sum square (RSS) method was used to evaluate the overall circuit accuracy. Care had to be taken when using the RSS method to assure that the variables, the errors of which were combined, were truly independent and random. Where this was not true, the errors simply were added. When using the RSS technique, the error magnitude for each function was taken as the 3 Sigma, 90 percent, confidence level for that function.

The use of the RSS method of error analysis places a different emphasis upon the relative importance of errors, For instance, observe the following relative importance of errors combined by addition and RSS:

Error Magnitude	Percentage of Total Error
	Addition	RSS
1	14	5
2	29	19
4	57	16
	100	100

It can be seen that the RSS method amplifies the importance of large errors.

B. ERROR EQUATIONS

Several types of error analysis, ranging from highly theoretical methods to reliance on test measurements, have been conducted on this system. A fully detailed mathematical analysis is quite involved and more appropriately handled by computer methods; the following equations are presented, not so much to show the absolute magnitude of errors, but to indicate the variables involved and the method used to evaluate their relative significance.

1. Total Injectant Error, W_T

The total injectant error may be expressed in the following general form:

W_T=(W_e² + W_i² + W_f²)^.5 [note: the enclosed part to the 1/2 power is the Square Root]

Where:

W_T = total injectant error

W_e = electrical error

W_i = injector mechanical error

W_f = fluid error

2. Electronic Error, We

The electronic error is subdivided as follows:

W_e = W_ecl + W_ec2 + W_ee

Where

W_ec1 = checkout leg no 1, electrical error

W_ec2 = checkout leg no 2, electrical error

W_ee = encoder leg, electrical error

These sub divide further into:

W_ec = t*K₁(E_c2 + D_c2 + F_c2)^.5

W_ee = t*K₂(E_e2 + N_e2 + F_e2)^.5

Where

t = operative time, at a given level

K₁ and K₂ = pounds per volt conversion

E_c = analog-to-digital conversion error, volts

D_c = checkout demodulator error, volts

F_c = feedback transducer error, volts

E_e = encoder module error, volts

N_e = mixing network error, volts

F_e = feedback transducer error, volts

Each of the subelements is further broken down into error characteristics such as linearity, gain, scaling, null shift, excitation, terminal error, etc. These values are, in some cases, dependent upon the flow level and thus require several computations of Eq 3 and 4 to cover a complete duty cycle.

3. Injector Error, Wi

The injector mechanical error, Wi and fluid error, Wf, are best explained by the basic flow equation:

W_s = A*C_d(2P_d/d)^.5

Where

Ws = injectant flow

A = injector exit port area

Cd = coefficient of discharge

Pd = differential pressure across the injector

d = fluid density

W_f covers variation due to P_d and d, and W_i covers variations due to A and C_d. W_i also includes mechanically caused errors in transducer voltage representation of position such as scaling, indexing, etc.

The injector error, W_i, is determined after an injector pintle shape has been developed by plotting the injectant flow vs feedback volts (Figure 20) for a number of fabricated units. computer-curve-fitting techniques are then applied to find the best-fit straight line that will account for the nonlinearities and unit-to-unit variations. The deviations of the flow envelope with respect to the best-fit straight line is then defined as the injector error, W_i.

Figure 20. Definition of Injector Error as a Function of Position

Data acquisition and curve fitting of flow versus volts is continued after designs are frozen and delivered. The versatility of the computer is used by modifying the computer volts-to-flow conversion factors in accordance with the latest curve-fitting data, thus minimizing the effect of injector mechanical errors.

The causes of injector mechanical error pose intriguing problems. Awareness of these problems is the first prerequisite to a good injector design. Referring again to Figure 13, region A and point B are both

critical. The accuracy at point B depends upon the ability to set the stroke and it's representation in volts at the desired full flow. The problems in region A are more subtle but may be expressed as follows:

1. Flow dead-band. This is the servo injector travel required before flow occurs and is due to spring effects in going from closed (by full force) to just open or vice versa.

2. Non uniform seating of injectors. This causes a changing flow when the flow is just initiated.

3. Misalignment of pintle and orifice. If the pintle is to one side of the orifice, the flow rate doubles. The effect is evident only just as the injector opens.

4. Temperature changes. Injector temperature changes cause a change in voltage output due to expansion or contraction of the injector parts relating the position transducer core to the transducer body.

5. Injectant pressure variation. Pressure variations also can effect the transducer core-to-body relationship.

Each of these effects adds together to cause a flow pattern of the nature shown in Figure 21 in the near seated position.

Figure 21. Flow us Volts Near Closed Position

4. Fluid Error, Wf

Wf = (Wp2 + W2).5

Where

Wp = [ too detailed to repeat]

W = [ too detailed to repeat]

Where

Pdn = nominal differential pressure

Pda = actual differential pressure

vn = nominal specific volume

Ta = actual temperature

Tn = nominal temperature

a = specific volume change per psi

b = specific volume change per degree F

Wn = nominal injector flow

Because differential pressure and injectant temperature both vary with the flow rate, the error must be calculated for various duty cycle conditions.

C. TOTAL ERROR TABULATION

A tabulation of total dump system relative error is shown in Table 4. This table points out another factor in the search for error reduction: the encoder demodulator is approximately twice as accurate as the check out circuit demodulator, yet it accounts for 30 times as much error.

Table 4. Total Dump System Relative Error

Symbol	Error due to:	% of total	% of total	% of total
Fc (2)	Position transducer	.25
Dc (2)	Demodulator	.25
Ec (1)	A to D converter	.50
Wec (2)		>>	1.0
Fe (4)	Position Transducer	10.5
De (1)	Demodulator	7.5
Ec (1)	Encoder module less Demodulator	8.0
Wee (1)	Encoder feedback leg	>>	26.0
We	Electronic		>>	27.0
Wi (4)	Injector			40.0
Wp	Pressure		30
W	Density		3.0
Wf	Fluid		>>	33.0
WT	Total error			100

D. EVALUATION OF SYSTEMS WHEN INSTALLED

Evaluation of the system's ability to control the expenditure of fluid when installed in a vehicle is quite difficult. The difficulty arises from the lack of a good injectant consumption reference to which the monitor

system can be compared. Ground tests can be run until the injectant supply is consumed and the monitored quantity expenditure compared with the theoretically expendable quantity.

The flight case poses a more difficult problem. It is not practical to expend all the fluid before flight termination just to prove that the monitor system works, and it is not practical to expend the fluid after thrust

termination. The simplest method is to scale the system, based on ground tests and pressure instrumentation, to verify that the injectant was still available at thrust termination. This method does not define error magnitude but it does indicate a successful vehicle.

Figure 6 indicates that the plus error determines the computer reference level, and that the plus and minus errors define the pounds of injectant error. A vehicle with characteristics similar to those shown in Figure 7 requires 2-lb injectant to be saved to equal 1 lb of fixed weight. The point here is that regions which render the most improvement or have the most value to the customer are not always obvious. This poses an obligation on the part of the system designer to communicate to the customer and those working on the program the value of a change to the vehicle rather than the value of a change with respect to subelement accuracy.

E. SUMMATION

Most vehicle control problems are more complex than this one. The main difficulties with this system are the quality control demands on the error-causing functions. This paper has presented one of the MINUTEMAN systems to illustrate the many interesting facets of flight control system design.

The new Integrated Circuits made advanced methods possible