US2890673A - Control system for stabilizing fins - Google Patents

Description

J. H.'cHADw|cK, JR 2,890,673 CONTROL SYSTEM FOR STABILIZING FINsJ June 16, 1959 Filed 'March 11. 1954 INVENTORh Joseph H. Chadwick, Jr.

ATTORNEYS United Sites Patent CONTROL SYSTEM FOR sTABrLlzlNG FINS Joseph H. Chadwick, Jr., Levittown, N.Y., assgnor, by mesne assignments, to the United States of America as represented by the Secretary of the Navy Application March 11, 1954, Serial No. 415,711

4 Claims. (Cl. 114-122) This invention relates to a control system for stabilizing fins and more particularly to a control system for fins which are used to stabilize marine craft.

It is Well known that conventional surface ships, submarines, hydrofoil boats, and other marine craft subject to disturbing effects, such as roll, pitch, and yaw, can be stabilized to counteract these effects or steered by means of moveable fins, fins with moveable flaps, or related control surfaces. It is also well known that the aforementioned fins, flaps, or other control surfaces can be incorporated into automatic stabilizing or automatic steering systems constituting servomechanism. In addition, it is known that the behavior of such control surfaces, hereinafter referred to simply as fins, depends on the speed of the vessel being stabilized or steered, hereinafter referred to simply as the ship. Furthermore it is known that when a fin is caused -to change periodically its angle of attack in response to an oscillating control signal produced by equipment sensing a periodically varying disturbance effect of the ship, the behavior of the fin is found to vary with the frequency of fin oscillation especially in two particulars:

(l) The relation between fin lift and fin angle of attack; and (consequently):

(2) The phase relation between the control signal and the fin lift (because in the usual servo system embodying fins the error-sensing device used to modify the control signal is tied to the fin angle rather than to the fin lift).

Prior art stabilizing fin control systems failed to account for the variation in fin lift with ship speed and the variation in fin behavior with frequency of an oscillating fin.

An object of the present invention is to provide a control system of the type described which compensates in a particularly simple way for the changes in fin behavior that occur with ship speed. Another principal object of this invention is to provide a conrtol system of the type described which enables the creation and maintenance at all speeds of an especially favorable response characteristic between the control signal and the fn lift.

Other objects and many of the attendant advantages of this invention will be readily appreciated as the same becomes better understood by reference to the following detailed description when considered in connection with the accompanying drawings wherein:

Fig.r l shows a block diagram of a preferred embodiment of the control system of this invention applied to a 'fin-stabilized ship; and

Fig. 2 shows a schematic diagram of the hydraulic positioning motor of Fig. 1.

Although the system of the present invention is applicable to stabilizing systems in general, it will be described for simplicity and by way of example only, in reference to a specific preferred embodiment involving a ship provided with fins, the angle of attack of which is varied by a hydraulic motor. In arrangements in which control systems of the type `herein described are used, control signals produced in response to disturbing conditions (such for example as wave forces exerted on a ship, roll of a ship, etc.) are used to actuate a train of mechanism directed toward altering the disposition of a fin to exert a fm lift just adequate to oppose the disturbing condition. The aim of the present invention is to provide a system which, with certain qualifications hereinafter explained, will cause the fin to lift to follow the combination of the control signals with a proportionality constant that is as nearly as possible independent of the speed of the ship and the frequency of the input signals.

Reference is now made to the drawing where it is seen that rthe system consists of three main parts; a control amplifier; a positioning motor; and the iin itself. The control amplifier will usually be electronic, as indicated in Fig. l. The control amplifier comprises a mixer 1 of some sort, well known in the art, for combining a plurality of control signals in a predetermined manner. The combination of the control signals produced by the mixer 1 may be simply an addition of signals related to such things as roll displacement, roll velocity, roll acceleration, etc., or it may be the result of modulating one such signal with another or various other combinations. The particular apparatuses for sensing disturbing functions `such as roll motion, Wave force, Wave slope, etc., arewell known in the art and are not a part of this invention. Mixers are so well known to those skilled in the servomechanism art that they are not usually illustrated in publications in this field but are commonly shown in detail in all good electronics texts such, for example, as Electronics by Elmore and Sands, McGraw- Hill Book Company, Inc., New York, 1949. Nor is the apparatus nor method for combining such signals. The control amplifier further comprises a gain control unit 2 for varying the overall gain of the servo or control system, adders 3 and 4 which add signals algebraically for comparing, respectively, feed back signals E., and E3 to control signals Ec and El, respectively, and gain control elements 5 and 6 whose function is to control the response of the positioning motor by adjusting the gain of its two closed loops. The positioning motor will usually be hydraulic. As shown in the second large block in Fig. l, it consists of a hydraulic preamplifier 7 and a hydraulic transmission 8 with selsyns 9 and 1t) which respectively repeat back as electric signals the position, X1 of the tilt-plate of the hydraulic pump 1S (Fig. 2) of the hydraulic transmission and the angle of tilt, a, of the n 11. The adders and amplifiers hereinbefore mentioned may be of any suitable construction, many varieties being well known to those skilled in the art. An adder, which performs the function of adding quantities algebraically, can assume the form of a summing amplifier, a difference amplifier, a transformer, or many another form. Some examples are shown in the cited Electronics by Elmore and Sands as being a species of mixer designated as a linear mixer in which the output voltage is the sum of linear functions of the input voltages. It is common in the control mechanism art to illustrate adders by a small circle with plus and minus signs to indicate the arithmetic operation involved. Such symbolism is shown and explained, along With other commonly used symbols, terminology, and physical embodiments of servo elements in any good text in the field of servo-mechanisms such as the following: Automatic Feedback Control, by Ahrendt and Taplin, first edition, copyright-1951, McGraw-Hill Book Co., Inc.; Principles of Servomechanisms, by Brown and ,y 1951, published by John- ,Wileyr & SonsLInc., New York.

3 Electronic amplifier construction Asuitable for use in this invention is taught in the Elmore and Sands volume as well as in many other electronics texts such, for example,

as itemsS: and331ofthe bibliography list inthe citedv of a tilt-plate varies the delivery of the pump usually'by varying thestroke of its pistons; Theoutputof the.vari able-delivery pumpA 15A isusedt to operatethe iin-tilting ram 16` which' drivesthe iin. The pump 15 and the iin-.tilting ram 16 comprises the hydraulic transmission. As mentioned hereinbefore, the tilt plate position and the fin angle are repeated back as electric sign-als E3 and Ei by means of selsyns 9 and .10;

Important novel features of the control scheme are the gain control unit 2 and the gain control elementsV 5 and 6 in the control amplifier. As` shown in` Fig. 1, these devices are adjusted by means of a mechanical signal correspondingrto the speed of the ship V. The` gain control elements and 6 in the position motor closed' loops may be simply variable attentuators or variable gain amplifiers which Iare well known in the electronic art. The gain control unit 2 may take a variety of forms, butV one particularly simple and desirable form is that shown in the block Z in Fig. l. The unit there shown includes a summing device or adder 17, a constant gainY amplifier 18, and a feed back element comprising a variable attenuator 19, all of which arewell known to the art. For reasons to be later explained, the variable attenuator is controlled by the mechanicalV signal responsive to ship speed in such a way that the equation holds, where is the transmission factor of the attenuator 19 and Kg is the gain of the constant gain amplifier 18. If Equation l holds it can be shown that the overall gain, Kg, of the unit, is given by K EKgl E-E-f z i+1/V2 Es Although, for simplicity, the control signal used to modify the behavior of elements 19, 5 and 6 istindicated merely as V, itis understood that the effect on element 19 must be such as to make vary directly as the square of the velocity. This can be accomplished by using a separate speed sensing device which is sensitive to the square of the velocity directly, as for example a pitot tube, or, on the other hand, a mechanical signal proportional to V can be used to attenuate the signal entering 19 directly in proportion to V2. This latter could be accomplished for example, by using a quadratically wound potentiometer, the arm of which is moved by a mechanical device, that moves vin direct proportion to V. If on the other hand, as previously suggested, the speed control signal is produced by a pitot tube which senses V2, then the output of the pitot tubewould beA used tocontrol the arm of a linearly wound potentiometer in block 19.

To understand the reason for choosing the gain functionI of vEquation 2 and to'determine the manner in which thegain control elements 5 and 6 should be controlled, reference is made to thebasic purpose of the system previously recited. It Was there stated 'that the aim ofthe-system is to-cause`the fin lift-to'be as nearly as possible proportional'to the-combination of the controlsignals. F'r'omFig; 1 it'issseen thatthe ultimateterror` signal used to control the operation ofthe servomechanism is the angle a which is the., angle of tilt or angle of attack of the iin 11. This is a rather usual practice since it is considerably easier to sense or measure iin angle than it would beto sense or measure the paramount parameter, iin lift. Because fin angle o: is not a direct measure of n lift, L, but the relationship between the two varies. with the frequency of'tin oscillation and with ship speed, it can be concluded from Fig. 1 that to acccmplish the aforementioned desideratum of causing the fin lift to be as nearly as possible proportional to the combination of control signals, the combined response of `the control amplifier and the positioning motor must be as nearly as possible the inverse ofthe response or relation between the iin angle oftilt and the tin lift, L, and furthermore this inverse relationship must be maintained at all speeds.

The first stepfinunderstanding the' openation ofi the deviceA is to consider the nature ofthe fin response.A It' isA proportional of the square of ship speed. It is the purpose of the gain control unit 2 to compensate for the variation expressed by Equation 3. the gain function of unit 2 (Equation 2) is nota perfect quadratic hyperbola i.e. is not exactly `inverse in form to Equation 3, the compensation is not quite perfect. Speel cifically the overall static gain of the system will have the form:

Overall static gam-1 F1/V2 (4) where-C2 and fy are constants. This overall static gain is simply the product of the gain of the gain control element 2 multiplied by the gain of the positioning motor system 20 multiplied by the gain of iinll, which latter is ClV2 from Equation 3. For yV2 appreciably greater than l, the static gain is essentially constant, but for low speeds Where V2 `approaches zero the gainfalls oif toward zero. This would seem to` be not consonant with the stated objective of the control system, but actually for practical purposes the overall gain function (4) is preferable to a constant. This is because the maximum allowable lift of the n drops off sharply as the ship speed falls below a certain critical speed, and hence keepingthe system gain constant at low speeds would cause the iin or fins to be overdrawn. off in the overall gain can be controlled by adjusting 'y in an approximate manner.

The firegoing takes care of the static response ofthe system. The next step is to take care of the dynamic response, which includes the static response as a special case. By dynamic response is meant, in general, the response of the fin when. it is subject to oscillations, that is, periodic variation of its tilt angle. This situation -occurs when the ship is subject to periodically varying disturbing effects such as roll, pitch, etc. In the commonly used stabilizing systems the frequency of oscillation of the iin is the same as the frequency of the disturbances producing the control signals since it`is found that for the best approach to stabilization the iin lift should follow as closely as. possible the control signals. It can be shown that the. dynamic lift of a tin with a small to moderate. aspect ratio is given quite closely by However, as

The dropping Where L and a here represent the complex amplitudes of lift and angle of tilt, respectively, and where s=a+jw is the complex frequency of oscillation of the n about its tilt axis which, as previously noted, is the same as the complex frequency of excitation of the ship and hence of the control signals. It can be shown furthermore that in the above equation [11, is a constant and w1, varies directly as ship speed, so that we may say where C3 and C4 are constants. In control terms Equation 5 represents a lead effect, i.e. the lift of the fin tends to lead its angle of attack for the higher frequencies of oscillation.

It is known to the control art that positioning devices such as depicted in Figs. 1 and 2 tend to introduce lags into the system response, i.e. their outputs tend to lag behind their inputs for the higherfrequencies of oscillation. To achieve the stated aim of the control system with respect to response, the invention contemplates causing the lag introduced by the positioning system to be equal and opposite to the lead introduced by the fin respense, and furthermore causing this relationship to hold at all speeds. This is done by means of the inherent response of the positioning devices together with suitable adjustment of the gain control elements 5 and 6.

It is known to the control art that to a first approximation both a hydraulic preamplifier such as 7 and a hydraulic transmission such as 8 act as ideal integrators, i.e. the positions of their output elements are respectively proportional to the integral with respect to time of their input signals, E2 and X1. This can be expressed mathematically by indicating that the transfer function of each of these devices is proportional to the reciprocal of the complex frequency of excitation of the fin. This transfer function is written in as on the block labelled 7 and as on the block labelled 8. The approximate response of the positioning motor system (which comprises the items on the block diagram lying between the signal labelled Ec and the signal a) can be determined from Fig. 1 in which C5C6K3 and K4 are constants, while K1 and K2 are proportionality factors that are independent of frequency but, as will shortly be demonstrated, should be and are adjusted by the mechanical signal corresponding to ship speed as shown. It follows from the block diagram of Fig. 1 that the overall response of the posi- 60 tioning motor system is w22 0505K 1K 3K4 and which can be re-written, after defining whence Having evaluated the suspectedly existing p2 and wg, Equation 7 can be rewritten thus:

The preceding equation says that the positioning motor system response exhibits a lag that has a form which is the inverse of the fin lead effect. Since the positioning motor system works in conjunction with the fin and does so in such a manner that the overall response of the two combined S given by a Ec then it is conceivable that the lead effect of the n and the lag effect of the positioning motor system could be made to cancel each other. From the full expression it is apparent that this can be accomplished by making the quantity in brackets [l in the denominator just equal to the quantity in brackets [l in the numerator so that they cancel each other. Such a cancellation can be achieved by making :p2=:p1, and w2=w1. From Equation 6 this means that @2:03 and w2=C4V but from Equation 8 and Equation 9 this means that To meet both of these conditions it is merely required to solve Equations 10 and 11 simultaneously. This solution is and y C708 which says that each of Kland K2 must be made to vary directly in proportion to V. ThisV can be accomplished by using as gain control elements 5 and 6 simply linear potentiometers or similar linear attenuators operated by a mechanical control signal, such as that shown at V in Fig. 1, directly proportional to ship speed. With this linkage in the ship speed sensingedevice and the type of attenuator properly chosen-to produce K1 and K2 equal to V multiplied by, respectively,

@man cec, then in Equation 9b the` denominator in brackets i] equals and just cancels, therefore, thee-numerator termin brackets il, That is, the response of the combined positioning motor system or loop and fin has been made free of frequency-dependent variations.

Now from Equations 2, 3, 4, 5, andv9a.and assuming that the gain control arrangement causes Equations 12 and 13 to be satisfied at-all speeds, the overall response of the control system is response of thesystemlbecausedto,fallgoif aslshp speed drops below a certain criticaljspeed.

Actually the overall response of the positioning motorn system is given only approximately by Equation 7, the degree of approximation depending on practical circumstances. Investigation shows that if the` hydraulic drive is carefully designed, the approximation can be quite good for typical stabilizing'ns and typical positioning motors.V

From:the foregoing it can be seen that a ,principal advantage of a control system ofthis invention isithat it compensates at one and the same time for. theeffect of ship speed on the response and the gainof stabilizing fins. It provides a simple means whereby the lift ofthe fins can be kept quite closely proportional to the control signal or signals over a widel range of ship speeds and control signal frequencies;

Obviously many modifications and variations ofthe present invention are possible in the light of the above teachings. It is therefore to be understood thatiwithin the scope ofthe appended claims the invention may be` practiced otherwise than as specifically described.

What is claimed is:V

1..In a systemiofv the character described comprising a ship-stabilizing iinexhibiting a leading lift: versus n tilt angle response that varies as a function of the frequency of excitation and ship speed; a positioning motor closedservo loop forcontrolling the finrtilt angle that 8 i exhibits a lagging iinstilt versusinput signal response of which the reciprocal, has the same general form in its frequency-dependent term'ssas the n'response; and means responsive to. shipA speed .'for. modifyingA the lagy of the positioning motor /loop i to, render: it fapproximately identicalto-the lead-ofthen response. whereby the lead of thefin-iscompensatedby the lag of the positioning motor loop.

2. A system of the type described comprising a shiplstabilizing iin adapted to be controlled in response to a control signal related to adisturbing condition'of the ship; means including an amplifying unit for amplifying saidcontrolsignal; apositioning motor closed loop actuated by the output of said amplifying unit for controlling the angle of tilt of said''n; means for varying the gain of said amplifying unit as a decreasing function of the squareY of ship speed; and means responsive to ship speed for modifying the lag of the -positioning motor loop to compensate for the -lead of the Yfin response whereby the -overall response of the system is rendered substantially free of dependence-0n ship speed and control signal frequency.

3. A vsystem ofthe character described comprising a ship-stabilizing-fin adapted to be controlled by control signals responsive to disturbance effects of a ship; a mixer for combining the Ycontrol signals; a gain control unit for receivingand amplifying-the output of said mixer; means fora-varyingthe gainv of saidgain control unit as a decreasing function of the square of ship speed; a positioning motor system actuated by the output of said gain control unit for controlling the tilt angle of said iin; said positioning motor system comprising a positioning motor in a first closed minor servo lop and a pre-amplifier for said motor; a second closed minor servo loop including said preamplifier; means in the direct arm of said positioning motor minor loop for varying theV gain of said rst minor loop in proportion to ship speed; and means in the direct arm of said pre-amplifier minor loop for varying the gain of said second minor loop in proportion to the speed of said ship; whereby the overall response of said system is rendered substantially free of dependence on ship speed or control signal frequency.

4. A system of the type described for stabilizing a ship comprising a stabilizing fin; a positioning motor for varying the angle of attack of said n; means for producing a signal in response to-a disturbance of the ship; means for amplifying said signal and feeding it ultimately into said positioning motor to control said positioning motor; and means responsive to the speed of the ship for varying the gain ofsaid amplifying means as a decreasing function of the square of the ship speed.

References Cited in the ile of this patent UNITED STATES PATENTS 2,179,179 Fischel et al. Nov. 7, 1939 2,352,649 Meredith July 4, 1944 2,387,795 Isserstcdt Oct. 30, 1945 2,550,220Y Bussei Apr. 24, 1951 UNITED STATES PATENT OFFICE Certificate of Correction Patent No. 2,890,673 June 16, 1959 Joseph H. Chadwick, Jr.

It is hereby certified that error appears in the printed svpecication of the above numbered patent requiring correction and that the .said Letters Patent should read as corrected below.

Column l, line 5l, for conltol read -control-; column 2, line 8, strike out to, tlst occurrence; column 3, line 28, for position read -positoning-; line 29, for attentuators read -a,ttenuators-; column 4, line 56, for overdmwn reed overdrVen.-; line 58, for approxnntte" read --approprete; line 59, for iregoing read foregoingcolumn 5, line 9, should read as shown below instead of as in the patent:

=03 and (01:04V column 8, line 33, for lop read l00p-.

Signed and sealed this 12th dey of April 1960.

[SEAL] Attest: KARL H. AXLINE, ROBERT C. WATSON, Attestz'ng Oyoer. Oommz'ssz'oner of Patents.

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