US 3736880 A Abstract A linear motor uses the same magnetic flux for suspension and propulsion of a high speed tracked vehicle and operates below a support rail without physical contact therewith. Displacement and inertial sensors carried by the vehicle sense the length of the motor-to-rail gap and any acceleration of the vehicle causing changes in the gap.
Claims available in Description (OCR text may contain errors) United States Patent 1191 Ross 45] June 5, 1973 Primary Examiner.1. D. Miller Assistant Examiner-H. Huberfeld AttorneyGeorge E. Pearson [75] Inventor: James A. Ross, La .lolla, Calif. [57] ABSTRACT [73] Assignee: Rohr Industries Inc., Chula Vista, A linear motor uses the same magnetic flux for Calif. suspension and propulsion of a high speed tracked vehicle and operates below a support rail without [22] 1972 physical contact therewith. Displacement and inertial [2]] App]. No.: 219,713 sensors carried by the vehicle sense the length of the motor-to-rail gap and any acceleration of the vehicle Related U-s. Application Data causing changes in the gap 1 continuatiomin-pal't 0f 1311041, April 16, A non-linear feedback circuit responds to the sensor 971, Pu 3,638,093 signals and controls the voltage applied to the phased windings of the motor to maintain the selected gap. 1 318/537, The feedback circuit provides uniform stability and 318/687 dynamic response over a wide range of gap, maintains [51] Int. Cl. .L ..I-I02k 41/02 the ele ted ga substantially constant notwithstand- [5 Field of Search ing track irregularities and variations in vehicle load- /8 ing, and gradually corrects for unevenness. 91,93,148 R, 148 LM,l48 MS The inertial sensor is made to be sensmve to vert1cal [56] References Cited acceleration of the vehicle and 1nsens1t1 ve to irr gular1t1es of the rail thereby assuring a smooth or UNITED STATES PATENTS easy ride notwithstanding irregularities of the rail. 3,102,217 8/1963 Bullen ..3l8/676X The frequency of the pp voltage is varied "P- 3,660,745 5 1972 Bertrand ..3l8/676 wards r zero t adjust the linear s eed of the mo- 3 125 964 3/1964 Silverman "104/148 MS x tor, and the voltage is increased with e frequency to 3:158:765 11/1964 "318/135 x compensate for the increase in inductive reactance of 3,407,749 10/1968 Frig ..31s/135 x the wmdmgs- 3,549,966 12/1970 Wilson ..3l8/l35 A wide d f ynamlc range 0 motor control voltage 1s pro- 3,611,944 10 1971 Reder ..104/l48 LM x vided to cover the propulsion range from standstill to FOREIGN PATENTS OR APPLICATIONS high speed without requiring a wide dynamic range in the feedback control elements. 1,035,764 7/1966 Great Britain ..l04/148 LM 1,537,842 7/1967 France 37 Claims, 13 Drawing Figures 643,316 4/1937 Germany 1 1 104/148 MS 707,032 6/1941 Germany ..104/148 MS SA 1 SA 2 1 1 VEHICLE S 1 F F 2 2 .iiiji i k i i l .1. b 211 I I l i 1 i \Rl L I R A i i l 1 I 1 F 2 h 1 1 M T M 1 1 0 0 2 01 02 PAIENIEDIIIII 5|975 3.736.880 SHEET 20F 8 COMPENSATING -4v SQUARE RooT R T ACCELE OME ER NETWORK cIRcuIT l f22 23 POSITION COMPENSATING TRANSDUCER NETWORK MULTIPLIER X (D.C. PATH) g95 96 AMPLIFIER PERFECT DIFFERENTIATOR rA.c. PATH) VEHICLE {RAIL 2 I 1. CONTROLABLE I f POWER 1 MOTOR SUPPLY PowER PAIENTEDJUH 5 I975 SHEET 8 BF 8 w GI NI uZm3GwmE FEEDBACK CONTROL CIRCUIT FOR MAGNETIC SUSPENSION AND PROPULSION SYSTEM CROSS-REFERENCE TO RELATED APPLICATIONS This application is a continuation-in-part of the U.S. Pat. application of James A. Ross for Magnetic Suspension and Propulsion System, Ser. No. 131,041, filed Apr. 16, 1971, now U.S. Pat. No. 3,638,093, hereinafter sometimes referred to as the parent application. BACKGROUND OF THE INVENTION Heretofore others have suggested linear motors utilizing the same magnetic flux for suspension and propulsion of tracked vehicles. United States Pat. No. 782,312 (1905) to Alfred Zehden and French Pat. No. 1,537,842 (1968) to Jeumont-Schneider Electromechanical Construction Company, for example, teach combined propulsion and suspension of a linear induction motor by magnetic attraction of the motor upwardly toward its support rail which also serves as the reaction rail. Zehden discloses triphase windings, and the French patent teaches changes in power frequency to effect changes in propulsion speed. The French patent further teaches the use of gap sensing operative in an electronic feedback circuit for maintaining suspension of the motor below its support rail at a controlled air gap therebetween, thereby to avoid physical contact with the rail both at standstill and during propulsion along the rail. Zehden employs a rail engaging wheel support and does not disclose a feedback control circuit. German Pat. Nos. 643,316 (1937), 44,302 (1938), and 707,032 (1941) to Hermann Kemper disclose the suspension of tracked vehicles by use of electromagnets disposed below a support rail and magnetically attracted thereto while maintaining a controlled air gap therebetween, thus avoiding physical contact of the electromagnets with the rail. The 1941 Kemper patent and the French patent disclose similar arrangements utilizing magnetic attraction for guidance and switching of the magnetically suspended vehicle. The 1937 Kemper patent suggests that the electromagnets used for suspension can be configured for polyphase operation for propulsion of the vehicle along the track, operating for this purpose in the manner of polyphase induction motors. Recent developments of German industry in the transportation field, however, while apparently following the teachings of Kemper with respect to achieving magnetic suspension, tend to follow Kempers suggested alternative propulsion arrangement of using separate electromagnets operative with their own reaction rail in a conventional polyphased linear induction motor mode. The suspension arrangement of the 1938 Kemper patent (Addition to the 1937 patent), in common with the teaching of the 1937 patent, senses motor position with respect to the rail (gap), but further senses rate of change of that position (motor velocity), and change in motor energy state (motor suspension current) to provide a motor control voltage which is operative over a wide range of gap X (twice normal gap a). The motor voltage may be d.c. or ac. and is characterized as being positive or negative over-voltages for achieving arbitrarily high acceleration of the energy level contained in the motor windings. The 1938 Kemper patent is concerned with providing feedback for preventing oscillations of the suspended vehicle caused by the kinetic energy acquired by the vehicle in response to a correction of position and, further, in preventing high acceleration of change of motor energy level from causing further changes in energy level when the correct level is reached. The position feedback voltage e, produces a directing magnetic force to return the suspended vehicle to the correct location relative to the rails, and the damping or velocity feedback voltage e assures that the correcting movement can be made to a more or less damped oscillation. A report feedback potential e, is made to be proportional to the motor current and, in turn, provides a measure of the momentary energy state of the motor magnet. The sum of the position feedback voltage e and the damping voltage e constitutes a command voltage e, which starts the energy addition or reduction when a change in gap is sensed. The report potential e, opposes the command potential e to prevent further changes in the energy state as soon as the correct level is reached. The feedback provided by the Kemper Addition Patent is made to produce a smooth ride of the suspended vehicle by designing a pull force curve (curve 111 of FIG. 4) wherein position feedback voltage e is caused to fall off for increasing gap distance, the directional pull force being sufficient, however, to return the vehicle to the correct location but being limited to a desirable maximum value which results in limiting the tracking of the vehicle in relation to the rail track when moving rapidly. Additional absorption of rail nonuniformities is achieved by avoiding excessive suppression of the electrical inertia characteristics of the feedback regulator circuits, the smooth ride resulting because the feedback is not required to force distance corrections for deviations which exist only in short sections of the rail track whereby the vehicle is caused to follow only the average from a number of different regulation impulses. Automotive News for October 1970 describes an active spring-hydraulic suspension system for an air cushion supported tracked vehicle which employs vertical and lateral acceleration sensor inputs to a computer which calculates the forces necessary to maintain the vehicle body on a smooth path and with banking on turns. In the aforesaid copending parent application, Ser. No. 131,041, of James A. Ross there is disclosed a tracked vehicular transportation system employing polyphased linear motors both for suspension and propulsion in which each motor is magnetically attracted upwardly by its magnetic field toward a support rail with a controlled air gap maintained therebetween, and its suspension magnetic field is also used to translate the motor and its supported vehicle along the track at a speed related to the frequency of the polyphase alternating current applied to the motor. Although any number of phases could be used, a three phase design is disclosed because it is the simplest motor construction having the desirable characteristic of providing nearly constant pole attraction as a function of phase rotation. The propulsion system is a variable reluctance, synchronous speed type wherein the rail is provided with repetitive magnetic discontinuities (notches), or alternatively, the propulsion system is a linear induction motor type wherein the rail is provided with either a continuous conductive reaction strip or a squirrel cage winding (shorted rotor). Other disclosed. propulsion systems are of the wound rotor and hysteresis types. The terminal voltage applied to the polyphased motor windings to produce the attractive suspension force as well as the moving field for propulsion is controlled by a non linear-feedback circuit which uses sig nals from displacement and inertial sensors carried on the vehicle for maintaining a selected air gap. The feedback is non linear in order to compensate for the nonlinearity of the motor characteristic as a function of gap length and of feedback operating frequency. The attractive force produced by the magnetic field of the motor is proportional to the square of the motor current and inversely proportional to the square of the gap length. The motor impedance, moreover, is resistive at zero frequency and largely inductive at frequencies such as to 30 hertz which are relatively high for the feedback apparatus. The circuit elements of the feedback circuit provide the motor terminal voltage in accordance with the following equation which expresses the relationship between the motor terminal voltage and the resulting attractive magnetic force produced between the motor and its support rail: E terminal voltage 1 air gap length f= frequency in hertz (cycles/second) K K constants F attractive magnetic force j= reaction symbol. In order to provide stable suspension of the vehicle, whether at standstill or some propulsive speed, and at a selective gap which may range from substantially zero to one-half inches, the motor terminal voltage E, whether d.c. at standstill or a.c. at the propulsive speed, produces an attractive magnetic force F which is opposite to the gravitational and inertial forces acting on the vehicle and sufficient to restore and maintain the same in stable suspension. The feedback circuit responds to signals from the displacement and inertial sensors to produce various voltages indicative of these gravitational and inertial forces. For example, in a specific circuit arrangement, a voltage input of 4 volts to the square rooter element of the circuit indicates a gravitational force of l g which, of course, is the weight of the vehicle including its support motors. When this is the only force on the vehicle, the magnetic attractive force F produced by the motor terminal voltage E is just sufficient to support the vehicle against gravity at the selected gap. Signals from the displacement and inertial sensors pass in parallel paths through displacement and accelerometer channels in the input portion of the feedback. circuit. The displacement channel produces displacement signals indicative of the length of the gap, velocity. signals which are derived from differentiated displacement and are indicative of the rate of change of displacement, and change in loading signals which are derived from integrated displacement. The velocity signals range in frequency from 1.2 to 5 hertz. The change in loading signals range in frequency from dc. to 1.2 hertz. The range of frequencies of maximum interest in the displacement channel thus extends from dc. to 5 hertz. Signals from the displacement channel are algebra ically summed with signals from the accelerometer channel which has a frequency range of maximum interest extending from 0.3 to 30 hertz. Partial integration of the accelerometer feedback signal provides a quasi-velocity feedback which is effective from a frequency of the order of 10 hertz down to 4 hertz below which the differentiated displacement signal provides the velocity feedback. The square rooter element of the feedback circuit takes the square root of the combined displacement and accelerometer channel signals to produce a voltage corresponding to the equation quantity VT which is thereafter multiplied by the displacement function (IR) and the frequency function 0K respectively, these equation functions being performed by mutliplier and amplifier-differentiator circuit elements. These circuit elements respectively provide d.c. and ac. paths for their inputs, the dc path providing a voltage which increases with the gap and the a.c. path providing a voltage which increases with increasing feedback frequency, as is required to linearize the motor response with frequency. The ac path includes a perfect differentiator which provides a first derivative of the input over a frequency range of from essentially zero to 200 hertz. The combined outputs of the multiplier and amplifier-differentiator elements produce a unidirec' tional feedback voltage which represents the equation quantity VF (lR jK w). The combined circuit gain required to produce suspension against gravity accounts for the constant K in the equation. The varying frequency voltage required for propulsion at speeds upward from zero is provided by a constant amplitude variable frequency three phase oscillator, the amplitude of each phase of which is increased as a function of the frequency by an imperfect differentiator for each phase to compensate for the increase in motor impedance due to the increase in inductive reactance with frequency. The differentiation is imperfect to assure an output at zero frequency and thus provide the magnetic flux required in the motor-to-rail gap to establish suspension when the system is in operation at standstill. The unidirectional variations of the feedback voltage are made essentially to modulate the imperfect differentiator outputs for each phase, it being a first input to each of three multipliers for the three phases, the other input for each of the multipliers being one of the differentiator outputs. Each of the multiplier outputs gives the product of the feedback voltage and the instantaneous value of each of the phased voltages in accordance with the three-phase variation thereof. The output from each multiplier for each phase passes into a controllable power supply having three outputs, one for each of the phased windings of the motor, the voltage output of each being controlled accord ing to the variation of three phase electrical energy with time, including the special case of zero frequency wherein the phased outputs constitute frozen" instantaneous values which do not vary with time until a frequency variation is again produced to provide propulsion. Highly efficient controllable amplifiers of high power capabilities such as the Class D type or the gated-silicon-controlled-rectifier type are employed to provide propulsive power for passenger-carrying railroad car type vehicles weighing thousands of pounds. An inertial or accelerometer type sensor which senses any acceleration in the vertical direction of the motor and its supported mass as the same moves up and down in space is preferred since it provides signals indicative of such movements without regard to the motor-rail spacial relationship. Thus, the accelerometer sensor is not sensitive to irregularities in the track and does not pass them on to the passengers in the form of vibrations or jolts. On the other hand, the gain of the displacement channel is reduced as a function of gap change frequency and only a mean gap is maintained by the displacement sensor. An alternative acceleration feedback sensor which senses relative acceleration of the suspended mass with respect to the rail is suggested for use as a substitute for the inertial-reference accelerometer in the feedback circuit when it is desired that the vehicle closely follow the rail for technical reasons or to avoid the higher costs of the inertial accelerometer. Hall-effect transducers which sense the flux in the air gap are suggested as a suitable sensor for such purpose. The feedback loop that includes the inertial sensor makes a second order correction to the overall feedback network of the order of db of feedback over the frequency of interest which is from 0.5 to 5 hertz. This makes the system insensitive to second order variations such as changes in coil resistance with temperature and variations in the d.c. gain and ac. gain of the feedback network which may change from day to day with weather changes, and for other reasons. As aforementioned, the force exerted magnetically by the motor to provide suspension varies as the square of the motor current and inversely as the square of the gap length. This is a non-linear relation. However, the d.c. flux in the air gap remains the same for different gap lengths when the current to gap ratio remains constant as it does, for example, when the current is doubled when the gap is doubled, the magnetizing force or ampere turns per unit length of gap remaining the same. Non-linear elements in the feedback circuit, such as the square-rooter circuit, linearize the voltage vs. force function for all gap lengths and thus allows the dynamic response of the feedback signals to be constant and provides constant stability for the system. The resultant linearization of the feedback circuit also provides constant gain at all operating frequencies of the polyphase power and corresponding propulsive speeds. This assures a smooth ride at all vehicle speeds. The smoothness of the ride, moreover, can be adjusted by adjustment of the feedback circuit, it being unnecessary to change the motor or any related parts of the structure. The feedback circuit assures the stability of the vehicle with respect to the track, compensates for varying passenger loading and thrust due to wind, and gradually corrects for unevenness of the track. The feedback circuit also inherently maintains lateral stability and any lateral perturbation is restored in a damped manner without overshoot. SUMMARY OF THE lNVENTlON The present invention relates generally to the transportation field and more particularly to a high speed tracked transport vehicle which uses the same linear electric motors for both suspension and propulsion, such as disclosed in the aforesaid copending parent application of James A. Ross, and which additionally may use such motors for vehicle guidance and banking. The present invention follows the basic principles and incorporates the fundamental features of the parent application while providing improvements in the composition and functioning of the non-linear feedback circuit which controls both the magnitude and frequency of the motor terminal voltage to achieve suspension and propulsion at selected propulsion speeds, or suspension alone at standstill. Specifically, the feedback control circuit of the present invention, while employing circuit elements for performing the multiplications and summations of the voltage vs. force function equation: as in the parent application, expresses this equation in the form where: F is the attractive magnetic force E is the terminal voltage I is the air gap length R is the winding resistance f is the propulsion frequency in hertz K K are constants j is the reaction symbol. The square root function V? is developed from the sensor signal paths, as in the parent application. The multiplication of this function times displacement and propulsion frequency, however, are performed in the propulsion frequency control channel. A first multiplier produces the product of the VT function times each phase of a constant applitude three phase voltage of selected frequency which may be zero at standstill or a specific frequency corresponding to a desired propulsion speed. This product which represents K V? in the equation is the input to a second multiplier operating in parallel with a perfect differentiator. The second multiplier produces the product K 1 VT IR and the differentiator produces the product K VI' K f, and these products are summed and provided as the input to the three phase controllable power amplifiers which supply the terminal voltages to the three phase motor windings. This improved feedback circuit arrangement eliminates the imperfect differentiator of the parent application which increased the amplitude of the oscillator signal, of each phase as the oscillator frequency increased. This required that the following multipliers be operated over an extremely wide dynamic range. A perfect differentiator which in the circuit arrangement of the instant case provides the voltage vs. frequency function, follows the multipliers and thus permits the motor terminal voltage to be increased with frequency for any desired propulsion speed without exceeding the dynamic operating range of the multipliers. The non-linear feedback circuit disclosed and claimed in the parent application is a species of the generic invention herein disclosed and claimed wherein an electroresponsive force field generator and a coacting member separated or spaced therefrom are attracted toward each other by the force field set up between them and are held separated from each other at a selected gap by an opposing force, it being the function of the non-linear feedback circuit to so adjust the voltage of the electroresponsive force field generator that the force produced by it is at all times sufficient relative to the opposing force to restore and maintain stable equilibrium at the selected gap. In the species of the invention disclosed and claimed in the parent application, the magnetic force field and feedback circuit arrangements are made to be responsive to opposing force relationships wherein the opposing force is gravity and other acceleration forces tending to upset the stable equilibrium of the suspended vehicle and its support motors. In the present invention, force field and feedback circuit arrangements embodying the generic invention are also made to be responsive to laterally directed displacement and acceleration forces on the vehicle such as may be caused by wind loads or may occur during turning movements, to thus accomplish controlled magnetic guidance and banking of the vehicle. The foregoing and other features of the invention will become more fully apparent from the following detailed description with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a schematic view of a force field generator embodying the voltage vs. force functions employed in the present invention; FIG. 2 is a schematic view of a tracked vehicle and its support motors for achieving magnetic suspension and banking in accordance with the feedback principles of the present invention; FIG. 3 is a schematic view of a tracked vehicle and its linear motors for achieving suspension and guidance of the vehicle; FIG. 4 is a block diagram of a feedback control circuit for supplying the motor terminal voltages E and E of FIG. 2; FIG. 4A is a schematic circuit diagram of one embodiment of the block diagram of FIG. 4; FIG. 5 is a complete block diagram of the electrical system for achieving suspension and propulsion of a tracked vehicle and its linear electric support motors; FIGS. 6A and 6B, taken together, constitute a schematic circuit diagram of one embodiment of the block diagram of FIG. 5; FIGS. 7A and 7B are graphs showing speed vs. frequency relationships for synchronous relucatance and inductance motors respectively; FIG. 8 is a plot of the open loop response of the system of FIGS. 6A and 68 to a disturbing force; and FIGS. 9 and 10 are graphs showing curves which represent the characteristic response of the system to load and track disturbances. DETAILED DESCRIPTION Referring to FIG. 1, an electroresponsive force generator M and a member R are separated physically by the air gap distance or length l. Generator M and member R are mutually attracted toward each other as indicated by the force field f set up therebetween by generator M when a voltage E supplies a I thereto, the attractivc force being designated F Assuming the member R to be fixed, that is, nonmovable, the force F is directed to depict that the generator M is attracted toward member R. When the generator M, for example, is an electromagnet, or an electric linear motor, and the member R, for example, is a ferromagnetic rail, the force F varies as the square of the current flowing in the winding of the electromagnetic device M and inversely as the square of the air gap length 1 between the device M and the rail R in accordance with the equation: where: A is the area of attraction in square centimeters N is the number of turns in the winding of electromagnetic device M Equation (l) is derived from two basic equations expressing magnetic circuit principles, one being that the magnetic force F between two parts of a magnetic circuit varies as the product of their area of attraction A and the square of the magnetic flux density B at their interface: F =AB /(81r X 981) where: B is the flux density in gauss F is the force in grams and the second principle being that the magnetizing force H required to set up a flux in an air gap 1 between the parts is equal to the flux density 8: where: NIH is ampere turns per centimeter l is air gap length in centimeters B is flux density in gauss Combining equations (1 and (1 F [A/(81r X 981)] (Mr-NI/IOI) [A/(81r X 981)] (41rN/IO) (I/l) l /l) 1( (1) It will be noted that the magnetic force F is the same for any air gap within a wide range of air gaps as long as the ampere turns per unit length or the air gap, namely, the ratio NIH, is constant. Thus, for example, the attractive force will remain the same if the current is doubled when the gap length is doubled. The linear relationship between the current and gap length is apparent from a re-write of equation (1): V FMD/ V 1 where the current varies directly with the air gap and as the square root of the force F The current varies directly as the voltage E across the winding of the electromagnetic device M and can be changed by changing the voltage: where: R jmL is the winding impedance R is the winding resistance L is the winding inductance j is the reactive symbol to is Zarf fis frequency in hertz (cps) E is the voltage across the impedance. Combining equations (1,) and (2): =l( VFM 1) +j The inductance of an electromagnetic device M separated from a ferromagnetic member R in a magnetic circuit the therewith having an air gap 1 therebetween varies inversely as the length of the air gap: Combining equations (2,) and (3): E= K, VTJ R K,,jw) E=K3 VT IIIHX, VFJK w In order to keep equation (4,) in balance, any changes in F,,,, and/or in l in magnitude and rate must be accompanied by a change in E, and any such changes in E must be both in magnitude and rate of change, the latter giving rise to a frequency component in E, and this, in turn, causing the reactive voltage component K V F M K jw to increase directly in proportion to the increase in the frequency. The voltage E, of course, must increase, as required, to compensate for the increase in the winding impedance due to the increase in inductive reactance with frequency. At zero, or very low frequencies, the winding impedance is substantially resistive, and the voltage E is substantially equal to the resistive voltage component K VFMIR, the voltage E in such case being characterized only by its magnitude, being essentially d.c. Referring again to FIG. I; assume that an opposing force F is acting on the force generator M in a direction opposite to the attractive force F If the attractive force F,, is made to equal the opposing force F the separation distance I will be constant and the generator mass M will be in a state of stable equilibrium. In the aforesaid parent application Ser. No. 131,041, a tracked, high speed vehicle is disclosed having four linear electric motors mounted at the four corners thereof for suspension and propulsion of the vehicle from and along the track by magnetic attraction. This arrangement is disclosed, in part, in FIG. 2, wherein the rear motors M, and M, are shown in spaced dependent relation to their respective support rails R, and R being separated therefrom by the air gaps l, and 1 The rails are supported in fixed relation on the track generally designated T. The vehicle V which moves along the track T is supported by and secured to the front and rear motors of which the rear motors M, and M, are shown secured to the vehicle as by the mounting brackets schematically designated 12, and b The magnetic attractive forces F and F, respectively of the motors M, and M, are opposed by the forces F and F These opposing forces may be considered generally to be acceleration forces expressed by the equation: F= Ma where: F is the acceleration force M is the mass of the body acted upon by the force F a is the acceleration of the body represent W When the air gaps l, and I are static, there being no change in the gaps, the corresponding forces F and F represent the weights supported respectively by the magnetic forces F and F of motors M, and M Weight W is the force which gravitation exerts upon a body and is equal to the mass of the body times-the local acceleration of gravity g, thus: F=Ma as before set forth in equation (5). Now with g substituted for a, and W substituted for F: W Mg and M W/g Motors M, and M by their attractive forces F and F support their own weights W and W and one fourth the weight Wv/4of the vehicle, thus: Vehicle V carries a pair of position or placement sensors S and S which respectively sense the length of the air gaps l, and 1 associated with motors M, and M Signals from these sensors operate in their respective feedback circuits, subsequently to be described, to produce voltages therein which represent the attractive forces F and F required to produce the voltages E, and E: for support of the motors M, and M at selected gaps l, and I such representative voltages corresponding to the voltage component F of equation (4). When it is desired to maintain constant motor gaps notwithstanding changes in passenger loading, or, wind loading, on the vehicle, such changes will, in turn, change the opposing forces and the gaps. The position sensors, however, sense the gap changes and produces signals which are integrated to produce appropriate adjustment in the feedback voltages representing the forces F and F These signals, moreover, are differentiated to provide velocity feedback for dampening adjustment of these voltages. Vehicle V further carries accelerometer sensors S and 8, which are made to sense up and down accelerations of the vehicle caused, for example, by variations in the vertical radius of curvature of the track to thus produce signals for the further adjustment of the feedback voltages representing the magnetic forces F and F and, further, by the integration of such signals, to develop velocity feedback voltages for the development of the reactive voltage component of equation (4). A second pair of accelerometers S and 8 are carried on the vehicle and directed to sense lateral accel erations occuring during turning movements of the vehicle so that signals therefrom may be used to produce relative adjustments of the gaps l and I for banking purposes, thereby obviating the need for banking the track and rails R and R Thus, for example, referring again to FIG. 2, and assuming that the vehicle V is caused to move in a turn to the left, the sensors S and S will sense acceleration forces directed to the right of the vehicle, and signals from sensor S associated with motor M will cause a decrease in gap 1 and sensor S associated with motor M will cause an increase in gap 1 thereby to effect the desired banking to negotiate the left turn. Referring now to FIG. 3, there is shown thereon a vehicle V having three linear electric motors M M and M of which M is used for suspension and propulsion, or for suspension alone, and motors M and M are used for guidance and propulsion, or for guidance alone. Their respective force fields are designated f ,f and f and are generated in relation to their associated fixed rails R R and R in the same manner as the force fieldsf and f of motors M and M of FIG. 2. The gaps l and will normally be equal so that the magnetic attractive forces F and F will also be equal and, being opposite, will present the required opposing force, each to the other, to maintain balance. In this case, the attractive forces, at equal gap lengths 1 1 may be set at any desired strength upwards from zero. At zero force setting, of course, there would be no force fieldsfl and f Considering first the zero force field setting at equal gaps, it will be presumed that provision is made, as subsequently described, for producing either of the forces F and P as its associated motor M M is moved with the vehicle to increase its gap 1 or 1 above the equal gap setting In such case, the generated attractive force will setting. in proportion to the increase in gap and will oppose the acceleration force on the vehicle which caused the particular gap 1., or I to increase. In this case, one of the accelerometer sensors S or S will aid in the development of the attractive force required to overcome the lateral acceleration force. When the acceleration ceases, the other sensor will generate an opposing attractive force to control the deceleration of the vehicle upon return of the same to the equal gap condition. When it is desired to use the force fieldsf, and f., for propulsion, in addition to guidance, some suitable strength of opposing attractive forces F and F is maintained at all times. The feedback circuits of FIGS. 4 and 4A are taken from the parent application and are incorporated in this disclosure as embodiments of suitable circuitry for developing the magnetic attractive forces F to F of FIGS. 1 to 3, the feedback circuits for this purpose performing the multiplications and summations of equation (4). Other disclosures of the parent application are incorporated herein by reference to that application. Referring first to FIG. 4, the accelerometer 20 represents any of the accelerometer sensors S and S of FIG. 2 and S of FIG. 3 which have a mass of relatively appreciable magnitude disposed to be sensitive to vertical accelerations. It also represents either of accelerometer sensors S and S as the same are employed in the FIG. 2 and FIG. 3 arrangements to sense lateral acceleration and thereby provide inputs to the feedback circuits of motors M and M and motors M and M respectively, in the same manner as sensors S and S provide inputs to their respective feedback circuits. Accelerometer 20 may be of a piezoelectric type, such as Endevco type 2200, or a servo type such as developed for space use which does not have the very low frequency noise and random variations characteristic of the piezoelectric types. Signals from accelerometer 20 pass through a compensating network 21 which alters the frequency vs. amplitude response thereof to provide about 10 db of feedback within the range of frequencies of the order of h to 5 hertz to make the suspension system insensitive to second order variations such as variations in motor magnetic structure, variations in the a.c. resistance of windings, winding resistance variations with temperature, d.c. and a.c. gain variations in the feedback network, and instability at certain gap lengths. Network 21 also integrates the accelerometer signals to provide velocity feedback which is effective over a range of frequencies of the order of 4 to 10 hertz. Position transducer 22 is a sensor element which provides length of gap information and represents any of the length of gap sensing position or placement sensors S to S of FIGS. 2 and 3. Sensor element 22 may employ mechanical contact, or optical, sonic or other suitable means to accomplish measurement of the gap which may range from substantially zero to one-half inchesv Position transducer 22, for example, may be a linear potentiometer having a mechanical roller which is carried by its slider and urged yieldably into contact with rail 2 whereby the potentiometer is adjusted as the roller and slider are moved in response to any changes in the motor-to-rail gap as the roller rides along the rail. Motor 1 and rail 2 represent the various motor and rail combinations disclosed in FIGS. 2 and 3, and the potentiometer may be suitable carried either by the vehicle or on the particular motor with which it is used. An optical displacement sensor 22 may be arranged with a photocell on one side of the motor-rail gap and illumination means on the other so that more or less light is caused to enter the photocell to change its electrical response as a function of gap length. An ultra-sonic sensor 22 may be arranged to produce ultra-sonic sound reflections from the rail so that detected changes in phase of the transmitted and reflected sound may provide a suitable measure of gap length and changes therein. Signals from position transducer 22 are supplied to a compensating network 23 and also to a multiplier 25, subsequently to be described. Compensating network 23 provides an adjustable reference for the gap measurement in electrical terms, that is to say, this reference may be adjusted to preset a selected gap which the position sensor will seek. The compensating network 23 also has provision for adjusting its position signal to zero for a selected gap, or to some strength other than its normal signal for that gap for purposes of the FIG. 3 vehicle guidance operation, aforedescribed. The compensating network 23, moreover, has provision for receiving signals from the accelerometer sensors S and S of FIG. 2 to provide banking adjustment of gaps l and 1 as aforedescribed. Network 23, in addition, provides velocity and integrated displacement feedback. Integration is performed over a range of frequencies from to about 1.2 hertz, and differentiation is performed over a range of frequencies from 1.2 to about 5 hertz. Signals from the compensating network 23 pass to compensating network 21 where they are combined, that is, are algebraically summed with the acceleration signals for common amplification to provide a forceproportional voltage representative of the function F in equation (4). This force-proportional voltage operates in the whole feedback system to enable motor 1 to produce a magnetic force P of l g, that is, an equal and opposite force in relation to gravity whereby the motor-vehicle mass is magnetically suspended. As hereinbefore discussed, the magnetic force F is proportional to the square of the motor current which is a non-linear relationship which must be linearized in order to provide feedback stability. Linearization is achieved by taking the square root of the forceproportional voltage output of network 21 in accordance with the mathematical requirement expressed by the function V F in equation (4). This required square-rooting of the forceproportional voltage output of network 21 is performed by the square-root circuit 24 which is typically an operational amplifier entity employing non-linear transistor characteristics to give an electrical output that is the equivalent of the square-root of the electrical input. The length of gap and square-root outputs of position transducer 22 and square-root circuit 24 are applied as first and second inputs to multiplier 25 and multiplied thereby to provide a product which corresponds to the product requirement VT"; X lR of equation (4). Multiplier 25 is an operational entity whose output is the product of two electrical inputs, and it thus provides an output voltage that increases with gap length. The electrical path through'multiplier 25 is independent of frequency so that an output is produced thereby at zero frequency which is the condition when the gap length is constant between the motor 1 and rail 2. The output of square-root circuit 24 is also applied to perfect differentiator 26 which is an amplifier having a resistance-capacitance circuit to perform electrical differentiation and thus provide the first derivative of its input over a frequency from substantially zero to 200 hertz. The capacitor is not shunted by any conductive path and so the output of the differentiator is zero for zero frequency, that is, for d.c., which is the condition when the motor-to-rail gap is constant. The amplifier-differentiator circuit of perfect differentiator thus produces and provides an ac. path for the voltage which represents the reactive componentj VHX K w of equation (4). The output of differentiator 26 thus provides a voltage which increases with the feedback frequency, that is, the frequency of the sensed signals. The outputs from multiplier 25 and differentiator 26 are summed algebraically to provide to the input of amplifier a feedback control voltage which represents the sum of the resistance and reactance voltage components of equation (4), namely, After amplification at level raising amplifier 95, and gain setting potentiometer 96, the feedback control voltage is applied to the controllable power supply 38 which is a power amplifier of the Class B type for low power output of about one kilowatt or of the Class D type or gated-silicon-controlled-rectifier type for higher power outputs. The basic source of power for these amplifiers, for example, is an external power supply 39 having 3rd rail connections 39' with the vehicle V. Controllable power supply 38 provides the terminal voltage E applied to motor 1 to develop the magnetic attraction force F The combined gains of potentiometer 96 and the voltage gain of amplifier 38 determines the constant K in equation (4) such that the motor terminal voltages becomes: which is equation (4). The motors may be built in a large range of sizes, but as an example, for a 30 inch long motor capable of supporting 2,000 pounds, the several aforementioned constants may have values expressed in inches as follows: Referring now to FlG. 4A, accelerometer 20 is a piezoelectric accelerometer of the Endevco type 2200 and is shown to have a mass 40 of appreciable magnitude which is so disposed on the vehicle V or on motor 1 of FIG. 4 so as to be sensitive to vertical acceleration to thus enable the accelerometer to perform its required feedback functions, as aforedescribed, as well as to provide the soft ride features which characterize this invention. Amplifier entities 41, 42 and 43 comprise elements of compensating network 21. Amplifier 41 is a known impedance-matching amplifier and is required to reduce the very high impedance of a piezoelectric accelerometer to an ordinary circuit value. The amplifier is a Motorola MC l456G integrated circuit amplifier, or an equivalent operational amplifier. It is connected as a source-follower and has no gain, nor phase shift. The input circuit includes resistor 44, of 250 megohms resistance, connected from amplifier terminal 3 to ground to provide an input bias current path for the amplifier. This is shunted by capacitor 45, of 1,000 picofarads (pf) capacitance, which acts as a padding capacitor to the stray capacitance of the input lead from the accelerometer to terminal 3. The several terminals of the integrated circuits, operational amplifiers, etc. have been given small numerals, corresponding to those given by the manufacturer on the device itself. The internal circuits for these devices are known from the manufacturers catalogs. Amplifier 41 has a feedback circuit between its terminals 6 and 2 comprised of a 250 megohm resistor 46, shunted by capacitor 47, of 1,000 pf capacitance. Terminal 7 is connected to a direct current energizing power source having a voltage of the order of 15 volts, while terminal 4 is connected to a similar source having the opposite polarity of- 15 volts. Each of these connections is filtered by a 0.1 microfarad (pf) capacitor connected therefrom to ground. Capacitor 48, of 200 uf capacitance, is connected to the output terminal 6 of amplifier 41 to restrict the low frequency signal amplitude from the accelerometer with a roll-off starting at 0.13 hertz. This removes the noise" from the accelerometer circuit at low frequencies. Resistor 49, of 6,800 ohms, connected in series with capacitor 48 and with resistor 50, of 0.2 megohms, sets the accelerometer channel gain. Amplifier 42 provides an accelerometer channel gain of 200/6.8 30. The second terminal of resistor 49 connects to input terminal 2 of amplifier 42, a Motorola MC 1741CG integrated circuit or equivalent. There is also another connection to terminal 2; from the output of the gap-length sensor circuit, to be later described. Amplifier 42 functions as a simple amplifier, having a feedback circuit connected between input terminal 2 and output terminal 6 comprised of resistor 50, of K ohms, shunted by capacitor 51, of 1,500 pf. The voltage supply and grounding connections are standard and are known. The gain of amplifier 42 is approximately 30, up to an upper cut-off frequency of 8 hertz. The algebraically summed signals from the accelerometer and gap-sensor now pass into terminal 2 of amplifier 43, of MC 1741G type, through resistor 53, of 30,000 ohms resistance, which is used for gain setting. The feedback circuit of amplifier 43 is the same as that of amplifier 42; i.e., resistor 50 of 0.2 megohm and capacitor 55 of 0.2 microfarad. Supply circuits are conventional. The gain of amplifier 43 is approximately 7, with an upper cut-off frequency of 4 hertz. Capacitor 55 acts as a partial integrator upon the acceleration feedback signal. This provides a quasivelocity feedback signal and prevents an oscillatory condition otherwise existing because of an 180 phase shift between acceleration and displacement. This is effective from a frequency of the order of 10 hertz down to 4 hertz. Below 4 hertz differentiation of the position (displacement) feedback occurs to provide the velocity component. This is produced by capacitor 58 in the input circuit to amplifier 61, hereinafter to be described. The combination of these two signals gives control of the phase of the feedback circuit so that displacement information can be fed into a system that has feedback from an accelerometer included in it. Actually, four aspects of feedback are present in the system to give a high degree of stability; the integral of displacement to bring the system back to a mean gap length after load changes in the vehicle, displacement feedback to stabilize the integral displacement feedback circuit, velocity feedback to stabilize and damp the displacement feedback, and acceleration feedback to stabilize and damp the velocity feedback. At the same time the acceleration feedback corrects second order non-linearities in the linearizing circuit comprised of square-root circuit 24, multiplier 25, and differentiator 26. This mode of operation is required for any system of the nature of a magnetically supported railroad, where the air-gap length is purposely allowed to vary to accommodate rough track." The gap is brought back to a mean value gradually, to provide a soft" ride. Position transducer 22 is shown to be a potentiometer 56 connected to ground and shunted by a source of voltage such as battery 57. Its slider or wiper carries the aforedescribed rail-engaging-roller, not shown. Typically, battery 57 may have a voltage of 10 volts and the travel of the slider have a travel of one-half inch. This range of travel normally covers the operating change in the length of the air gap, the preferred length of which is one-quarter inch or perhaps slightly less. These constants give a voltage of 20 times I; i.e., 20 times the length of the air gap as measured in inches. Battery 57 may, alternately, be a regulated power supply of the same voltage. The output from position transducer element 22 passes to compensating network 23. Capacitor 58, of 0.1 pf, in series with resistor 59, of 4,700 ohms, all shunted by resistor 60, of 1.5 megohms, are the initial elements of compensating network 23. This network has a resistive impedance of 1.5 megohms from d.c. to 1.2 hertz, decreasing to about 4,700 ohms at 350 hertz. This provides a velocity signal (i.e., differentiated displacement) at frequencies above 1.2 hertz. This output passes to input terminal 2 of operational amplifier 61, an MC 1741G type. Both input terminals 2 and 3 of this amplifier are individually returned to ground through resistors 62 and 63, of 22,000 ohms, to provide a path for the input bias currents of this amplifier. The feedback circuit for amplifier 61 is comprised of resistor 64, 10,000 ohms, in series with capacitor 65, uf; with resistor 66, 100,000 ohms, shunted across the capacitor. This gives an impedance of 110,000 ohms for d.c. and of 10,100 ohms at 14 hertz, approximately. This results in the gain of amplifier 61 at frequencies below 1 hertz being considerably greater than at higher frequencies. This is to increase the loop gain at low frequencies and to provide an integral of displacement function as a feedback signal to gradually correct for changes in load. Since the purpose of the feedback system is to correct for changes in loading of the vehicle, wind pressure and unevenness of the track, the frequency of the feedback signals is very low with respect to the frequencies handled by usual electrical networks. Feedback must be maintained at zero frequency (d.c.). The range of frequencies of maximum interest extends from 0 to 5 hertz for the displacement channel and from 0.3 to 30 hertz for the accelerometer channel. Potentiometer 67, of 50,000 ohms total resistance, is connected between positive and negative voltage supply sources, each of which has a voltage of 15 volts with respect to ground. Bypass capacitors, of 50 at, are provided from each to ground to remove extraneous variations, as known. Potentiometer 67 provides a voltage adjustment for any initial offset voltage in amplifier 61. Its slider is connected to input terminal 3 thereof, through isolating resistor 67 of 1 megohm. An additional input to terminal 3 of amplifier 61 is from potentiometer 68, of 2,000 ohms, and passes through attenuating resistor 68' of 1.5 megohms, to provide a reference displacement proportional voltage. Amplifier 61 generates an output voltage proportional to the difference between the voltage reference input to resistor 68' and the input to resistor 60, which is the voltage from displacement transducer 22. Voltage dropping resistor 69, connected in series with potentiometer 68 from the positive voltage connection to ground, typically has a resistance value half as great as the resistance value of potentiometer 68. The output of amplifier 61, from terminal 6, passes to terminal 2 input of amplifier 42 through resistor 66', of 22,000 ohms, a summing resistor. It is at this point that compensating network 23 joins that of 21, for the inclusion of amplifiers 42 and 43 in common. The output from amplifier 43 is taken from terminal 6 and passes through diode 54 with the cathode thereof connected to the terminal so that only negative signal variations will be passed on. Additionally, diode 52 is connected as a feedback element on amplifier 43 to prevent positive voltage excursions. Only negative voltages are allowable at the input of the square-root circuit which follows because inversion therein to positive signal polarity occurs before the square-root function takes place. This prevents taking the square-root of negative numbers, which are imaginary. Herein the square-root circuit becomes inoperative because feedback of positive polarity drives it to current saturation. The force-proportional voltage output at amplifier 43 is made to be linearly proportional to a force between the load mass and the rail. Referring to equation (4), to develop the proper voltage E to be applied to the motor windings, the force-proportional voltage is to be square-rooted and multiplied by (IR +jK.,w). The first electrical device to significantly execute the mathematics of linearization is the square-root circuit 24. This may be an integrated circuit 24', of type MC 1494L (Motorola) normally known as a multiplier of electrical signals fed into it. This multiplier is placed in the feedback circuit of an operational amplifier 70 and the square-root of the signal input is provided therefrom. The theory and practice of this square-root performance is known, being set forth in the (Motorola) manufacturers, Specifications and Applications Information, October 1970 DS 9163. Operational amplifier 70 may be an MC1741G integrated circuit. The output from the previously mentioned diode 54 is connected to gain-setting resistor 71, of 52,000 ohms, and also to ground through resistor 72, of 1,000 ohms. The latter resistor provides a path for any leakage current in diode 54. The input from resistor 71 is connected to terminal 14 of multiplier 24' and also to terminal 2 of amplifier 70. The output of this amplifier, at terminal 6, is connected to terminals 9 and 10 of the multiplier and also to ground by a small capacitor 73, of 10 pf capacitance, in series with resistor 74, of 510 ohms. Zener diode 75 is also connected between the output of amplifier 70 and ground to prevent accidental latch-up (malfunctioning) of the circuit. A type 1N524l may be used. The feedback path for amplifier 70 is the multiplier 24' connected between input terminal 2 and output terminal 6 of amplifier 70 and terminals 9 l and 14 of the multiplier. Capacitor 76, of pf capacitance, is connected between amplifier terminals 2 and 6 for the purpose of phase-compensating the amplifier. Input terminal 3 thereof is connected to the slider of potentiometer 77, which potentiometer has a resistance of 20,000 ohms. This provides a voltage reference for the amplifier. This potentiometer is connected in parallel with a duplicate potentiometer 78, which is connected between terminals 2 and 4 of multiplier 24'. A resistor 79, of 62,000 ohms, and a resistor 80, of 30,000 ohms, are respectively connected between terminals 7 and 8 and 11 and 12 of multiplier 24'; and a resistor 81, of 16,000 ohms, is connected between terminal 1 and ground. A voltage source, typically of 15 volts of positive polarity, is connected respectively to terminals 7 and 15 of the amplifier and multiplier, whereas a voltage source typically of 15 volts of negative polarity, is respectively connected to terminals 4 and 5 of the amplifier and multiplier. At the input to the square-root circuit 24, a negative signal voltage of 4 volts produces in the whole system a force of l g; that is, there is produced an equal an opposite force in relation to that of gravity, whereby the motor-vehicle mass is magnetically suspended. With the connections and voltages given, the output of the square-rooter circuit 24 at terminal 6 of amplifier is the square-root of 10 times the input. This is the square-root of 10 in efiective amount and is taken into consideration in establishing the whole feedback gain. Mathematically, such functioning of the electrical circuits is accounted for in the values of the several K constants. The output from the square-root circuit is connected to the input of multiplier 25 to perform the IR portion of equation (4), and also to the input of perfect differentiator 26 to perform the jK w term. The input to multiplier 25 is terminal 10 of multiplier 25' and to the perfect differentiator is capacitor 83 through resistor 90. The above input to the multiplier may be termined the x input. The y input is connected to input terminal 9 and comes directly from potentiometer 56 of position sensor 22 through resistor 84 for isolation. The resistance value of resistor 84 may be 0.1 megohm. Both input terminals 10 and 09 are also connected to ground through capacitors 85 and 85, of 10 pf capacitance, in series with resistors 86 and 86, of 510 ohms resistance, respectively. These prevent high frequency parasitic oscillations. Resistors 79, and 81 are identical in resistance value and connection to multiplier unit 25 as these were with respect to unit 24 of square-root circuit 24. So also are potentiometers 77' and 78', except that the resistance value of potentiometer 77 is 50,000 ohms. An additional potentiometer 87, of 20,000 ohms, is connected across terminals 2 and 4 of units 25', with the slider connected to terminal 6. These three potentiometers are adjusted to give proper x, y and output offset bias, as outlined in the manufacturers Specification and Application Information previously referred to. An MC 1741G operational amplifier 89 coacts with multiplier unit 25' to give the complete multiplier 25. Feedback capacitor 76', of 10 pf, is connected to the amplifier at terminals 2 and 6, and is shunted by resistor 88, of 52,000 ohms. Positive and negative voltage supply sources are as previously described. Perfect differentiator capacitor 83 has a capacitance of 0.2 pf. It is in series with resistor 90, of 1,000 ohms resistance. The capacitor connects to input terminal 2 of operational amplifier 91, which may be a MC 17416 type. The feedback circuit of this amplifier is comprised of capacitor 92, of 0.0068 at, and resistor 93, of 0.1 megohm, in parallel and connected between amplifier terminals 2 and 6. Second input terminal 3 is grounded. Positive power supply voltage is connected to terminal 7, while the same in negative polarity is connected to terminal 4. This amplifier-differentiator provides the first derivative of the input over a frequency range of from essentially zero to 200 hertz. The output from amplifier 91 is taken through summing resistor 94, of 62,000 ohms, to input terminal 2 of amplifier 95. The latter mainly raises the signal level, after providing for the summing, for parallel feeding all of the three-phase multipliers that follow. Similarly, the output from multiplier operational amplifier 89 is taken through summing resistor 94, of 62,000 ohms, and connects to input terminal 2 of amplifier 95. This provides the total electrical representation of FUR jK w) of equation (4). The feedback circuit 92', 93 of amplifier 95 is the same as the feedback circuit 92, 93 of amplifier 91; also, input terminal 3 is connected to ground and the power supply connections are the same as for amplifier 91. The output at terminal 6 of amplifier 95 passes to potentiometer 96, which is grounded, as shown. The slider of the potentiometer is connected to the controllable power amplifier 38 of FIG. 4 which provides a motor terminal voltage and motor current which, in turn, produces a magnetic force F equal to 1 g when a negative voltage input to the square root circuit is 4 volts. Considering operative details of the feedback circuits of FIGS. 4 and 4A which are designed to provide a smooth ride in the transportation of people, adjustment of the suspension gap length l is accomplished by varying the voltage at input 3 of amplifier 61, as determined by the setting of potentiometer 68. The gain of amplifier 41, of course, is unity. The gain of amplifier 42 is approximately 30, up to an upper cut-off frequency of 8 hertz. The gain of amplifier 43 is approximately 7, with an upper cut-off frequency of 4 hertz. When the output of this amplifier is -4 volts, the force exerted by motor 1 is l g; i.e., the vehicle is suspended. In forming the feedback circuits according to this invention use is made of the fact that the ac. flux density in the motor to rail air-gap does not vary if the length of the gap changes. This flux density is affected only by the value of the volts-per-turn in the magnetic structure, and so the voltage only in any given magnetic structure. Multiplier 25 provides compensation for d.c. flux density changes with change in the length of the aingap. Position transducer element 22 senses the dc gap length and the gain of the feedback circuit is modulated to increase with gap length, maintaining the overall system gain, including the characteristics of motor 1, constant. In a typical motor the inductive reactance of the coils is equal to the resistance of the coils at a frequency of the order of 2 hertz. The inductance varies inversely with the length of the air-gap. Proper feedback performance is maintained, however, by provision of the dc. path through multiplier 25 and the ac. path through perfect differentiator 26. The exciting current through the motor coils increases with gap length, thus the dc. flux remains constant. In practical operation, this necessary mode of operation requires that extended periods of suspension at long air-gaps cannot be allowed. It is good practice to rate the amplifiers comprising controlled power supply 38 for the average length of gap encountered and to return the vehicle to that length within a few seconds without causing an artificial jolt after a gap-lengthening perturbation. The force exerted magnetically by the motor in providing suspension varies as the square of the current in the windings of the motor. This is a non-linear relation. Non-linear elements in the feedback circuit, such as the square-root circuit 24 of FIGS. 4 and 4A make the output of the feedback circuit linear, from a voltage input to a force output. This results in a constant feedback loop gain at all values of alternating current frequency and at all gap lengths of the motor to the rail. Moreover, this results in a uniform easiness of ride. A typical variation of gap may extend from percent to nearly 100 percent of a normal value of 1.0 inch. To prevent the motor from actually contacting the rail, a flat automotive type brake shoe may be arranged to bear upon the rail instead, as a safety measure. Because an inertial reference, accelerometer 20, is used in the vertical plane, the feedback circuit ignores small track irregularities and does not pass them on to the passengers in the form of vibration or quick jolts. Only a mean gap is maintained by the displacement (position) transducer 22. Referring again to the FIG. 4A showing of compensating network 23, a selected gap 1 for suspension would normally be set by adjustment of potentiometer 68. If the same magnetic forces involved in suspension are applied laterally as in FIG. 3, and the motors M M therein have selected gaps which are equal, the magnetic forces F and F will be equal and opposite and each have a magnitude corresponding to their equal gaps determined by adjustment of their respective potentiometers 68. When it is desired that the forces F and F be generated only upon deviations from the equal gaps, offset voltage adjusting potentiometer 67 is set to reduce the voltage applied to input terminal of amplifier 61 to zero. When it is desired that some magnetic coupling between the rails R, and R and motors M, and M be maintained at all times, as for increased stability in guidance control notwithstanding the accompanying magneti drag, or to provide propulsion, the potentiometers 67 for the respective motors may be set at some suitable value to provide strengths F and F which are greater than zero at equal gap settings. For purposes of achieving banking of the vehicle V shown in FIG. 2, banking control channels for accelerometer sensors S and S respectively comprise its accelerometer and an amplifier such as amplifier 41 together with its associated input and output circuit elements. In such case, the output resistor 49 of each banking control channel is connected as shown in FIG. 4A to the slider of potentiometer 67. Any input from the banking channel will thus alter the gap as long as the lateral turning force sensed by its accelerometer persists. Reference is now directed to FIGS. 5 and 6 which disclose the preferred embodiment of a complete feed back circuit for controlling both the suspension and propulsion of a tracked vehicle-linear electric motor system such as disclosed in FIG. 2. Referring first to FIGS. 5 and 2, the accelerometer 20, as before, provides a signal proportional to an upward or downward inertial force acting on the vehicle V. The position transducer 22, as before, provides a signal proportional to the length of the motor-torail gap 1. The frequency compensating networks 21' and 23' have generally the same composition as their counterpart circuit networks 21 and 23, of FIG. 4, and function, moreover, generally in the same manner to produce at the output of network 21 a force-proportional voltage which represents the quantity F in equation 4). When this voltage is a negative 4 volts, the terminal voltage at the motor windings is just sufficient so that the motor produces a suspension force F of lg. Square root circuit 24" also has generally the same composition and functions generally in the same manner as its counterpart-element 24 in FIG. 4 whereby the square root of the force-proportional voltage represented by V F in equation (4) is provided in its output. For the purposes of explaining the feedback circuit arrangement of FIG. and its manner of functioning to perform the summations and multiplications required by equation (4), this equation preferably is expressed in the form: where: j represents the reaction symbol f is the propulsion frequency K and K have constant values hereinafter to be described. The multiplications and product summations involving the square-root quantity mas set forth in equation (9) are performed in a frequency control channel presently to be described. This channel comprises speed control 30, three phase variable frequency oscillator 31, multipliers 120 to 122 and 135 to 137, and differentiators 143 to 145. Speed control 30 controls the frequency of oscillator 31 which preferably provides the three phase voltages A, (b3 and C, although any number of phases from two upward may be used. The three phases typically are separated by 120 electrical degrees in time, and the circuits and windings 111, 112 and 113, FIG. 6B, are typically star (i.e., Y) connected. Oscillator 31 supplies alternating current at constant amplitude and essentially of sinusoidal shape over a frequency range from zero frequency at standstill to a low audio frequency of the order of 80 hertz at high speed. When the system is in operation at standstill and zero frequency, each phase of the oscillator is required to produce an output to enable the feedback circuit to provide the suspension magnetic flux in the motor-torail gap. It will be understood, however, that the system may be operated at standstill at any frequency providing at least one of the three phase windings is disconnected so that the moving field required for propulsion is not established, and at least one of the phased circuits is in operation to enable the feedback circuit to develop the suspension flux. Oscillator 31 may be comprised of three mechanically driven sine-wave-generating potentiometers to provide relatively low frequencies, the potentiometers being rotated by hand for testing or by a geared-down variable speed motor for relatively low speed transport use. In such case, speed control 30 is a rotatable shaft, hand or motor driven, having three potentiometer sliders attached thereto and angularly spaced apart from each other thereon by electrical degrees. The potentiometers are of circular configuration and suitable for full and repeated rotation of the sliders thereon. The potentiometers preferably are wound to provide sinusoidal voltage variations with rotation of the sliders, the three phase output being provided therefrom when a dc. source is applied across the potentiometers connected electrically in parallel. Oscillator 31, alternatively, may be a function generator such as type 120-020-3, manufactured by the Wavetek company of San Diego, Calif. Such oscillators are voltage responsive, the frequency output increasing with the input voltage. In such case the speed control device 30 may be a potentiometer. The three phase output from oscillator 31, namely, phased voltages (11A, B & 42C, are applied as the X inputs to multipliers 120, 121 and 122, respectively, the aforementioned square root voltage from the squareroot circuit 24" being applied to the Y inputs thereof. The resulting product output of each of these multipliers is a sinusoidal voltage having a magnitude represented by the equation product K VF The outputs from multipliers 120, 121 and 122 are applied, respectively, as the X inputs to multipliers 135, 136 and 137, the aforementioned air gap length proportional signal from transducer 22 being applied to the Y inputs thereof. The resulting product output of these multipliers is a sinusoidal voltage having a magnitude represented by the equation product K VHIR. This voltage is the resistive or non-reactive component of the feedback control voltage E of equation (9A). It will be understood that each of multipliers 120, 121 and 122 and 135, 136 and 137 gives the product of its X and Y inputs whether or not there is propulsion, that is, whether or not, the qSA, B and C voltages are varying sinusoidally or are frozen to instantaneous values at standstill. A common control is thus exercised over the control signals and suspension is maintained both at standstill and during propulsion. It will also be understood that multipliers 120 to 122 and to 137 have substantially the same composition and function as the aforedescribed multiplier 25 of FIGS. 4 and 4A and thus, like multiplier 25, are not influenced by the frequency of the signal inputs thereto since the paths therethrough are essentially do. The varying frequency of the X inputs to the multipliers will thus have no effect on the magnitude of their outputs, and the frequency can be varied as required for vehicle speed control without affecting the feedback voltage control required to maintain suspension. The impedance of the motor windings, however, increases with frequency, as before discussed, and it is necessary therefore to increase the feedback voltage E accordingly so that the motor current will be of the proper strength to keep the suspension flux constant at all motor speeds. This increase in control voltage E as a function of propulsion frequence and speed, is provided by differentiators 143 to 145 which are connected in parallel across their associated multipliers 135 to 137, that is, the differentiators also receive the X input signals to their respective multipliers and supply their outputs to the inputs of the multiplier amplifi- Patent Citations
Referenced by
Classifications
Legal Events
Rotate |