A sensor for deriving a value of differential of acceleration.

Abstract: In order to control a movable object (100) such as an automobile, the differential of acceleration is derived and used as control information. In order to derive that differential, a value representing the acceleration may be differentiated, but preferably a sensor (111,112) is provided which generates a direct measurement of the differential of acceleration. In one example of such a sensor, a pendulum (1) has a coil (3) thereon which interacts with the magnetic field of a magnet (2) on a casing (10) supporting the pendulum (1). A current is supplied to the coil (3) such as to generate a force resisting movement of the pendulum (1). It is then found that the voltage across the coil corresponds to the differential of acceleration.

Description: The present invention relates to a sensor for deriving a value of differential of acceleration. The sensor may be used in a wide variety of applications, examples being given. Existing arrangements are known in which sensors are provided for detecting at least one of: position, velocity, angular velocity, acceleration and angular acceleration. For example, a sensor may detect the acceleration of an object and the information thus obtained may be used to control the acceleration so as to obtain a smoothly increasing velocity. For a human observer being carried by a moving object; position and velocity are not sensed directly, but only by observing change relative to stationary objects. However, acceleration is readily sensed. Furthermore, it is suggested in an article entitled "Development of Acceleration Sensors for Automobiles" published in the Nissan Technical Bulletin No. 23, of December 1987, that human beings are particularly sensitive to the rate of change of acceleration, i.e. the differential of acceleration. That article suggested that differential acceleration relates closely to feelings of comfort or discomfort experienced by a human being moving with the object. According to the present invention there is provided a sensor for deriving a value of differential of acceleration comprising: a first member; a second member movable relative to said first member; a magnet fixed relative to said first member for generating magnetic flux; at least one coil fixed relative to said second member in said magnetic flux of said magnet; means for detecting movement of said second member relative to said first member and, on the basis of the detected movement, for generating a current in said at least one coil such as to generate a force between said at least one coil and said magnet due to said magnetic flux, said force being such as to resist said movement of said second member relative to said first member; and means for detecting the voltage across said at least one coil due to said current, said voltage corresponding to said value of differential of acceleration. Therefore, a sensor is provided with two members movable relative to each other, with one of the members carrying a magnet and the other a coil. Then, if relative movement occurs, a current may be generated which, when passed through the coil, generates a force due to the interaction of the current with the magnetic flux of the magnet. If that current is generated such that the force resists relative movement of the members, it has been found that the voltage across the coil then provides a direct measurement of the differential of acceleration. In such a sensor, one of the members is preferably a pendulum mounted via a pivot axis on the other member. Whilst it is possible for such a pendulum to have two degrees of freedom of movement, so that the differential of acceleration can be derived in more than one axis, the processing circuitry then necessary is complex, and it is preferable that the movement of the pendulum is limited to a single plane. If the differential of the acceleration is needed in more than one direction, then a plurality of such sensors may be provided. Furthermore, although it is normally easier to mount the coil on the moving part, e.g. the pendulum, it is also possible to mount the magnet thereon, with the coil being mounted on the other member. Embodiments of the present invention will be described in detail, by way of example, with reference to the accompanying drawings, in which: Figs. 1(a) and 1(b) are schematic diagrams for explaining the general principles of systems utilising one or more of the sensors of the present invention. Figs. 2(a) to 2(c) are block diagrams illustrating control rule arrangements which may be used. Fig. 3 is a schematic diagram of an automobile application. Fig. 4 shows the configuration of a first embodiment of the invention which may be used in the automobile of Fig. 3; Fig. 5 is a diagram showing the forces applied to the pendulum of the sensor of Fig. 4; Fig. 6 is a circuit diagram of part of the sensor of Fig. 4; Fig. 7 is a circuit diagram of a modification of part of the sensor of Fig. 4; Fig. 8 is a circuit diagram showing signal processing circuitry for the sensor of Fig. 4; Fig. 9 is a second embodiment of the invention which may be used in the automobile of Fig. 3; Fig. 10 is a schematic diagram for explaining control of an automobile on the basis of information corresponding to the differential of acceleration; Figs. 11(a) to 11(e) illustrate transverse slipping of an automobile, Fig. 11(a) showing the movement of an automobile on a road, Fig. 11(b) showing the change in steering angle of the automobile, Fig. 11(c) showing the change in steering angle speed, Fig. 11(d) showing the change in lateral acceleration, and Fig. 11(e) showing the differential of lateral acceleration; Figs. 12(a) and 12(b) show the correction of steering of an automobile in dependence on the differential of transverse acceleration, Fig. 12(a) showing the spinning which can occur and Fig. 12(b) showing the control of the rear road wheels to avoid spinning; Figs. 13(a) to 13(f) illustrate control of an automobile when accelerating, Fig. 13(a) illustrating the movement of the automobile on a road, Fig. 13(b) illustrating the position of the accelerator of the automobile, Fig. 13(c) illustrating the speed of the accelerator, Fig. 13(d) illustrating the driving wheel speed, Fig. 13(e) illustrating the forward/backward acceleration, and 13(f) illustrating the forward/backwards differential of acceleration; Fig. 14(a) to 14(f) illustrate the control of an automobile when braking, Fig. 14(a) showing the movement of the automobile on a road, Fig. 14(b) showing the brake oil pressure, Fig. 14(c) showing the change of brake oil pressure, Fig. 14(d) showing the forward/backward acceleration of the automobile, Fig. 14(e) showing the forward/backwards differential acceleration of the automobile, and Fig. 14(f) showing the wheel speed; Fig. 15 is a schematic diagram of an automobile having six acceleration differential sensors; Fig. 16 shows an automobile having suspension control; Fig. 17 is a schematic diagram of an engine vibration control arrangement using acceleration differential sensors; Fig. 18 shows a further engine mounting arrangement using acceleration differential sensors; Figs. 19(a) and 19(b) illustrate engine vibration in the arrangement of Fig. 18, Fig. 19(a) showing the variation in acceleration and Fig.19(b) showing the variation in the differential of acceleration; Figs. 20(a) and 20(b) show graphs corresponding to Figs. 19(a) and 19(b) respectively, but at the time of flameout of the engine; Fig. 21 shows an elevator control system application. Fig. 22 shows a sensor for detecting the differential of rotational acceleration; Fig. 23 shows an earthquake simulator application Fig. 24 shows an XY stage application. Fig. 25 is a schematic diagram of a damped building application; Fig. 26 shows a railway vehicle application; Fig. 27 shows a modification of the railway vehicle of Fig. 26. Figs. 28(a) and 28(b) show a further modification of the railway vehicle of Fig. 26; Fig. 29 shows a magnetic levitation vehicle application. Fig. 30(a) and 30(b) shows a manipulator application. Figs. 31(a) and 31 (b) show an airplane application. Fig. 32 is a diagram of a circuit for deriving the differential of acceleration using an acceleration sensor; Fig. 33 is a diagram of another circuit for deriving the differential of acceleration using an acceleration sensor; Figs. 34(a) and 34(b) are graphs illustrating acceleration and differential of acceleration; and Figs. 35(a) and 35(b) show alternative arrangements for deriving information relating to the differential of acceleration. Fig. 1(a) is a schematic diagram showing the overall structure of a movement control system using information relating to the differential of acceleration. The movement control system has an acceleration differential sensor 51 which is fixed to a body 50 and detects the differential of acceleration of the body 50 under external force f(t), a controller 52 for controlling the movement of the body 50, and an actuator 53 for generating force F(t) for acting on the body. The controller 52 controls the movement of the body 50 using the actuator 53 according to the information relating to the differential of acceleration detected by the acceleration differential sensor 51. In the movement control system using information relating to the differential of acceleration shown in Figs. 1(a) and 1(b), a movement will now be considered in which the body 50 is restricted to a virtual fixed surface 54 together with a spring element 56, thus giving the movement configuration shown in Fig. 1(b). Assuming that the mass of the body shown in Fig. 1b is M, the displacement of the body is x o , the force generated by the actuator 53 is F c (t), the external force acting on the body 50 is f g (t), the viscous damping coefficient of a damper element 55 is C, and the spring constant of the spring element 56 is K, the body 50 moves according to the movement equation given by Equation 1. M d 2 x o ( t ) dt 2 + C dx o ( t ) dt + Kx o ( t ) = f g ( t ) - F c ( t ) When considering position control in the movement model shown in Fig. 1(b), the control rule by the controller 52 may be assumed to have a transmission function such as shown in Fig. 2(a), represented in Equation 2 below. G x =K 2 s 2 +K 3 s+K 4 In Equation 2, K 2 , K 3 , and K 4 represent feedback gain constants of acceleration, velocity and displacement respectively. The transmission function between the external force and displacement is then given by Equation 3 below. Equation 3 shows the acceleration feedback functions actively to increase the mass under position control, and the velocity feedback functions actively to increase the damping value under position control, and the position feedback functions actively to increase the rigidity under position control. Equation 3 also shows that, by selecting the three gain constants, the movement characteristics can be changed freely. Next, the velocity control in the movement model shown in Fig. 1(b) will be considered. When both sides of Equation 1 are differentiated with respect to time t, Equation 4 is obtained. M d 3 x o ( t ) dt 3 + C d 2 x o ( t ) dt 2 + K dx o dt = df g ( t ) dt - dF c ( t ) dt Equation 3 is substituted as shown in Equation 5 below then Equation 6 is obtained. v o ( t ) = dx o ( t ) dt f 1 g ( t ) = df g ( t ) dt F 1 c ( t ) = dF c ( t ) dt M d 2 v o ( t ) dt 2 + C dv o ( t ) dt + Kv o ( t ) = f 1 g ( t ) - F 1 c ( t ) Fig. 2(b) shows a block diagram corresponding to the case where the control rule of the controller 52 is a transmission function given by Equation 7 below. G v = K 1 s 2 + K 2 s + K 3 In Equation 7, K 1 , K 2 , and K 3 represent feedback gain constants of the differential of acceleration, acceleration and velocity respectively. The transmission function between the external force and velocity obtained from this block diagram is then given by Equation 8 below. Equation 8 shows that the differential of acceleration feedback actively increases the mass under velocity control, the acceleration feedback actively increases the damping value under velocity control, and the velocity feedback actively increases the rigidity under velocity control. Equation 8 also shows that, by suitably selecting the three gain constants, the movement characteristics can be changed freely. Next, acceleration control in the movement model shown in Fig. 1(b) will be considered. When both sides of Equation 7 are differentiated with respect to time t, Equation 9 is obtained. M d 3 v o ( t ) dt 2 + C d 2 v o ( t ) dt + K dv o ( t ) dt = df 1 g ( t ) dt - dF 1 c ( t ) dt When Equation 10 is substituted as shown in Equation 11 below, then Equation 12 is obtained. a o ( t )= dv o ( t ) dt f 2 g ( t ) - df 1 g ( t ) dt F 2 g ( t ) - dF 1 c ( t ) dt M d 2 a o ( t ) dt 2 + C da o ( t ) dt + Ka o ( t ) = f 2 g ( t ) - F 2 c ( t ) Fig. 2(c) shows a block diagram corresponding to the case where the control rule of the controller 52 is a transmission function given by Equation 12 below. G g = K 0 s 2 + K 1 s + K 2 In Equation 12, K 0 , K 1 and K 2 represent feedback gain constants of differential of the differential of acceleration differential of acceleration, and acceleration respectively. The transmission function between the external force and acceleration obtained from this block diagram is then given by Equation 13 below. Equation 13 shows that the differential of the differential of acceleration feedback actively increases the mass under acceleration control, and the differential of acceleration feedback actively increases the damping value under acceleration control, and the acceleration feedback actively increases the rigidity under acceleration control. Equation 14 also shows that, by suitably selecting the three gain constants, the movement characteristics can be changed freely. The movement control bases on each of position, velocity, and acceleration is described above. By adding information relating to the differential of acceleration, which is a new physical value reflected by the body movement status, to the conventional control methods using only position, velocity and acceleration information, the mass is actively changed under velocity control and the damping value is actively changed under acceleration control, so that the efficiency of control can be increased. (Information relating to the differential of the differential of acceleration can be used as first order differential circuit output of the output of the additional acceleration speed sensor.) A first example of the application of the sensors of the present invention to an automobile control system will now be described with reference to Figs. 3 to 15. Fig. 3 shows the overall configuration of the control system for the movement of the automobile, which is an example of a movable object, in which sensors measuring the differential of acceleration are used. The automobile 100 has four road wheels which are steerable. The automobile includes an engine 101 (including the transmission), road wheels 102, a brake for each road wheel 103, a steering wheel 104, a steering angle sensor 105, an accelerator 106, a brake 107, a rear wheel steering motor 108, an oil pressure controller 109, a controller 110, an acceleration differential sensor 112 used to detect the differential of lateral acceleration, and an acceleration differential sensor 111 used to detect the differential of the forward/backward (longitudinal) acceleration. The configurations of the traverse acceleration differential sensor 112 and the forward/backward (longitudinal) acceleration sensor 111 are as shown in Figs. 4 to 9. Those sensors can also detect acceleration. Fig. 4 shows the overall configuration of a first embodiment of an acceleration differential sensor 111 or 112 of the invention which may be used in the example of an automobile control system shown in Fig. 3. This acceleration differential sensor, as shown in Fig. 4, consists of a pendulum 1 attached to a casing 10a using a joint 13 providing one degree of freedom of movement (i.e. the pendulum 1 is constrained to move in one plane only). A coil 3 is fixed to the pendulum 1, and a movable electrode 41 is attached at or adjacent the free end (moving direction) of the pendulum 1. A casing 10 supports a magnet 2 so that the magnet is adjacent the coil 3, and an electrode 42 is fixed to the casing 10, facing the movable electrode 41. A pendulum displacement detector 40 is used to detect the displacement of the pendulum 1 from its equilibrium position, and a servo-amplifier 5 is connected in series to the output side of the pendulum displacement detector 40 and the output of the servo-amplifier 5 is fed to one end of coil 3. A read resistor 6 is connected such that one end thereof is grounded and the other end is connected to the coil 3. The information relating to the differential of acceleration thus detected then corresponds to the terminal voltage of coil 3 as shown in Fig. 4. As mentioned above, the pendulum 1 has one degree of freedom of movement (in the plane of the paper in Fig. 4), so the sensor detects movement, and the differential of acceleration of that movement in that direction. The movable electrode 41 and electrode 42 fixed to the casing 10 form two pairs of plate capacitors. The electrostatic capacitance C of such a plate capacitor is inversely proportional to the size of the gap between the capacitor plates, and is given by Equation 14 below. C = ε · S d In Equation 14, ε is the permittivity of air, S is the electrode area, and d is the gap size. Thus, the displacement of the pendulum 1 can be detected from the change C in the electrostatic capacitance between the two pairs of capacitors formed by movable electrode 41 and fixed electrode 42. The pendulum 1 supports the coil 3. When a current flows in this coil 3, the current generates a magnetic flux and the pendulum experiences a force generated by the interaction of that magnetic flux with the magnetic field of the magnet 2 fixed to the casing 10. Hence, the pendulum 1 can be maintained substantially at its equilibrium position regardless of the magnitude of the external force. This is achieved by controlling the current flowing in the coil 3 so that the change ΔC in the electrostatic capacitance between the two pairs of capacitors detected by the servo-amplifier 5 is substantially zero. Assume now that the acceleration differential sensor is fixed to a moving object, such as the automobile in the example of Fig. 3. If the mass of the pendulum 1 is M, and a transverse acceleration α(t) (i.e in the effective direction of the sensor) to the left in Fig.4 is sensed by the sensor at a time t, then an inertial force of F(t)=M.α(t) is applied to the pendulum 1 to the right in Fig 5. The movement of the pendulum 1 is then given by Equation 15 below. M . d 2 x ( t ) dt 2 = F ( t )- f ( t ) In Equation 15, M is the mass of the pendulum 1, x(t) is the displacement from the equilibrium position of the pendulum 1 at time t, F(t) is the inertial force acting on the pendulum 1, f(t) is a controlling force generated through the position feed-back. The controlling force f(t) is proportional to the current I(t) flowing in the coil 3, which is given by Equations 16 and 17. F(t) =  . I(t)  = 2πrBN In Equations 16 and 17,  is an electromagnetic interlinkage coefficient, r is the radius of coil 3, B is the magnetic flux density of the magnet 2, and N is the number of turns of the coil 3. When the controlling force f(t) corresponds to F(t) it changes with time so that pendulum 1 may be held at the equilibrium position. Then the left side of the Equation 15 becomes zero. As a result, Equation 18 holds. F(t) - M.α(t) = f(t) = .I(t) Thus, the acceleration to be detected by the acceleration differential sensor is given by Equation 19 as follows: α(t) =  M . I(t) The acceleration mentioned above can be detected by measuring the current flowing in coil 3. On the other hand, if the differential of acceleration to be detected by the acceleration differential sensor is assumed to be η(t), then Equation 20 holds, as shown below. η(t) = dα(t) dt =  M . dI(t) dt The circuit equation for the current flowing in the coil 3 is, as can be seen from Fig. 6, then given by Equation 21. e = L . dI(t) dt In Equation 21, L is the inductance of the coil 3. Thus, the differential of acceleration to be detected by the acceleration differential sensor η(t) is given by Equation 22 as shown below. η(t) =  M . e L The differential of acceleration mentioned above can be measured by detecting the voltage across the coil 3. The configuration of the acceleration differential sensor of the first embodiment is such that the pendulum 1 is displaced when an acceleration is applied in the direction in which the pendulum 1 moves. This displacement is detected by the displacement detector 40 as a voltage signal and is amplified in the servo-amplifier 5. The servo-amplifier 5 converts the voltage signal into a current instruction. This current is then supplied to the coil 3 attached to the pendulum 1. Hence, a force is preferably generated between the coil 3 and the fixed magnetic electrode 42, which force provides a displacement force on the pendulum 1 which balances the force due to the movement of the object to which the sensor is attached. Therefore, the output of the displacement detector 40 becomes substantially zero. The displacement of pendulum 1 is prevented automatically. The current flowing in the coil 3 at this time, as mentioned above, is proportional to the acceleration applied. The voltage across the coil 3 is proportional to the differentiated value of the current, that is, the differential of acceleration. Fig. 7 shows a method for deriving information relating to the differential of acceleration when the coil 3 has a resistance R. Equation 23 applies for the circuit shown in Fig. 5. e = R.I(t) + L.dI(t) dt In Equation 23, e is the voltage across the coil 3, R is the resistance of the coil 3, and L is the inductance of the coil 3. If the current flowing in the coil 3 is assumed to pass through the read resistor 6 as shown in Fig. 7, then Equation 24 holds. e r = r . I(t) Thus, the differential of acceleration can be detected by the acceleration differential sensor in the same way as in Fig. 6, by measuring the voltage across the coil 3. The voltage across the read resistor 6 is then given by Equation 25. η( t ) =  M . e - R r . e r L Fig. 8 shows the signal processing block configuration of the acceleration differential sensor represented by Equation 25. An operational amplifier is used in the signal processing block. This configuration enables the differential of acceleration that affects the acceleration differential sensor to be detected even when the resistance of coil 3 cannot be ignored. Fig. 9 shows the overall configuration of a second embodiment of the acceleration differential sensor of the invention. The configuration is generally similar to that shown in Fig. 4. The sensor consists of a pendulum 11, a magnet fixed to the pendulum 11, a movable electrode 141, a casing 10, a coil 130 fixed on the casing 10, a fixed electrode 142, a pendulum displacement detector 140 used to detect the displacement of the pendulum from the equilibrium position, a servo-amplifier 15, and a read resistor 16. Thus this embodiment differs from that of Fig. 4 in that the coil 13 is attached to the casing 10, whilst the magnet 12 is fixed to the pendulum 11. With a sensor according to this embodiment, and in the same way as the sensor in Fig. 4, information relating to the differential of acceleration corresponds to the terminal voltage of the coil 13 shown in Fig. 9. In the acceleration differential sensors shown in Figs. 4 and 9, the magnets 2 and 12 may be replaced with a permanent magnet or an electromagnet respectively that keep the magnetic flux density at a fixed level. In this embodiment, a method using the difference of the electrostatic capacity, which is constructed with a pendulum and casing, is used for displacement detection of the pendulum. However, the present invention is not restricted to this. For example, the pendulum displacement may be detected optically by using a light emitting element, lens, and photo detector. Furthermore, as is evident from Equations 21 and 25, it is not necessary to take into account the materials or structural characteristics (Young modulus, cross-section moment, etc.) of the pendulum 1, so that the differential of acceleration can be detected more accurately. Furthermore, Equation 26 below can be derived from Equations 19 and 24. α( t ) =  M 1 r e r Therefore, the terminal voltage e r of the reading resistors 6 and 16 is a value proportional to the current, i.e. acceleration. As mentioned above, the acceleration differential speed sensor shown in this embodiment can detect acceleration and the differential of acceleration at the same time. In the above embodiment of the acceleration differential sensor, the detection direction is limited to one axis. However, when it is necessary to detect the differential of acceleration in many axial directions, and the number of parts and cost must be reduced, a multi-axis acceleration differential sensor can be achieved by using the arrangement discussed below. A pendulum is used with a magnet or coil aligned in each axial direction. The pendulum can be displaced in many axial directions according to acceleration in many axial directions. Also, a coil or magnet is mounted to be aligned in each axial direction at a location where force in each axial direction is generated independently in the magnet or coil of the pendulum. Then, a displacement detector detects independently the displacement in each axial direction from the reference opposition of the pendulum. A servo amplifier in each axial direction controls the current flowing through the coil in each axial direction. Hence, the displacement is detected by the displacement detector in each axial direction, and the current flowing through the coil in each axial direction so as to compensate for displacement in each axial direction of the pendulum in each axial direction which is generated by the acceleration acting on the pendulum in each axial direction so that the displacement is substantially zero. In such an arrangement, the differential of acceleration acting on the pendulum in each axial direction can be detected from the induced electromotive force generated across the coil in each axial direction, such detection being e.g. by an induced electromotive force detector in each axial direction. A thin plate-like cantilever may be used in an acceleration differential sensor of the present invention to replace the pendulum of the first or second embodiment. The cantilever is arranged so that its wider plane is set vertically to the detection direction. The sensor is used to detect directly a physical amount proportional to the change in the acceleration. If the cantilever is located in a magnetic field, the magnetic flux changes according to the change in the position of the cantilever. Therefore, the differential of acceleration, which is the rate of change of the acceleration, can be detected by detecting the electromotive force generated, using a suitable pick-up coil. The electromotive force is proportional to the differentiated value of the magnetic flux in accordance with the rules of electromagnetic inductance. Thus, the voltage generated may be output from the sensor. In this method, however, accurate detection of the differential of acceleration is more difficult to achieve. This is because bending of the cantilever due to acceleration is used to detect the differential of acceleration and various nonlinear factors then affect the result. Returning now to Fig. 3, the four wheels of the automobile 100 are steered, the rpm of the engine changes, or the brake 103 is used when the driver operates the steering 104, accelerator 106, or brake 107 respectively, in the same way as when driving a normal automobile. However, under normal driving conditions, the performance of the automobile can be improved by use of the present invention, as will now be described. According to this example of the present invention, the rear steering motor 108, the engine 101, and the oil pressure controller 109 are controlled respectively by controller 110 making use of information corresponding to the traverse and longitudinal (forward/backward) differential of acceleration. In this way, it becomes possible to control the automobile even at the limits at which it is difficult to control the automobile movement manually. Fig. 10 illustrates an example of control of an automobile on the basis of information corresponding to the differential of acceleration when the movement of automobile 100 suddenly changes, for example due to skidding of the automobile due to a change in road conditions. When an automobile is turning normally, there is a balance of forces between the centrifugal force M. and the surface reaction F. If the movement of the automobile changes due to a sudden change of road conditions, etc., the balance of the forces is broken. In the conventional control of the movement of an automobile at such a time, the time at which this balance of forces breaks cannot be detected and the automobile cannot be controlled appropriately; it is only controlled in the same way as for normal driving. Acceleration and differential of acceleration correspond to information that a driver can sense and recognize, in addition to visual information. Of that information, the change of acceleration, that is, the differential of acceleration, is useful to control automobiles when the balance of forces referred to above is broken; the automobile is controlled by detecting the differential of acceleration. Thus, both the acceleration information and the differential of acceleration information can be used for controlling the movement of an automobile. Figs. 11(a) to 11(e) show how to detect the traverse slipping of an automobile on the basis of the differential of acceleration transverse to the longitudinal axis of the automobile 100 (hereinafter differential of transverse acceleration). In Fig. 11(a), the road is assumed to have a gentle right turn. When a ditch crosses the road at point a in Fig.11(a), both the ground contact area and the friction coefficient will change at that point for an instant. The angle at which the automobile 100 is being steered (hereinafter "steering angle") (see Fig. 11(b), the change in that angle (hereinafter "steering angle speed") (see Fig. 11(c), the transverse acceleration of the automobile (see Fig. 11(d), and the differential of transverse acceleration of the automobile (see Fig. 11(e)) change when the automobile 100 runs on such a road, as is discussed below. In general, the cornering force acting on the tires of the automobile 100 increases in proportion to the size of the steering angle. When the steering angle is fixed (steering angle speed is zero), the centrifugal force accompanying the turning of the automobile, and the cornering force are balanced as long as the road conditions remain the same. When automobile 100 passes point (a) at which the ditch crosses the road, the automobile 100 skids laterally for an instant. This lateral skid causes the transverse acceleration of the automobile 100 to be reduced for a short time, but the steering angle remains fixed. As a result, a large peak is detected in the differential of transverse acceleration. This is why the moment when the automobile 100 begins to skid can be detected from the steering angle speed and the differential of transverse acceleration of the automobile 100, by detecting the differential of transverse acceleration for the increased steering angle. Figs. 12(a) and 12(b) shows an example which seeks to prevent excessive changes of the movement of the automobile 100 by correcting the steering of the rear road wheels 102 using the steering mechanism in dependence on the differential of transverse acceleration. Excessive changes of movement of the automobile 100 can thus be prevented by making use of both the steering angle speed and the differential of transverse acceleration information to turn the rear wheels 102 slightly in the same steering direction as the front wheels 102. Figs. 13 and 14 show methods for detecting a longitudinal (forward/backward) slipping of the wheels, making use of the forward/backward differential of acceleration. Fig. 13 relates to backward slipping of the wheels at the time the automobile starts or accelerates and Fig. 14 relates to forward slipping (skidding) when the automobile brakes. In Fig. 13(a), the road on which the automobile 100 is moving is considered to be straight, but a ditch crosses at point (a) and the ground contact area and the friction coefficient will change for an instant when the automobile passes the point. The position of the accelerator 106, the speed of the accelerator, the driving wheel speed, the forward/backward acceleration, and the forward/backward differential of acceleration of the automobile 100 when the automobile is accelerating on such a road, are shown in Figs. 13(b) to 13(f) respectively. In general, the traction force acting on the tires of the wheels of the automobile 100 increases in proportion to the engine torque. Hence, when the accelerator is not at its undepressed position, the traction force and the road reaction when the tires are driven by engine 101 are balanced as long as the road conditions remain the same. However, when the automobile passes the ditch at point (a), the driving wheel 102 may begin to slip backwards relative to the road surface. Then, the forward/backward acceleration of automobile 100 is reduced for an instant irrespective of the position of the accelerator 106. A large peak is then detected in the forward/backward differential of acceleration of the automobile 100. Therefore, the time when the driving wheels 102 begin to slip can be detected by detecting the movement of the accelerator and by detecting the forward/backward differential of acceleration in relation to the change in accelerator position. As a result, the output of the engine 101 and idling of the driving wheels 102 can be reduced. Thus, excessive changes of the movement of automobile 100 can be prevented if the controller 110 makes use of information corresponding to the forward/backward acceleration. In a conventional control unit which seeks to prevent the driving wheels 102 from idling, it is difficult to prevent such idling because the conventional unit determines that idling has started when the RPM value of the driving wheels 102 increases more than that of any undriven wheels 102. It takes a long time to detect such idling of the driving wheels 102, and the driving wheels 102 must be braked to stop the idling. Once idling has started, the idling does not stop because of the inertial moment of wheels 102. In this example information corresponding to the forward/backward differential of acceleration is used. This enables the moment when the wheels 102 begin idling or the moment when the maximum friction force is exceeded can be detected readily. Therefore, the engine torque can be reduced before driving wheels 102 begin idling, and the slipping of the driving wheels 102 can be reduced when starting or accelerating the automobile 100, without using the brake 107 of the driving wheels 102. Hence, excessive changes of automobile 100 movement can be prevented. The backward slipping (skidding) of the wheels of the automobile 100 can also be detected when the automobile reduces speed using the forward/backward differential of acceleration information, as shown in Fig. 14. In this example, as shown in Fig. 14(a) the road on which the automobile 100 is moving is assumed to be straight and a ditch crosses at point (a), and the ground contact area and the friction coefficient change for an instant when the automobile passes the ditch. The brake oil pressure, the change in brake oil pressure, the accelerator speed, the speed of wheels 102, the forward/backward acceleration, and the forward/backward differential of acceleration of the automobile 100 when the automobile reduces speed during running on such a road are shown in Figs. 14(b) to 14(f). In general, the force acting on the tires of wheels 102 increases in proportion to the brake torque. Hence, if the brake oil pressure is not zero, the force generated when brake 107 is used for braking the tires and the road reaction are balanced as long as the road conditions remain the same. However, when the automobile passes such a ditch at point (a), the driving wheels may lock (the speed thereof at this time is zero). Thus, the deceleration is reduced for an instant while the brake oil pressure is not zero, and a large peak can be detected in the forward/backward differential of acceleration of the automobile 100. Therefore, the time when the wheels 102 lock can be detected by detecting the brake oil pressure and by detecting the forward/backward differential of acceleration of the automobile in relation to the change of brake oil pressure. Excessive changes in the movement of automobile 100 can thus be prevented by having the brake oil pressure controller 109 controlled by the controller 110 to reduce the brake oil pressure at the time of slipping and hence the locking of the wheels 102 using information relating to the forward/backward differential of acceleration. In the anti-lock unit for wheels which is used in conventional anti-skid braking systems (ABS), an estimate is made of when the RPM value of the driving wheels 102 decreases sharply relative to the automobile speed, the latter being estimated from the RPM value of trailing (undriven) wheels 102. This is used to determine when the wheels are locked. Therefore, it takes a long time to detect whether or not the wheels are locked. In addition, because the estimate of the speed of the automobile is not accurate, it is impossible to control the speed of the automobile accurately. In the examples described above, information corresponding to the forward/backward differential of acceleration is used. So, the time when wheels 102 start to lock, or the time when the maximum friction force is exceeded can be detected. The brake oil pressure can be reduced before the wheels 102 are fully locked, so that wheels 102 lock less frequently under braking, thereby preventing undesirable changes of the movement of automobile 100. Control methods for the automobile 100 using information relating to the differential of acceleration in the forward, backward, right and left directions have been described above in the three examples. However, the automobile 100 can make movements in six degrees of freedom; three translation movements of forward/backward, right/left, and up/down and three rotation movements of rolling, yawing, and pitching. So, six acceleration differential sensors 111a, 111b, 112a, 112b, 113a, 113b are provided to collect information corresponding to each of those six degrees of freedom, as shown in Fig. 15. The six sensors form three pairs, with the sensors of each pair detecting changes along the same linear axis. Hence, translational movements give the same output from the corresponding pair, whilst rotation movements give different (opposed) outputs. The output of each sensor; or pair of sensors, can be used to detect differential of acceleration information for a corresponding degree of freedom. When the movement of automobile 100 is controlled using information relating directly to the differential of acceleration, instantaneous changes acting on the automobile 100 can be detected. Thus, any changes of automobile movement within a suitable range can be detected immediately and the automobile can be controlled so that the maximum value of the friction force of the tires is maintained. At the same time, control can be corrected appropriately to changes in the automobile movement caused by disturbances which are not expected nor desired. In the three examples discussed above, only information relating to the differential of acceleration and driving information are used to explain how automobiles may be controlled. Of course, more sophisticated control is possible using various other types of information such as acceleration wheel speed information, etc., which have been used in conventional automobile movement control, in addition to information relating to the differential of acceleration information. Fig. 16 shows a second application. In this application acceleration differential sensors are used to control the ride comfort of an automobile. In this case, an automobile 100 has a variable suspension mechanism 151a, 151b. Other components of the automobile may be the same as those shown in Fig. 3. The automobile 100 has a plurality of acceleration differential sensors (although only two acceleration differential sensors 152a and 152b near the front wheels and the rear wheels respectively are shown in Fig. 16). It is assumed that the acceleration output of the "ith" acceleration differential sensor is G i and the differential of acceleration output is J i . It can be noted that the acceleration value G i can be derived from the voltage across resistor 6 in the sensor of Fig. 2, and the differential of acceleration value J i obtained from the voltage across coil 3 for any sensor. The evaluation function ψ s for ride comfort is then given by Equation 27 below In Equation 27 d i and e i are weighing constants at the "ith" observation point and may be selected according to the desires of the driver and/or passenger. The ride comfort can be optimized if the controller 153 controls the suspension mechanism 151a, 151b so that the comfort evaluation functions are minimized. The controller 153 controls the suspension mechanism 151a and 151b. However, when the controller 153 is provided with a function for calculating the riding comfort evaluation function from information relating to the acceleration and the differential of acceleration at each observation point of the automobile 11 and for outputting calculation results, it can be used as an evaluation testing machine for evaluating the riding comform of the automobile 100. Figs. 17 to 20 show another application. Fig. 17 shows a configuration in which acceleration differential sensors are used to control ride comfort in the automobile and to reduce engine vibration. In this case, the automobile is assumed to have a variable engine mounting mechanism. In this application an acceleration differential sensor 263 is mounted on the engine 161, the engine being supported by engine mounts 162a and 162b. Two further acceleration differential sensors 164a and 164b are mounted on the steering wheel 166 and in the seat 165 for the driver. The acceleration differential sensors 163a, 164a, 164b supply signals to a controller 167 which controls the engine mounts 162a 162b. Other parts of the configuration may be the same as those in the arrangement shown in Fig. 16. An acceleration value can be derived from the voltage across resistor 6 in the sensor of Fig. 4, and the differential of acceleration value obtained from the voltage across coil 3. The engine 161 and body are provided with a plurality of additional acceleration detectors (only three sensors 163a, 164a, 165b are shown in Fig. 17. It is assumed that the acceleration output of the "jth" acceleration differential sensors is G j and the differential of acceleration output if J j . Then riding comform evaluation function ψ m is defined by Equation 28 below, in the same way as Equation 27. In Equation 28 d j and e j indicate weighting constants for information relating to the acceleration and differential of acceleration at the "j"th observation point and may be tuned in accordance with the desires of the driver and/or passenger. The comfort can be optimized by having controller 167 control the suspension mechanism so that comfort evaluation function ψ m is minimized. Fig. 18 shows an application in which an acceleration differential sensor 171 is used to detect misfiring of the engine 171 of an automobile. Because fuel combustion occurs intermittently in the engine 171, the engine torque changes synchronously with combustion. The reaction of this change in torque makes the engine vibrate, and vibration is transmitted to the automobile body through engine mounts 172a, 172b causing the body of the automobile to vibrate. This vibration of the engine 171 is forcible vibration caused by the change in torque which is synchronized with the fuel combustion frequency. Thus, the combustion status of the engine can be detected by detecting this vibration using controller 174. Fig. 19 shows changes of vibration acceleration and differential of acceleration occurring in the engine rolling direction during normal fuel combustion. Fig. 20 shows the changes of vibration acceleration and differential of acceleration occurring in the engine rolling direction when a misfire occurs in the engine. A misfire occurs at point (m) in Fig. 20. Then, a change occurs in the engine acceleration and a large peak is observed in the differential of acceleration. Misfiring of the engine 171 can be detected by detecting those two signals, and carrying out a suitable filtering calculation. Thus, engine vibration can be reduced if the controller 174 then controls the ignition of the engine 171 in dependence on this information. The controller 174 controls the variable engine mount mechanisms 172a and 172b. However, when the controller 174 has a function for calculating the riding comfort evaluation function from information relating to the acceleration and differential of acceleration at each observation point of the automobile 100 and for outputting calculation results, it can be used as an evaluation testing machine for evaluating the riding comform of the automobile 100. It should be noted that the controlling methods for automobiles mentioned above can be applied to other vehicles, or indeed any other moving object. Fig. 21 shows yet another application. In this example, an acceleration differential sensor is used to control ride comfort in an elevator. An elevator cabin 281 is suspended by a wire rope 185. A motor 183 moves the rope 185, and is controlled by a controller 184. Acceleration differential sensors 182a and 182b are attached to the elevator cabin 181. In this configuration, the speed of the elevator cabin is defined as V when the cabin is moved up/down by motor 183. As in the arrangement of Fig. 16, A acceleration value can be derived from the voltage across resistor 6 in the sensor of Fig. 2, and the differential of acceleration value obtained from the voltage across coil 3. The information relating to the differential of acceleration is inputted into the controller 184 and used as control instructions for the motor 183. For a plurality of acceleration differential sensors (e.g. sensors 182a, 182b), if it is assumed that the acceleration output of the "k"th acceleration differential sensor is G k and the differential of acceleration output is J k and the rotational speed of the motor is V, a riding comfort evaluation function ψ a may then be defined according to Equation 29. In Equation 29, a is a weighting constant for the elevator lifting and lowering speed and b k and c k and weighting constants for the information relating to the acceleration and differential of acceleration at the "i"th observation point and tuned in accordance with the desires of the users of the elevator. The evaluation function of ride comfort in the elevator is defined as ψ e = (a. |V| -b. |G| -c. |J|). In this case, a, b, and c are weighing integers. The ride comfort can be optimized if the controller 204 controls the current to the motor 203 so that the comfort evaluation function is maximi zed. The differential of acceleration can be detected directly and accurately, so comfort is affected less by noise than in the case in which a differential circuit is used for the acceleration to be detected. The evaluation function is not restricted to that of Equation 29 and may be an optional function which matches the desires of the users of the elevators. The controller 184 controls the motor 183. However, when the controller 184 has a function for calculating the occupant riding comfort evaluation function from the information relating to the acceleration and differential of acceleration at each observation point of the elevator body 201 and for outputting calculation results, it can be used as an evaluation testing machine for evaluating the elevator riding comfort. When it is difficult to detect the information relating to the differential of acceleration due to environmental problems, a method in which the motor rotation information (the rotational speed, rotational acceleration, and rotational additional acceleration of the motor) are used to modify Equation 29 may be used. The controlling methods mentioned above are all for automobiles and elevators, but they can also be used to control high-speed positioning etc. of robot arms etc. and as a slope angle speed-meter when the gravity is used as the reference. Effects of the invention will now be discussed. First, because the present invention permits an automobile or other movable vehicle to be equipped with acceleration differential sensors according to the invention and controlled by a controller according to the information from the sensors, it can detect the differential of acceleration that the driver usually can sense and instantaneous changes occurring in the automobile. It can detect changes of automobile movement within a suitable range, so as to control the automobile to maintain the maximum value of the tire friction force. Control of the automobile can be appropriately corrected quickly in response to any change caused by a disturbance not expected nor intended by the driver, thus preventing excessive changes of automobile movement. The present invention permits an automobile or other vehicle to be equipped with acceleration differential sensors to detect at least the traverse differential of acceleration. A controller may then control the steering angle of the rear wheels according to the information from the sensors. Thus, the moment when the automobile begins skidding or slipping can be detected and the rear wheels can be turned slightly in the steering direction of the front wheels, thus preventing excessive changes of automobile movement. An automobile or other vehicle may have a controller which controls the output torque of the engine or motor according to information from acceleration differential sensors, so the moment when the wheels begin idling or the moment when the maximum friction force is exceeded can be detected. In addition, because the engine or motor torque can be reduced before the driving wheels begin slipping, slippage of the driving wheels can be reduced when starting or accelerating without braking the driving wheels, thus preventing excessive changes of automobile movement. Also an automobile, or other vehicle may be equipped with acceleration differential sensors to detect at least the forward/backward differential of acceleration. A controller may then control the oil pressure of the brake oil pressure controller according to the information from the sensors. Thus, when the wheels of the automobile lock, the brake oil pressure can be reduced. Also, since the moment when the maximum friction force is exceeded can be detected, the brake oil pressure can be reduced before the wheels lock, reducing the frequency of locking of the wheels when braking, thus preventing excessive changes of automobile movement. In addition, because such an automobile or other vehicle may be controlled by the controller according to acceleration and differential of acceleration information from the acceleration differential sensors, more sophisticated automobile control is possible. In addition, an automobile or other vehicle may be equipped with an acceleration differential sensor near the engine which detects both acceleration and differential of accelerations. In this way engine misfiring can be detected on the basis of acceleration information from the sensor. A controller may then control the ignition of the engine. Hence, engine misfiring can be detected immediately and the ignition of the engine controlled, reducing vibration of the engine. Also an automobile may be equipped with acceleration differential sensors to detect both acceleration and differential of accelerations. Hence, an evaluation function of ride comfort can be determined on the basis of information relating to the acceleration and differential of acceleration from the sensors. A controller may then control the suspension mechanism so that the comfort evaluation function may be minimized. The evaluation function of comfort may be defined as when G i is the acceleration, J i is the differential of acceleration, and f i and g i are weighing integers to optimize comfort for observation point "i". Of course, there may be only one observation point. Furthermore an elevator may be equipped with a cabin, a wire rope used to suspend the cabin, a motor used to wind up/down, a controller used to control the motor, and an acceleration differential sensor attached to the cabin. The sensor is used to detect both the acceleration and differential of acceleration of the cabin. A comfort evaluation function for the elevator may then be determined on the basis of the information from the sensor. The motor can then be controlled by the controller according to the evaluation function. The evaluation function of the comfort is defined as when G i is the acceleration, J i is the differential of acceleration, the cabin speed is V i , and a i , b i and c i are weighing integers for observation point "i". Of course, there may be only one observation point. Thus, the ride comfort to the elevator can be optimized. An acceleration differential sensor of this invention makes use of the feedback current flowing in a coil, which is proportional to the differential of acceleration experienced by a movable member. The voltage across the coil is proportional to the differentiated value of the feedback current in accordance with the rules of electromagnetic inductance. Thus, the differentiated value of the feedback current, that is, the physical amount proportional to the differentiated value (differential of acceleration) of the acceleration to be applied to the movable member, can be detected accurately by detecting this voltage. In addition, acceleration can also be measured accurately at the same time by measuring the current value. In other words, the differential of acceleration itself can be detected directly with high precision. As a result, detection is less influenced by noise than when using a differential circuit after detecting the acceleration. Detection does not depend on the characteristics of the materials and the structure of the sensor (which would otherwise include strong non-linear elements), so high-precision detection is possible. Fig. 22 shows the construction of a rotational acceleration differential sensor embodying the present invention. The rotational acceleration differential sensor comprises a rotation pendulum 191, a coil 102 fixed to the rotation pendulum 191, movable electrodes 194, a casing 190, a magnet 193 fixed to the casing 190, fixed electrodes 195, a pendulum displacement detector 196 for detecting displacement of the pendulum 191 from a balanced position, a servo amplifier 197 and a reading resistor 198. Rotational acceleration differential information is derived from the terminal voltage of the coil 192 as shown in Fig. 22. The pendulum 191 can rotate about an axis perpendicular to the plane of the paper in Fig. 22. This direction will be referred to as "the sensor sensing direction". The movable electrodes 194 are arranged on both sides of a thin lever 194' projecting from the pendulum 191. The fixed electrodes 5 form two pairs each of which form a flat plate capacitor. Displacement of the pendulum 191 is detected by detecting the difference ΔC in electrostatic capacitance between the pair of capacitors, causing the pendulum displacement detector 196. The pendulum 191 also carries the coil 192. When current flows in the coil 192 magnetic flux is generated and the pendulum 193 is subject to a torque due to the magnetic field which is caused by the magnet 193 fixed to the casing 190. Therefore, the current flowing in the coil 192 is feed-back controlled by the servo amplifier 197 so that electrostatic capacitance difference detected by the pendulum displacement detector 196 will be zero. Thus, the sizes of the upper and lower air gaps in the capacitors will be equal so that the position of the pendulum 191 can be kept at a balanced position irrespective of its inertia. Now consider the case when the rotational acceleration sensor according to the embodiment is fixed to an object which is rotating. As shown in Fig. 22 when a rotational torque β(t) is applied to the whole sensor in the leftwards direction (sensor sensing direction) at a time t, then a moment of inertia W(t)=J.β(t) is applied to the pendulum 191 of inertial mass J in the rightwards direction. The kinetic equation of the pendulum 191 is then given as follows J . d 2 ( t ) dt 2 = W ( t ) - w ( t ) wherein: J is inertia mass of the pendulum 1; (t) is the rotational displacement of the pendulum 1 from the balanced position at time t; W(t) is the inertia moment acting on the pendulum 101, and w(t) the control force by position feedback. The control force w(t) is proportional to the current flowing in the coil 192 so that the following equations are established; W(t) = I(t)  = 2πrBN wherein:  is the flux crossing coefficient; r is the radius of the coil 102; B is the flux density of the magnet 3; and N is the number of windings of the coil 102. If the control force follows the inertia moment W(t) so that the pendulum 191 is always in the balanced position, the left side of the Equation 30 becomes zero, and the following equation holds: W(t) = Jβ(t) - w(t) - I(t) Therefore, to rotational acceleration acting on the whole of the sensor is as follows: β(t) = I J (t) and the rotational acceleration can be detected from the current flowing in the coil. On the other hand, the rotational acceleration differential acting on the whole of the sensor y (t) is given as follows: γ( t ) = d β( t ) dt =  J dI ( t ) dt Hence, the circuit equation for current flowing in the coil 103 is as follows: e = L. dI(t) dt wherein L is the inductance of the coil. Therefore, the rotational acceleration differential γ(t) is as follows: γ(t) =  J · e L Hence, the rotational angular acceleration can be measured by detecting the terminal voltage between the ends of the coil 192. This embodiment describes an arrangement in which the rotary pendulum supports the coil and the casing supports the magnet. However, even when the rotary pendulum supports the magnet and the casing supports a coil, or an arrangement in which the magnet is a permanent magnet or electromagnet, the differential of angular acceleration can be detected. Thus, in a similar way to the derivation of information relating to the differential of acceleration, information relating to the differential of angular acceleration may be obtained by converting analog signals to digital signals by adding a second order analog differential means (filter) to a general angular velocity sensor or via an A-D converter and by performing digital processing, or by converting analog signals to digital signals by adding a first order analog differential means (filter) to an angular acceleration speed sensor or via an A-D converter and by performing digital processing. Therefore, any one of such arrangements may be selected in dependence on the hardware structure, controller processing speed, and necessary detection accuracy. By using information relating to the differential of angular acceleration in addition to various types of control using information relating to the differential of acceleration which are shown in the other embodiments of the present invention, movement control and a movement controller with higher accuracy can be achieved and an evaluation testing machine with high performance can be achieved. Fig. 23 shows the construction of an earthquake simulator employing information relating to the differential of acceleration. The earthquake simulator controls the movement of an oscillating table 200 so that earthquake acceleration, earthquake acceleration differential or displacement input, (which is pre-input to a controller) will be reproduced correctly. The oscillating table 200 is controlled for movement in the x direction by oil pressure actuators 241, 242 driven by a table controller 203 and for movement in the y direction by actuators 243, 244. The oil pressure actuators are each provided with a displacement sensor therein, and displacement information is input to the table controller 203. The differential of acceleration in the x direction and y direction of the oscillator table 200 are detected by the acceleration differential detectors 201, 202 on the oscillating table 200. The resulting information is converted into acceleration and velocity in the x and y directions by integrators 261, 262, 263 and 264 and input to the table controller 203. Displacement information can be obtained by supplying velocity information to the integrator in series. These four kinds of signals are fed back to the table controller 203. The table controller 203 compares those signals with earthquake acceleration, earthquake acceleration differential displacement input in advance, and the oscillating table 200 is driven (vibrated) to a target value. Using this construction, a component of the differential of the acceleration can be used as control information, in addition to the information used in a conventional simulator, so that the earthquake simulator has a good response and stable behaviour. A two-dimensional earthquake simulator has been described. However, similar effects can be achieved with a three-dimensional earthquake simulator control using information corresponding to the differential of acceleration in addition to the information conventionally used. Fig. 24 illustrates the construction of an XY stage apparatus using information corresponding to the di differential of acceleration. The XY stage apparatus controls movement of an XY state 300 so that it follows correctly a position pre-input to a controller 303. Movement of the XY stage 300 in the X direction is controlled by linear actuators 341, 342, driven by a stage controller 303 and movement of the XY stage 300 in the y direction is controlled by linear actuators 343, 344. The linear actuators include displacement sensors and displacement information is input to the stage controller 3. The differentials of acceleration in the x and y directions are detected by sensors 301, 302 on the X Y stage 300 which detect the differential acceleration. The resulting information is converted into information corresponding to acceleration and velocity in the x and y axis direction by integrators 361 to 364 and input to the stage controller 303 position information for the XY stage 300 can be obtained by supplying velocity information to the integrators. Alternatively the integration operation can be carried out within the stage controller 307. Information to the position, velocity, acceleration and differential of acceleration is fed back to the stage controller 303, compared with a position pre-input to the stage controller 303 advance, and the XY stage 300 is moved to a target position. Thus, information relating to the differential acceleration is used, in addition to the information used in a conventional XY stage apparatus, so that the XY stage apparatus has a good response and stable behaviour. A two-dimensional XY stage has been described, similar effects can be achieved with a one-dimensional or three-dimensional XY stage apparatus. The stage controller 303 controls each actuator 343, 344. However, when the controller 303 has a function for calculating the control performance evaluation function from the information relating to the acceleration and differential of acceleration at each observation point of the stage and for outputting calculation results, it can be used as an evaluation testing machine for evaluating the control performance of the XY stage. Fig. 25 shows the construction of a building 400 with a damper controlled using information relating to the differential acceleration. As shown in Fig. 25 an oil pressure actuator 403 and an active mass 404 are provided on a suitable floor of the building 400. The oil pressure actuator 403 is fixed to the building and the active mass 404 is movable relative to the oil pressure actuator. A controller 402 has a signal processor incorporated therein which can calculate acceleration velocity and displacement information on the basis of information from acceleration differential sensors 411, 412, 413, 414 on each floor. The controller 402 controls the oil pressure in the actuators 403 on the basis of such information so that vibration of the whole building can be minimised. By using information corresponding to the differential of acceleration, small changes in acceleration can be detected. The controller 402 controls the actuator 403. However, when the controller 402 has a function for calculating the control performance evaluation function from the information relating to the acceleration and differential of acceleration at each observation point of a building and for outputting calculation results, it can be used as an evaluation testing machine for evaluating the control performance for a building with vibration-proof equipment. Fig. 26 shows the construction of a railway vehicle using information relating to the differential of acceleration. As shown in Fig. 26, a railway vehicle body 501 is mounted on front and rear pairs of bogies, 551, 552 each of which can turn freely around the center of bolster spring actuators 541, 542. The bogies 551,552 are supported by wheels 521, 522, 523 524 through axle spring actuators 543, 544, 545, 546, 547, 548, 549, 550. Acceleration differential sensors 531, 532, 533 are provided on the vehicle body 501 and can detect information rotating to the differential of acceleration of the vehicle body 501 in the vertical direction. A controller 506 has a signal processor with integration circuits incorporated therein, and can calculate acceleration, velocity and dispLacement information on the basis of information from acceleration differential sensors 531, 532, 533. The controller 506 controls the bolster spring actuators 541, 542 and the axle spring actuators 543, 544, 545 on the basis of the information so that riding comfort is not reduced during travelling even if the railway track has a slight irregularity. By using information relating to the differential of acceleration, changes in acceleration can be detected. At the same time, changes in height and/or attitude of the vehicle body 501 can be controlled positively so that derailment of the vehicle is unlikely. Fig. 27 shows an embodiment which is a modification of that Fig. 26. Corresponding parts are indicated by the same reference numerals. In Fig. 27 the differential sensors of acceleration of the vehicle body 501, bogie 555 and bearings 551, 552 is detected. Usually, the vehicle body 501, bogie 555, bearings 521, 522 each have different resonance point. By detecting resonance vibration using the acceleration differential and feeding signals back to the controller 506, control giving a more comfortable ride can be achieved. Figs. 28(a) and 28(b) show the construction of a power control system of a railway vehicle using information relating to the differential of acceleration. As shown in Figs. 28(a) and 28(b) drive wheels 621, 622 are driven by a motor 602 controlled by a controller 606. Brake wheels 623, 624 are braked by a brake 604 controlled by the controller 606. The vehicle body 601 has an acceleration differential sensor which detects the differential of acceleration in the direction of travel. The controller 606 has a signal processor incorporated therein which has an integration circuit so that the controller 606 can calculate acceleration, velocity, and displacement information from information from the acceleration differential sensor 605 on the vehicle body 601. Figs. 28(a) and 28(b) illustrate the time at which the wheels are about to turn on the rail. If the adhesion coefficient between a wheel and the rail, and the weight of axle are µ and W respectively, the maximum traction force which can be generated by frictional force F between the wheel and the rail can be expressed as follows: F= µ W If the rotational force is increased above this value, the wheel spins on the rail. As the rotational force of the wheel increases gradually from zero, acceleration of the vehicle body increases. However, as mentioned above, once spinning of the wheels start, the acceleration decreases significantly. This can be detected using information relating to the differential of acceleration in the direction of travel. In a railway vehicle, as in an automobile, adhesion of the wheels can be improved by detecting the differential of acceleration in the direction of travel and controlling the motor accordingly. Braking also can be improved for the same reason. If the braking torque increases above the maximum traction force F, slipping of the brake wheel 623, 624 takes place. As the brake torque increases gradually from zero, deceleration of the vehicle body 601 also increases. However, once the brake wheel 623, 624 starts to slip (wheel lock), the deceleration decreases significantly. Again this can be detected using information relating to the differential of acceleration. Thus for a railway vehicle, as for an automobile, adhesion of the wheels can be improved by detecting the differential of acceleration in the direction of travel and controlling the brake accordingly. The arrangement described above relates to the case where the drive wheels 621, 622 and the brake wheels 623, 624 are separate. However, the same concept can also be applied to a vehicle in which the same wheel is used for driving and braking. Fig. 29 shows a sectional view of the construction of a magnetic levitation railway vehicle employing information relating to the differential of acceleration. As shown in Fig. 29, the body 701 of the railway vehicle floats due to magnetic repulsion between levitation coils 773, 774 on the ground and superconductive magnets 733, 734 on the vehicle body 1. When current flows in propulsion coils 771, 772 there is an attractive force between those propulsion coils 771, 772 and superconductive magnets 731, 732 on the vehicle body 701. This attractive force propels the railway vehicle. Sensors 721, 722, 723, 724 are provided on the vehicle body 701, which detects the differential of acceleration in the forward, backward, upward, downward and lateral directions. A magnet controller 704 has a signal processor incorporated therein, the signal processor being formed by integrating circuits. The magnet controller 704 calculates information corresponding to the acceleration, velocity and displacement of the vehicle body 701 on the basis of information from the sensors 721, 722, 723, 724. The magnet controller 704 controls the magnetic force generated by the superconductive magnets 731, 732, 733, 734 and also passes information to a coil controller 706 on the ground via an antenna 705. The coil controller 706 controls the current flowing in the propulsion coils 771, 772 and the levitation coils 773, 774. This then controls levitation attitude, position, velocity and acceleration of the vehicle body 701. By using information corresponding to the differential of acceleration, small changes in the acceleration can be detected so that vibration of the magnetic levitation railway vehicle can be reduced. Also, changes in height of the vehicle body 701 and attitude changes can be controlled, so that satisfactory movement of the railway vehicle can be achieved. Figs. 30(a) and 30(b) show the construction of a manipulator using information corresponding to the differential of acceleration. As shown in Fig. 30(a) movement of a manipulator 801 is controlled so that it follows position information pre-input to a controller 803. The movement of the manipulator 801 is controlled by motors 841, 842, 843 for driving the joints of the manipulator, the motors 841, 842, 843 being controlled by the controller 803. Each motor has an encoder and rotation angular information is input to the controller. The differential of acceleration in the X, Y and Z directions of a coordinate system defined by the orientation of the jaw 811 of the manipulator 801 (see Fig. 30(b)) are detected by the sensors 821, 822, 823 arranged on the jaw 811. The controller 803 calculates acceleration, velocity and displacement information on the basis of information from the sensors 821, 822, 823. That information is compared with position, velocity and acceleration information pre-input to the controller 803 and the manipulator 801 can thus be moved to a target position. Thus, information corresponding to the differential of acceleration is used in addition to the information used in a conventional manipulator, so that a better performance can be achieved. In Fig. 31(b) three acceleration differential sensors 821, 822 and 823 are mounted on the manipulator 801. However, in the same way as the additional acceleration information detection method with 6 degrees of freedom an automobile 100 shown in Fig. 13, by detecting the movement of the manipulator 801 with 6 degrees of freedom, more accurate control may be achieved. The controller 803 controls each motor. However, when the controller 803 has a function for calculating the control performance evaluation function from the information relating to the acceleration and differential of acceleration at each observation point of the manipulator 801 and for outputting calculation results, it can be used as an evaluation testing machine for evaluating the control performance of the manipulator 801. Figs. 31(a) and 31(b) show the construction of an airplane using information corresponding to the differential of acceleration. In Figs. 31(a) and 31(b) the body 901 of the airplane has sensors 921, 922, 923 which sense the differential of acceleration in the upward, downward and lateral directions. Also, the main wings 942 of the airplane have acceleration differential sensors 924, 925 for sensing twist and bending moments of the main wing 942. A controller 903 calculates acceleration velocity and displacement information on the basis of information from the sensors 921, 922, 923, 924 and 925 on the body 901. By using information corresponding to the differential of acceleration, small changes in the forces applied to the body 901 can be sensed as small changes in acceleration. The controller 903 controls a horizontal control surface 841, a flap in the main wing 942, a vertical control surface 943, a horizontal stabilizer 944, a vertical stabilizer 945 and the output of the engine (not shown). In this way, a control configured vehicle (CCV) can be designed in which the six axes of freedom of the body 901 can be controlled independently. The attitude and direction of flight can be controlled separately. For example, direct force control, airplane direction control and airplane translation control can be effected. Since the main wing also has sensors 924, 925 for sensing any twist or bending movement of the main wing 942, fluttering of the airplane can be prevented by artificially decreasing the critical flutter mode by strengthening damping of flutter by driving air controls on the basis of the information corresponding to twist or bending movement of the main wing 942. Fig. 32 shows a differential of acceleration detection method using an acceleration sensor and analog differential circuit which is a modification of example of the acceleration differential sensor 51 shown in Fig. 1. Fig. 33 shows a differential of acceleration detection method using an acceleration sensor and a digital differential circuit which is a further modification of the acceleration differential sensor 51 shown in Fig. 1. Information relating to the differential acceleration may be obtained by converting analog signals to digital signals by adding an analog differential means (filter) to a general acceleration speed sensor as shown in Figs. 32 and 33 and or via an A-D converter and by performing digital processing. In Fig. 33, the signal from the acceleration sensor is passed to an analog/digital converter, and then to a delay circuit (D). The resulting signal is multiplied by -1 and fed to an addition circuit which sums it with the direct output of the analog/digital converter. Figs. 34(a) and 34(b) show the acceleration and differential of acceleration detected by the sensors in this embodiment and the output of the acceleration analog differential circuit. Fig. 34(a) shows the acceleration output detected by the acceleration sensor. The upper part of Fig. 34(b) shows the output after the acceleration output shown in Fig. 34(a) passes through an analog differential circuit. The lower part of Fig. 34(b) shows the differential of acceleration output detected by an acceleration differential sensor. The acceleration analog differential output the differential of acceleration output detected by the acceleration differential sensor match in Fig. 34(b) showing that both the outputs in Fig. 34(b) match the output in Fig. 34(a). Figs. 35(a) and 35(b) show two different ways of obtaining information corresponding to the acceleration, and the differential of acceleration. In Fig. 35(a), an acceleration differential sensor 1011 generates two outputs 1021, 1022 corresponding to acceleration and differential acceleration respectively. A controller 1051 receives those outputs 1021 or 1022 and converts them to digital information using respective analog/digital converters 1031, 1032. With such an arrangement, the controller 1051 needs two input ports, for the signal 1021, 1022, and two analog/digital converters 1021, 1032. In such an arrangement, the acceleration differential sensor 1011 may be as shown in and as described with reference to Figs. 4 to 7, with the signal 1021 being that across the coil 3 and the signal 1022 being that across the resistor 6. In Fig. 35(b), an acceleration sensor 1012 is provided which measures the acceleration. Such an acceleration sensor 1012 may be a conventional one. The output 1023 of that sensor 1012 is passed to a controller 1052, which has therein an analog/digital converter 1033 which converts the signal 1023 to digital information. Information corresponding to the acceleration is then derived directly, but that information is also passed via a delay circuit 104 and a multiplier 1042 to an adder 1043, where the delayed acceleration information is compared with the current acceleration information. From this, information corresponding to the differential of acceleration can be derived directly. With the arrangement of Fig. 35(b), the controller 1052 needs only one input port, and only one analog/digital converter 1033.

Claims: A sensor for deriving a value of differential of acceleration comprising: a first member (10,190); a second member (1,191) movable relative to said first member (10,190); a magnet (2,193) fixed relative to said first member (10,190) for generating magnetic flux; at least one coil (3,192) fixed relative to said second member (1,191) in said magnetic flux of said magnet (2,193); means (40,41,42,197,198) for detecting movement of said second member (1, 191) relative to said first member (10,190) and, on the basis of the detected movement, for generating a current in said at least one coil (3,192) such as to generate a force between said at least one coil (3,193) and said magnet (2,193) due to said magnetic flux, said force being such as to resist said movement of said second member (1,191) relative to said first member (10,190); and means for detecting the voltage across said at least one coil (3,192) due to said current, said voltage corresponding to said value of differential of acceleration. A sensor according to claim 1, wherein said means for detecting movement of said second member (1) relative to said first member (10) includes capacitor plates (42,41) mounted on said first and second members (10,1) respectively, and sensing means (40) for sensing the variation of capacitance of said capacitor plates (42,41) due to said movement of said second member (1) relative to said first member (10). A sensor according to claim 1 or claim 2, wherein said second member (1) is a pendulum. A sensor according to claim 1 or claim 2, wherein said first member (1) is a pendulum. A sensor according to claim 3 or claim 4, wherein said pendulum is constrained to move only in a single plane. A sensor according to claim 1 or claim 2, wherein said second member (191) is mounted so as to be rotatable relative to said first member (190). A sensor according to any one of the preceding claims, wherein a servo amplifier (5) is electrically connected to said movement detecting means (40,41,42,197,198) and said at least one coil (3,192) so that current from said movement detecting means (40,41,42,197,198) is directed to said coil (3,192) through said servo amplifier (5). A sensor according to any one of the preceding claims, wherein a read resistor (6) having resistance (r) is connected in series with said coil (3) having resistance (R) so that the current flowing in said coil (3) passes through said read resistor (6), whereby the differential of acceleration may also be determined by the formula: η( t ) =  M . e - R r . e r L where: η(t) = differential of acceleration  = electromagnetic interlinkage coefficient M = mass of the pendulum e = L. dI(t) / dt (where I(t) = current through the coil) L = inductance of the coil e r = r.I(t) A sensor according to claim 8, wherein a signal processing block comprising an operational amplifier is electrically connected to ends of said coil to provide an output of the voltage which corresponds to the differential of acceleration.

Inventors: KADOMUKAI YUZO, YAMAKADO MAKOTO, KADOMUKAI, YUZO, YAMAKADO, MAKOTO
Applicants: HITACHI LTD, HITACHI, LTD.
Application year: 1993
Main classification: G05D13
IPC codes: G01P15, E04H9, B60G17, E04H3