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Mass measurement using relay feedback of velocity and restoring force compensation is investigated for determining the mass of an object under weightless conditions. In the measurement system, the velocity of the object is fed back through a relay with hysteresis and the force acting on the object is switched from a positive value to a negative value when the velocity reaches a positive threshold and vice versa. As a result, a limit cycle is induced in the measurement system and the mass is estimated based on the period of the limit cycle. In addition, restoring force compensation with a spring is introduced to avoid the drift of the trajectory. This compensation makes the static equilibrium state unique. However, the trajectory still drifts slightly. It causes some error in measurement when a simple formula of estimating mass is applied. To eliminate such an error, a new formula is derived to estimate the mass independently of the position of the trajectory that is determined by the switching positions in the relay actions. When the switching positions deflect from the origin at which the spring is in the natural length, the trajectory is not at the center and becomes asymmetric. It is analytically shown that the period of the limit cycle is minimum when the switching positions are at the origin. It indicates that mass is overestimated with the simple estimation formula when the trajectory is not at the center. The validity of the modified formula and the analytical results are confirmed experimentally.

A mass measurement system using relay feedback of velocity was developed. In this system, the velocity of the object was fed back through a relay with hysteresis. Although the efficacy of the propo...

This paper focuses on compatibility of zero-compliance and zero-power characteristics in a single system. To realize such compatibility, a horizontal zero-compliance system is developed, in which a zero-power controlled voice coil motor is connected with a normal spring (positive stiffness) in series. Since the zero-power control results zero-current in the steady states, permanent magnets are attached with the developed system to provide bias forces in the steady state. The compatibility of zero-compliance and zero-power with integral control is investigated as well. Because an integral controlled system consumes power even in the steady state, low positive stiffness and deformations in the positive and negative isolators are kept equal in the developed system to reduce such power consumption. The developed zero-compliance system with zero-power and integral controls individually is studied theoretically as well.

A zero-compliance mechanism is fabricated which uses a one-piece parallel spring movement and a voice coil motor to achieve force measurement. The conceptual zero-compliance mechanism is a series connection of a spring with positive stiffness and a spring with negative stiffness whose amplitude is equal to the positive one. When force acting on the end of the connected springs (point of action), the point does not displace because the displacement of the negative spring cancels that of the positive spring; meanwhile, the connection point displaces in proportional to the force. Therefore, the force can be estimated from the displacement of the connection point. The efficacy of the proposed method was demonstrated by an experimental apparatus using double series magnetic suspension. However, it used magnetic force to achieve negative stiffness so that the accuracy of measurement was limited because of the nonlinearity. To solve such a problem, a zero-compliance mechanism is fabricated which uses a one-piece parallel spring movement and a voice coil motor as an actuator. The structures of the mechanism are described and its modeling is presented. The control system is designed based on the derived model. Measurement tests for both static and dynamic forces are carried out with the developed apparatus.

The stabilization of a magnetic suspension system is achieved by using a low-pass filter (LPF) with a nonlinear integrator without any other element. A proportional-derivative (PD) control is commonly used as the simplest method of stabilizing a magnetic suspension system. Meanwhile, a first-order reset element (FORE) was applied to improve transient characteristics. The original FORE was a first-order LPF with a nonlinear reset integrator element. A magnetic suspension system cannot be stabilized by a linear LPF, nor the original FORE. In this work, the reset conditions of the FORE were modified for magnetic suspension. This modified FORE succeeded in stabilizing a magnetic suspension system. The efficacy of the modified FORE was demonstrated by simulations and experiments. A single degree of freedom magnetic suspension system was used in the experiment.

A frequency-following servocompensator is applied to a rotary gyro with flexures gimbal to eliminate the oscillating components from the estimated signals. In the targeted gyro, a synchronous motor is fixed to a rectangular holder and a disk-type rotor is driven by the motor to generate gyroscopic couplings. The coupled two rotational motions of the holder are controlled by four electromagnets on the stator; the angular velocities are estimated from the control currents to regulate the relative displacement of the holder to the stator. The other four-degree-of-freedom motions of the holder are constrained by the flexures gimbal. Such suspension using flexures makes the system less damped so that high accuracy is expected to this gyro. However, one of the problems is that an oscillating component caused by rotor unbalance appears in the estimated signal because the estimation is based on the control input. To solve this problem, the frequency-tracking servocompensator is applied to eliminate the oscillating component. The virtually perfect elimination of the component from the estimated signal was achieved.

The controllability and observability of parallel magnetic suspension systems are investigated analytically. A parallel magnetic suspension system has multiple floators and electromagnets driven by a single amplifier. In this paper, the multiplicity is set to an arbitrary counting number n. Parallel systems are classified into four types based on the output of the power amplifier and the connection of the coils. This paper treats three of them: current-controlled with series-connected coils; voltage-controlled with series-connected coils; and voltage-controlled with parallel-connected coils. The conditions of controllability and observability of each system are clarified. The feasibility of parallel magnetic suspension is demonstrated by simulations and experiments.

Two vibration control techniques, negative stiffness and displacement cancellation, are characterized and employed to achieve active vibration isolation. A horizontal vibration isolation system is developed and then used to investigate each of these techniques theoretically and experimentally. The respective responses of the developed system are measured separately while closed-loop poles of the system are kept unchanged; these measured responses are compared. The developed system is based on a series combination of two isolators and consists of two moving tables; one of the moving tables is mounted on the series-connected isolators and the other is placed between the isolators. Using the negative stiffness technique, the isolators are controlled so that one of them has a negative stiffness and the other has a positive stiffness of equal absolute magnitude; using the displacement cancellation technique, one isolator is set to cancel displacement while the other behaves as a positive-stiffness isolator. The active negative, positive, and displacement cancellation isolators are created using voice-coil motors guided by a negative stiffness controller, proportional derivative controller and integral-proportional derivative controller, respectively.

A mass-spring system with a dynamic vibration absorber has a fixed point in its frequency response curves. A method of measuring mass using this property was proposed. It has an advantage that mass is estimated independently of the damping in the absorber. The developed system was characterized by using a phase-looked loop to achieve the tuning condition. However, because the actuator producing the harmonic force was mounted on the base, the reaction force was transmitted to the surrounding structure. It may cause a severe vibration of the surrounding structure. Therefore, it is necessary to prevent transmission of force to the surrounding structure in measuring. In this paper, a new type of mass measurement system is proposed which uses an inertial-mass vibrator to reduce the transmitted vibration. The tuning conditions are derived for both systems with a damped absorber and with an undamped absorber. The principles of measurement are described based on a mathematical model. An experimental apparatus is designed and fabricated. The efficacy of the measurement system with an inertial mass-type vibrator is studied both analytically and experimentally.

A basic single-degree-of-freedom magnetic suspension system consists of one floator, one electromagnet and one amplifier. For multi-degree-of-freedom control, multiple electromagnets and multiple amplifiers are necessary, which increases the cost of total system. As a means of overcoming this problem, parallel magnetic suspension has been proposed which controls multiple floators or multi-degree-of-freedom motions with a single power amplifier. This paper focuses on the zero-power control in a two-degree-of-freedom double parallel magnetic suspension system. The steady-state characteristics of this system are clarified by theoretical analysis. When the disturbance acts on one of the suspended points, a steady displacement appears only in the corresponding suspended point. The direction of the steady displacement is opposite to the direction of the disturbance. In addition, the direction of the transient response depends on the point that the disturbance acts on. In experimental apparatus, step response and frequency response are measured to verify the predictions.

The controllability of gyroscopic systems is studied analytically. Two rotational motions of the rotor interact each other due to gyroscopic effects when the rotor is rotating. They are usually controlled with two control inputs in totally active magnetic bearing systems. Meanwhile, two degrees of freedom are controlled with a single control input in double parallel magnetic suspension systems. Such an approach is applied to gyroscopic systems in this article. Two rotational motions are controlled with a single control input. The conditions for gyroscopic systems to be controllable are clarified.

The feasibility of zero-power control in flux-path control magnetic suspension is discussed. In the flux-path control magnetic suspension system, ferromagnetic control plates are inserted between a permanent magnet (magnetic source) and a floator and moved to vary the flux from the magnetic source to the floator. The zero-power control has been applied in active magnetic suspension with a DC electromagnet. In the zero-power controlled system, the control current was kept virtually zero in the steady states. The applicability of the zero-power control to the flux-path control magnetic suspension is discussed in this paper. The conditions required to achieve the zero-power control is presented in an analytical form. Experiments are carried in a fabricated apparatus to certify the theoretical predictions.

A compact axial active magnetic bearing with a function of two-tilt-motion control is fabricated which has a new configuration of magnetic poles. They consist of four cylindrical poles with coils and a single common pole whose opposite plane of the rotor has a permanent magnet to achieve multi-degree-of-freedom zero power control. Modal control is applied because local zero power control may make the whole system unstable when the number of control channels is larger than the number of freedoms of motion to be controlled. In the developed system, a disk-shape rotor is sandwiched between two axial magnetic bearing stators that are operated differentially. Such a configuration makes it possible to rotate the rotor without disturbing the axial motion. The characteristics of the fabricated magnetic bearing system including rotation are studied experimentally.

A magnetically suspended gyro (MSG) is developed and its performances is estimated. In the MSG, a disk-type rotor is connected to a synchronous motor through a fluid bearing and the motor is fixed to the frame of the floator. The floator is suspended by magnetic force without any mechanical contact so that highly accurate measurement is possible. In accordance with this concept, a three-degrees-of-freedom (DOF) active MSG was developed. However, because of poor damping in the passive suspension and the low resolution of the displacement sensors, the measurement accuracy was relatively low. To solve these problems, a six-DOF (totally) active MSG is designed and fabricated. The frame of this gyro is an octagonal. The motion of the frame is controlled by eight electromagnets. The performance of the gyro is evaluated through measurement of the double-axis angular velocity. The advantages of totally active suspension are investigated. Sufficient damping rapidly reduces the influence of disturbances. Then, the influence of sensor noise is examined. The results of this examination show that the accuracy of the angular velocity measurement is improved by using highly sensitive displacement sensors. Next, the dynamic range is measured. This experiment shows that the MSG can provide precise angular velocity measurement in a low-frequency region.

The effect of friction on a negative stiffness control system is investigated. The negative stiffness control system is used to obtain zero compliance needed for a vibration isolation system. However, the performance of a negative stiffness control system is significantly affected by friction. In this paper, the friction-induced limit cycle in a negative stiffness control system is identified theoretically through describing function approach. Moreover, the relationship between the magnitude of the control parameters used in designing the negative stiffness controller and the behaviors of the induced limit cycle is determined. Finally, the theoretical limit cycle is verified with an experimental limit cycle measured by the time response to the self-oscillation of the system.

A vibration isolation module with zero-power magnetic suspension is developed to retrofit a passive vibration isolation system to improve the performance against direct disturbance. In the module, the zero-power magnetic suspension mechanism is connected in series with a normal spring through a middle mass. This structure can generate zero compliance to direct disturbance while the transmitted vibration is still reduced. Such zero- compliance module was actually designed and fabricated. The characteristics of the fabricated module were studied experimentally. A passive vibration isolation system using air springs were retrofitted with four modules. It was demonstrated that the performance against direct disturbance was improved significantly.

A positioning device for placing a magnetized component on a ferromagnetic plate without collision has been fabricated. When the magnetized component approaches to the plate, the attractive force between them increases sharply as the gap decreases. It sometimes causes them to collide. To prevent such collision, a force compensation control is applied to cancel such nonlinear disturbance force by the actuator driving the component. In addition, a command revision control is implemented to avoid collision even in the presence of errors in modeling and positioning. The effectiveness of the proposed control schemes is demonstrated experimentally.

In near-field levitation, an object can be levitated vertically upward above vibrating surface of an ultrasonic transducer. In this case, a repulsive force acts on the object. On the other hand, it has been reported that a minute object can be suspended vertically downward under the vibrating surface with a small gap in the air. We call this phenomenon ultrasonic suspension. Under the suspension, an attractive force acts on the object. When an object is suspended, there is restoring force, which pulls the object to the center of the vibrating surface. Our aim is to characterize the actuation forces under the suspension. Simultaneous measurement of vertical and horizontal actuation forces is required. A servo type measuring mechanism was proposed. A 1 DOF mechanism with a cantilever and a voice coil motor (VCM) was fabricated as a prototype. The prototype was calibrated and utilized for measurement of vertical actuation force. The result showed enough accuracy and repeatability. Then, a 2 DOF actuation force measurement mechanism was fabricated. The mechanism was consisted of a base to fix the object and two thin wires to support the base. Position of the base was controlled by three VCMs based on PID control. The ultrasonic suspension actuation forces were characterized successfully.

In this paper we present an improved zero-power controlled magnetic suspension system that has the capability to adjust stiffness. The conventional zero-power control system produces constant negative stiffness, and the stiffness solely depends on the capacity of the permanent magnets or the gap–force coefficient of the magnets. This becomes an obstacle to the fields of application of zero-power control where the adjustment of stiffness is necessary, such as developing a vibration isolation system. In this research, the basic zero-power control system is modified such that it can adjust stiffness by adding a minor proportional feedback of displacement to the zero-power controller. Finally, a vibration isolation system is developed by combining a positive stiffness spring in series with a negative stiffness suspension realized by the modified zero-power controller. The proposed control system and the developed vibration isolation system are investigated both analytically and experimentally.

This paper proposes a module-type three-degree-of-freedom vibration isolation system using modified zero-power control. Three vibration isolation modules are connected together using parallel mechanism to control 3-DOF motions. Each module consists of a common base, an individual middle mass and a common isolation table. The base to the middle mass is suspended by positive springs generated by active and passive system, and the middle mass and the isolation table is connected by negative spring realized by active-type modified zero-power control. The developed system could realize zero-compliance to direct disturbances as well as good ground vibration isolation. Furthermore, the isolation table is supported by a weight support mechanism for supporting heavy payloads. In the previous research, a concentrated middle mass with redundant actuators, in the vertical and horizontal directions, were used. Therefore, a vibration isolation system is proposed in this work using modular concept to overcome those drawbacks. Each module is controlled separately by decentralized control technique, and three modules can be used for three-degree-of-freedom of motion control. Therefore, no redundancy of actuator is occurred. Moreover, an improved zero-power controller is presented that can adjust negative stiffness instead of conventional zero-power controller. The results obtained from analytical and experimental studies show that the modular technique is reliable and efficient approach to vibration control, and represents a suitable alternative to the conventional active vibration isolation systems.

This paper discusses the feasibility of zero-power control in parallel magnetic suspension systems. In parallel magnetic suspension systems, multiple floators are suspend with a single power amplifier. The zero-power control has been used in magnetic suspension systems with permanent magnets providing bias flux. This control realizes the steady states where the attractive force produced by the permanent magnets balances the weight of the suspended object and the electromagnet coil current converges to zero. This paper shows that parallel magnetic suspension systems incorporating zero-power control can assign the poles arbitrary if the original parallel suspension systems are controllable. The feasibility of the zero-power control in a parallel magnetic suspension is demonstrated experimentally.

This paper presents a vibration isolation system using negative stiffness suspension. The vibration isolation system is developed by combining a positive stiffness suspension in series with a negative stiffness suspension. The developed system could realize zero-compliance to direct disturbance, as well as ground vibration isolation. In the previous system, the ground vibration and, the static and low frequency sinusoidal direct disturbances were efficiently suppressed. However, there was a reverse action in case of impulse or step wise disturbance. Therefore, a peak was appeared which was, sometimes, larger than the displacement caused by the step load. This unpleasant response might hamper the objective function of many advanced systems. In this research, a feedforward controller is added in combination with zero-power control to overcome this problem. Some experimental results are presented to verify the proposed control system in a vibration isolation apparatus.

A flux-path control magnetic suspension system with multiple magnetic sources is realized. The principle of the flux-path control magnetic suspension system is to control flux from a permanent magnet to the floator, and the attractive force acting on the floator by the motion control of control plates inserted between the permanent magnet and the floator. Stable suspension and 3-DOF control with a single magnetic source was achieved. However, the horizontal control force was much less than the vertical control force. Multiple magnetic source system can overcome such problem. A variable flux-path unit is developed for the realization of multiple magnetic source system. An experimental apparatus with two variable flux-path units is constructed. Stable levitation is achieved by applying PD and PID controls. In addition, stable levitation with zero-power control is also achieved.

A three-degree-of-freedom (3-DOF) active vibration isolation system using displacement cancellation control technique is developed. The displacement cancellation concept is presented and implemented in this research to obtain zero compliance of vibration isolation table against direct static force as well as to suppress the dynamic disturbances acting on the isolation table. In the displacement cancellation control technique, relative movements of the vibration free table are followed with I-PD control and movements of the middle mass respect to base are controlled with PD control. The corresponding controllers are designed in such way so that actuator can generate opposite force against disturbance to cancel the effect of displacement of the middle mass on the vibration isolation table, which finally leads zero compliance of the isolation table. Voice coil motors (VCMs) are used for getting linear actuating effect and corresponding displacements of the table are detected by eddy-current gap sensors. The experimental results showed that the developed system with displacement cancellation mode control has capability to maintain zero compliance against direct static force in the 3-DOF motions associated with horizontal translations and a vertical rotation. Moreover experiments have been conducted to measure the dynamic responses of the vibration isolation table to direct disturbance.

In series-type multiple magnetic suspension systems, multiple floators are suspended in tandem by one electromagnet. The nearest floator to the electromagnet is directly suspended by the electromagnet. The others are indirectly suspended by the attractive force due to the magnetization of the floators. The controllability and observability of series-type multiple magnetic suspension systems with an arbitrary number of floators are discussed. They are controllable and also observable even when only the displacement of the floator nearest to the electromagnet is detected. A series-type multiple magnetic suspension system was fabricated in order to verify the analyses experimentally. In the fabricated system, magnetic suspension units that are equipped with a sensor and an electromagnet are used instead of normal floators to carry out experiments in various conditions. As the first step to realize the levitation of multiple floators using one electromagnet and one sensor, a basic trial was carried out in the fabricated system.

This paper studies the controllability of parallel magnetic suspension. The most basic magnetic suspension system consists of a suspended object (floator), an electromagnet and a power amplifier. In parallel magnetic suspension, multiple floators and electromagnets are controlled with a single power amplifier. The concept and the fundamental properties of parallel magnetic suspension systems have been already presented. They are classified according to the output of power amplifier and the connection of coils. However, the polarity of electromagnet has not been treated yet. In this work, the effect of the polarity is taken into consideration. It is shown that the controllability is independent of the polarity.

A review of mass measurement devices developed by the author is presented. According to the measurement principles, the treated devices are classified into two types. The first type uses a dynamic vibration absorber as a device for both mass measurement and vibration control. The main advantage is no vibration transmitted into the surrounding structures during measurement. The second type uses relay feedback. The advantages are simpler mechanism and robustness against disturbances. In this article, the principles of measurement of each type are presented.

Parallel electrostatic suspension is proposed and studied analytically. In this suspension system, a single power amplifier is operated to suspend multiple floators or to control the multiple-degre...

This paper presents a six-degree-of-freedom hybrid vibration isolation system integrated with an active negative suspension, an active–passive positive suspension and a passive weight support mechanism. The aim of the research consists in maximizing the system and control performances, and minimizing the system development and maintenance costs. The vibration isolation system is, fundamentally, developed by connecting an active negative suspension realized by zero-power control in series with an active–passive positive suspension. The system could effectively isolate ground vibrations in addition to suppress the effect of on-board generated direct disturbances of the six-axis motions, associated with vertical and horizontal directions. The system is further reinforced by introducing a passive weight support mechanism in parallel with the basic system. The modified system with zero-power control allows simplified design of the isolation table without power consumption. It also offers enhanced performance on direct disturbance suppression and large payload supporting capabilities, without degrading transmissibility characteristics. A mathematical model of the system is presented and, therefore, analyzed to demonstrate that zero-compliance to direct disturbance could be generated by the developed system. Experimental demonstrations validate the proposed concept that exhibits high stiffness of the isolation table to static and dynamic direct disturbances, and good transmissibility characteristics against ground vibration. Further improvements of the vibration isolation system and the control system are discussed as well.

A gyroscopic sensor using active magnetic bearing (AMB) is studied both theoretically and experimentally. The sensor has been proposed to realize high accuracy, compact and low-cost sensors, and it utilizes the control function of the AMB. The sensor works as a two-axis gyroscopic sensor and also as a three-axis servo-type accelerometer. Angular velocities and accelerations are measured based on the control signals for cancelling the inertial effects that act on the AMB rotor. The methods to detect the accelerations and angular velocities have been validated from several experimental results. In addition, it has been indicated that there is an upper limit in the measurement bandwidth of the sensor when the two-axis angular velocity is measured simultaneously. However, factors determining the limit have not been presented in a concrete manner. This paper discusses these factors and presents a methodology that can extend the measurement bandwidth of the sensor. The limiting factors are investigated extensively by analysis, numerical simulations and experiments with the AMB. The relationship between the measurement bandwidth and the control system is also investigated. In addition, the measurement range of the gyro is discussed.

A control method for achieving zero compliance to direct disturbance is proposed for a vibration isolation system. The structure of the proposed zero-compliance system is as follows. A middle mass is suspended by a spring from the base. The isolation table is suspended and moved by a linear actuator that is fixed to the middle mass. When direct disturbance acts on the isolation table, the middle mass begins to move in the same direction as the disturbance. The actuator operates to move the isolation table in the opposite direction to cancel the displacement of the middle mass to the base. To verify the effectiveness of this principle, a single-axis apparatus was fabricated. In this apparatus, the isolation table and the middle mass are guided to move horizontally to study characteristics without the influence of gravity. A voice coil motor (VCM) is installed between the isolation table and the middle mass, and integral—proportional—derivative (I-PD) control is implemented to achieve displacement cancellation control. Another VCM is installed between the middle mass and the base, and PD control is implemented for realizing the prescribed stiffness and damping. The efficacy of the designed control system is confirmed experimentally.

Rotor unbalance in an AMB-based gyroscopic sensor is studied in this paper. An AMB-based gyroscopic sensor has been proposed to realize a high-accuracy, low-cost and compact gyroscopic sensor. In this sensor, an active magnetic bearing (AMB) is applied as a rotating gyro, which is an instrument for measuring angular velocity. The relative position and attitude of the AMB rotor to the AMB stator are maintained using magnetic forces. Two-axis angular velocities of a measurement object are estimated from the control currents required to cancel the gyroscopic torque acting on the AMB rotor. However, the estimated signals of angular velocities include several undesirable frequency components. These components are caused by rotor unbalance and the induction motor used to spin the AMB rotor. A beat appears due to composition of these components. The beat component cannot be eliminated by filtering because it is in the measurement bandwidth of the AMB-based gyroscopic sensor. In this study, two unbalance compensation methods are applied to the AMB-based gyroscopic sensor to eliminate the beat component from the estimated measurements of angular velocities. The efficacy of each compensation method is examined experimentally.

This paper presents a control system for active magnetic bearings (AMBs) considering the motions of the stator. AMBs require active control for stable support of the rotor. Many control methods for AMBs have been proposed. Most of them are designed with no regard to the stator motions because the stator is usually fixed on the base. However, in some applications, the stator moves with the object in which the AMB is mounted. In this paper, the influences of the stator motions on the relative angle of the rotor to the stator are investigated both theoretically and experimentally. In addition, the signals estimated by a disturbance observer are used to compensate the influences. The influences become remarkable at a low frequency range. The upper side of the remarkable range extends to higher frequency range when the gyroscopic effect is large. The influences are cancelled by the compensation using the observer. The effect of the cancellation depends on the estimation speed of the observer.

A surface acoustic wave (SAW) linear motor is a kind of ultrasonic motor. The advantages of the SAW linear motor are thin structure, high thrust force, high velocity and precise positioning. The relationship between applied current and output velocity is, however, unstable in the low velocity range due to the friction drive principle. Therefore the SAW linear motor cannot obtain stable driving without feedback control in the low-velocity region. In this research, to realize low velocity, a pulse width modulation (PWM) control and flexible slider structure are employed. Flexible structure is installed to cancel vibration due to the PWM carrier wave. A lower velocity in the unstable range is realized. Moreover we change the calculation algorithm for the slider velocity measurement. As a result, the SAW linear motor can be driven at an ultra low velocity of 30μm/s. Additionally, driving characteristics are improved using a feedforward controller.

The applicability of relay feedback to mass measurement was investigated. Two mass measurement systems were studied both theoretically and experimentally. One of them uses an on-off relay with hysteresis and switches force acting on the object in relation to the velocity of the object. The other contains an on-off relay with dead zone and switches force acting on the object in relation to the displacement. The principle of measurement, a fabricated apparatus and measurement results were presented for each measurement system.