Method and system for determining a physical quantity of a particle

Abstract

Method of determining a physical quantity (QP) of a particle (2) comprising the following steps: Directing the particle (2) to a test mass unit (3), wherein an impact of the particle (2) causes a test mass (4) to deflect, Controlling a physical quantity (QT) of the test mass unit (3) according to a reference value (R) by means of a feedback-control-loop (18), the feedback-control-loop (18) comprising a measurement unit (6) which outputs a measurement signal (y(t) ) related to a measurement quantity (QM) of the test mass unit (3), a feedback-controller unit (7) which outputs a controller output signal (u(t) ) for controlling the physical quantity (QT) of the test mass unit (3) and an actuator unit (5) which actuates the test mass unit (3) based on the controller output signal (u (t) ); and Determining the physical quantity (QP) of the particle (2) on the basis of a feedback-loop signal (19) of the feedback-control-loop (18). The invention further relates to a system (1) for determining a physical quantity (QP) of a particle (2).

Description

[0001]Method and System for determining a physical quantity of a particle The invention relates to a method of determining a physical quantity of a particle, which is preferably an atom or molecule, comprising the following steps: Directing the particle to a test mass unit, wherein an impact of the particle on the test mass unit causes a test mass of the test mass unit to deflect. Further, the invention relates to a system for determining a physical quantity of a particle, which is preferably an atom or molecule, the system comprising a test mass unit having a test mass to which the particle is directable. The invention also comprises a method of performing a spectrometry, in particular mass spectrometry, and a spectrometer, in particular a mass spectrometer. Understanding the properties of particles, particularly theirphysical quantities, is crucial across various technical fieldsand also non-technical fields that employ commercially available technical methods. Knowledge of material properties enables important insights into the characteristics of the specimenunder investigation. A prominent technique for acquiring suchknowledge about particle properties, and consequently thespecimen from which these particles originate, is massspectrometry. Mass spectrometry typically measures the mass-to-charge ratio ofparticles, which may be molecules and other chemical compounds.Mostly, the particles are charged ions. However, also massspectrometry with uncharged particles is basically possible. Theresults of mass spectrometry are usually presented as a mass spectrum, which is a plot of intensity versus the mass-to-chargeratio. Mass spectra are helpful in elucidating the chemicalidentity or structure of the particles and hence in determiningthe elemental or isotopic signature of a specimen. In the prior art, many different types of mass spectrometrymethods are known. A prominent and widely used example of a massspectrometry method is time-of-flight mass spectrometry, where ions are accelerated by an electrical field of known strength towards a detector. The resulting velocity depends on the mass- to-charge ratio of the ions. The time that it subsequently takes for the ion to reach a detector is measured. This time depends on the velocity of the ion, and therefore is a measure of its mass-to-charge ratio. From this ratio and known experimentalparameters, one can identify the ion und thus gain informationabout the specimen under investigation.Further, EP 2 884 520 A1 discloses a device for nano massspectrometry comprising a sensing member which is deformable inresponse to particle impacts and a deformation detector arrangedand configured to determine the deformation of the sensingmember. Based on the detected deformation, properties of theparticles can be derived. The sensing member can be a nanotubeor a membrane. Detection of the deformation is made by anoptical or electronic measurement arrangement.US 2012 / 0305760 A1 relates to a device and a method fordetecting, sensing and analysing analytes in samples. Said device and system use MALDI (Matrix Assisted Laser Desorptionand Ionization) to generate ions. The generated ions aredirected to a membrane detector comprising a membrane. A voltageis applied to the membrane. Upon impact of the ions, electronsare emitted and influence a field emission of the membranedetector. Based thereon, properties of the analytes can be determined. EP 1285 455 B1 discloses a sensor structure with a cantilever that is deflected by the impact of a particle. In one embodiment, a switch element is provided, which may be a transistor, for example, and is connected to a controller. Whenthe switch element is activated by the cantilever beingdeflected by a particle, the controller discharges the sensorstructure, if required.The methods described above both use membranes as detectors.However, problems with such membranes are that they are typically weakly damped, which leads to a very long settling time to a steady state, and that they exhibit a non-linearbehaviour when largely deflected, which negatively influencesmeasurement results and / or exacerbates their interpretation. Byusing stiffer or mechanically damped membranes, deflection of the membranes and hence non-linear behaviour could be reduced;however, the sensitivity of the measurement methods is limitedin this way. Further, the membranes in the prior art havethermomechanical vibrations which negatively influence measurements. In general, it is an objective in metrology to provide robust measurement methods with high accuracy and reproducible results. Measurement engineers and scientists thus strive for permanent improvement and development of new measurement methods. In the light of the above said, it is thus an objective of the present invention to eliminate or at least alleviate at least some of the disadvantages of the prior art. Preferably it is an objective of the present invention to provide a method and a system of determining a physical quantity of a particle asintroduced above which exhibit a high measurement accuracy, ahigh measurement speed, and a high measurement sensitivity atthe same time. The objective is solved by a method of determining a physical quantity of a particle according to claim 1 and a system for determining a physical quantity of a particle according to claim 19. Said method and said system may be used in a method of performing a spectrometry according to claim 18 and a spectrometer according to claim 20. The invention according to independent claim 1 relates to a method of determining a physical quantity of a particle of the type mentioned above and comprises the following steps: Controlling a physical quantity of the test mass unit ac- cording to a reference value by means of a feedback-control- loop, the feedback-control-loop comprising a measurement unit which outputs a measurement signal related to a measurement quantity of the test mass unit into the feedback-control-loop, a feedback-controller unit which outputs a controller output sig- nal for controlling the physical quantity of the test mass unit and an actuator unit which actuates the test mass unit based on the controller output signal; and Determining the physical quantity of the particle based on afeedback-loop signal of the feedback-control-loop. Advantageously, by controlling a physical quantity of the test mass unit, the test mass unit can be operated in a linear rangein which the test mass unit exhibits an essentially linearbehaviour with respect to the physical quantity of the test massunit, the measurement quantity and / or physical quantity of theparticle. Of course, in the linear range, also other physicalquantities related to the test mass unit, the particle and / orthe feedback-control-loop can exhibit an essentially linearbehaviour. As a result of the essentially linear behaviour,operation of the test mass unit and determination of thephysical quantity of the particle can be facilitated and theaccuracy and speed of the determination of the physical quantityof the particle can be improved. At the same time, a highmeasurement sensitivity is provided as test mass units with alow stiffness can be used. In the inventive method, the use of afeedback-control-loop allows for a reliable restoration of thetest mass unit into a desired condition, in particular a desiredposition or an oscillation with a desired frequency andamplitude. The use of a feedback-control-loop also allows to supress unwanted disturbances, such as thermomechanicalvibrations, that may negatively influence the test mass unit andthus the determination of the physical quantity of the particle.Also, by using a feedback-control-loop, excess energy fromimpacting particles can be removed, which reduces the effectivetemperature and contributes to the accurate and fastdetermination of the physical quantity of the particle. Without a feedback-control-loop, the mechanical energy stored in the weakly damped test mass would lead to large deflections, which may cause the system to behave nonlinearly, and the oscillationswould only slowly decay, significantly increasing themeasurement time. Moreover, the system is prone to stochasticdisturbances. The use of an active feedback-control-loop is alsoadvantageous over passive damping mechanisms, since passivemechanical damping systems lower the sensitivity of the testmass unit with respect to the impact on the particle. Moreover,feedback-control-loops can be actively adapted to compensate fordrift phenomena, which is not possible with passive dampingsystems. The particle, the physical quantity of which shall bedetermined, may be an atom or a molecule. The particle may becharged or uncharged. The particle is directed to the test mass unit, where the particle hits the test mass, thereby deflecting the test mass, as the test mass or at least parts of it aremovable. If the test mass is oscillating, the deflection causesa disturbance of the oscillation, in particular a jump in phaseand / or amplitude. The test mass may be, for example, suspended,preferably by a frame, or be levitated. In a preferredembodiment, the test mass unit comprises a membrane, inparticular a trampoline, or a cantilever as a test mass ontowhich the particle can be directed. The test mass unit may alsocomprise multiple test masses. With the inventive method, one ormore physical quantities of the particle can be determined. Theinventive method can also be used to determine one or morephysical quantities of multiple particles parallelly or oneafter another. To facilitate parallel analysis of particles,multiple test mass units or one or more test mass unitcomprising multiple test masses may be used. In the following, determination of only one physical quantity of only one particlewill be described. The physical quantity of the particle may bea physical quantity inherently related to the particle, such as mass or a charge, or a physical quantity depending on thecurrent state of the particle, such as velocity or momentum. Inorder to determine the physical quantity of the particle, the particle is directed to the test mass unit. For directing theparticle, an electric, a magnetic and / or an electromagneticfield may be used, for example. Preferably, the particle is also accelerated when being directed to the test mass unit. The particle causes the test mass of the test mass unit to deflect, at least initially. When the test mass unit is kept oscillating by means of the feedback-control-loop, the deflection causes a phase jump of the oscillation. According to the invention, a physical quantity of the test mass unit is controlled according to a reference value by means of a feedback-control-loop. The physical quantity of the test mass unit may be, for example, a motional quantity, such as a position, a velocity or an acceleration, or a quantity used to directly or indirectly influence a motional quantity of the test mass unit, such as avoltage or a current generating a force that acts on the testmass. The feedback-control-loop controls the physical quantity of the test mass unit such that said physical quantitycorresponds to a reference value. The reference value can bestatic or change with time. The reference value can, forexample, define a desired position or velocity of the test massor an oscillation of the test mass with a desired frequency andamplitude. However, preferably oscillations of the test mass aresuppressed by the feedback-control-loop. It is preferred that the feedback-control-loop keeps the test mass at a desired position, thereby suppressing oscillations. The desired position may be a center position. The reference value may be set such that the test mass unit is in a desired condition, in particulara desired position or a desired oscillation, when the controlledphysical quantity corresponds to the reference value. In a particularly preferred embodiment of the invention, the test mass unit is operated in a linear range that exhibits an essentially linear behaviour between the measurement quantity and the physical quantity of the particle and / or a linear behaviour between the measurement quantity and the physicalquantity of the test mass unit. This may be achieved byincreasing the restoring force of the actuator unit when thetest mass approaches a non-linear range. The feedback-control-loop is a closed feedback loop that actively controls the testmass unit. The feedback-control-loop measures a measurementquantity of the test mass unit, processes the measurementquantity, and acts on the test mass unit such that the physical quantity of the test mass unit corresponds to the reference value. The measurement unit may measure the measurement quantity of the test mass unit, such as a motional physical quantity, in particular a position, a velocity or an acceleration of the test mass. In one embodiment, the measurement unit may measuremultiple measurement quantities of the test mass unit. However,in the following, measurement of one physical quantity will bedescribed. The measurement unit outputs a measurement signalwhich is a measure of or contains the one or more measurementquantities. The measurement signal may be an analogue or a digital signal. In one embodiment of the invention, the measurement signal may be directly fed into the feedback-controller unit. The feedback-controller-unit may comprise oneor more non-linear or linear controllers, such as a P-, a PI- ora PID controllers. In a preferred embodiment, a LQ-Controller orLQ-Regulator (LQ = Linear Quadratic) is used, preferably inconnection with an observer as described below. Of course, anyother suitable control scheme may be used. The controller maycomprise a mathematical model defined by equations of motion andparameters of the test mass unit or the controller may bedeveloped on the basis of such model. The mathematical model maycomprise sets of equations for different modes of the test mass unit, which can be treated essentially independent from each other. Each mode can be assigned an own controller or sub-controller. The control unit may be a digital or analoguecontrol unit. In one embodiment of the invention, the controllerunit may be implemented in a microprocessor or an FPGA (=FieldProgrammable Gate Array). The feedback-controller-unit outputs acontroller output signal such that the controlled physical quantity of the test mass unit corresponds to the referencevalue. Of course, also multiple physical quantities of the testmass unit may be controlled. Said physical quantities may be dependent or essentially independent from each other. Also, multiple reference values may be provided, each associated todifferent physical quantities of the test mass unit. However, inthe following, controlling one physical quantity will be described. The controller output signal may be forwarded to theactuator unit. The actuator unit may comprise one or moreactuators. The controller output signal may be an analogue ordigital signal. The actuator unit may actuate the test massunit, in particular the test mass, based on the controlleroutput signal. The actuator unit may be at least partially orfully included into the test mass unit. Alternatively, the actuator unit may be separate from the test mass unit. The actuator unit may generate a force, such as a magnetic, anelectric or an electromagnetic force, which acts on the testmass. The actuator unit may comprise an amplifier that generatesvoltages and / or currents based on the controller output signalto drive the test mass. In order to determine the physicalquantity of the particle, a feedback-loop signal of thefeedback-control-loop is used. The feedback-loop signal may beany signal used in the loop comprising the feedback-controllerunit, the actuator, the measurement unit, and the test mass. Ina preferred embodiment, the feedback-loop signal may be a signal output of the measurement unit or input into the measurementunit, the feedback-controller unit, or the actuator. The signalsof the signal loop contain information about the impact of theparticle on the test mass, as the signals in the feedback-control-loop are used to directly or indirectly act on the testmass unit bring back the physical quantity of the test mass unitto the reference value. In one embodiment, the feedback-loopsignal may contain information about the energy required tobring the physical quantity of the test mass unit back to thereference value. After the impact, the particle may remainattached to the test mass. Said energy is related to themomentum pP = mP*vP of the particle, as the energy required tobring the physical quantity of the test mass unit back to the reference value essentially corresponds to the kinetic energyEkin_P = mP*v 2P of the particle at the time of impact on the testmass. Here, mP is the mass of the particle and vP the velocity ofthe particle. Thus, in one embodiment, the momentum pP of theparticle at the time of impact on the test mass can bedetermined based on the energy used to restore the physicalquantity of the test mass unit back to the reference value. Inanother embodiment, the kinetic energy Ekin_P may be calculated,for example, based on a charge qP of the particle and the voltageU applied by an acceleration unit, which voltage accelerates thecharged particle to Ekin_P = qP*U. The charge qP of the particleand the voltage U may both be known. Taking into account themomentum p , E can be expressed as E 2P kin_P kin_P = pP / (2mP). Thus, themass of the particle may be calculated as m 2P = pP / (2* Ekin_P). Themomentum pP may be determined as described further below withreference to the figures, where the momentum is determined fromthe controller output signal and curve fitting. The momentumdue to the particle’s impact may also be determined by thediscontinuity in velocity of the state of the test mass uponimpact. A preferred way to achieve this is by using Rauch-Tung-Striebel (RTS)- or similar smoothing algorithms, which utilizemeasurements before and after the impact to estimate the discontinuity in velocity. The Rauch-Tung-Striebel-algorithm isdescribed in S. Särkkä and L. Svensson, Bayesian filtering andsmoothing, Vol. 17, Cambridge university press, 2023 and in H.E. Rauch, F. Tung, and C. T. Striebel, Maximum likelihood estimates of linear dynamic systems, AIAA 3,1445 (1965). In a preferred embodiment of the invention, the physical quan- tity of the particle is a mass of the particle, a velocity of the particle, a momentum of the particle or an electrical charge of the particle. As outlined above, the momentum may be derivedfrom a feedback-loop signal. If one of the velocity or the massof the particle is known, for example, by measurement, the other one of the velocity or the mass of the particle may be calcu- lated from the momentum. Preferably, the mass unit comprises, as the test mass, a test particle, which is preferably levitated, a membrane, a cantile- ver and / or a nanowire. The test mass unit may also comprise mul- tiple test masses. If a membrane is used as test mass, said mem- brane can be suspended by a frame that allows deflection of themembrane. The membrane may be referred to as trampoline. Themembrane can have a mass between 1 * 10-18kg and 1 * 10-8kg. Themembrane can have an effective spring constant between 100 µN / mand 10 N / m. If the test mass is a cantilever, at least one endof the cantilever may be suspended by a holding element. Also,another end of the cantilever may be suspended by another hold-ing element. The cantilever can have a mass between 4 * 10-15 kgand 1 * 10-10 kg. The length of the cantilever may be between 1µm and 10 mm. The cantilever can have an effective spring con-stant between 100 µN / m and 10 N / m. If the test mass is a testparticle, the test particle can be levitated, for example by anoptical trap, in particular an optical tweezer, a magnetic trapor a Paul trap. The test particle may be a nanoparticle. Thetest may have a mass between 1 * 10-22 kg and1 * kg. The test particle may have a diameter between 10 nmand 20 µm.In a preferred embodiment, the physical quantity of the test mass unit is a motional quantity of the test mass, preferably a position, a velocity or an acceleration, or a physical quantity which is preferably proportionally related with said motionalquantity of the test mass. The motional quantity may also be ahigher derivative of the position, the velocity or the acceleration. The motional quantity may also be an oscillationfrequency, an amplitude or a phase. If a cantilever, a membraneor a nanowire is used as test mass, the motional quantity mayrefer to a predetermined spot on the cantilever, the membrane orthe nanowire. A physical quantity, which is preferablyproportionally related with said motional quantity of the testmass, may be, e.g., an induced voltage or an induced currentinduced by the movement of the test mass. The measurement quantity of the test mass unit may be a motional quantity of the test mass, preferably a position, a velocity oran acceleration, or a physical quantity, which is preferablyproportionally related to said motional quantity of the test mass. The measurement quantity of the test mass unit may be the same as the physical quantity of the test mass unit that is controlled. However, it is also possible that the measurement quantity of the test mass unit is different from the physical quantity of the test mass unit that is controlled. If acantilever, a membrane, or a nanowire is used as test mass, themotional quantity may refer to a predetermined spot on thecantilever, the membrane, or the nanowire. The motional quantitymay also be a higher derivative of the position, the velocity, or the acceleration. The motional quantity may also be anoscillation frequency, an amplitude, or a phase. The measurementquantity may be measured by the measurement unit. The measurement unit may be independent of the test mass unit or atleast partially included into the test mass unit. A physicalquantity, which is preferably proportionally related with saidmotional quantity of the test mass, may be, e.g., an inducedvoltage or an induced current induced by the movement of the test mass. The reference value may be a motional quantity of the test mass, preferably a position, a velocity or an acceleration, or a physical quantity which is preferably proportionally related with said motional quantity of the test mass. The motionalquantity may also be an oscillation frequency, an amplitude, ora phase. In one embodiment of the invention, the type of thereference value of the test mass unit may correspond to the typeof the physical quantity of the test mass unit that iscontrolled and / or the measurement quantity of the test massunit. In another embodiment, the type of the reference value isdifferent from the type of the physical quantity of the testmass unit that is controlled and / or the measurement quantity of the test mass unit. For example, the reference value and the physical quantity of the test mass that is controlled may be a position of the test mass, while the measurement quantity is avelocity or acceleration. A physical quantity, which ispreferably proportionally related with said motional quantity ofthe test mass, may be, e.g., an induced voltage or an inducedcurrent induced by the movement of the test mass. In a preferred embodiment of the invention, the feedback-con- trol-loop comprises an observer unit that estimates at least one physical quantity of the test mass unit, in particular at least one motional physical quantity of the test mass or a physicalquantity, which is preferably proportionally related with saidmotional quantity of the test mass. The observer unit may, forexample, estimate at least one physical quantity of the test mass unit that is not measured by the measurement unit. The es- timated physical quantity may, in a preferred embodiment, be a motional quantity, such as a position, a velocity, an accelera-tion, or a higher derivative thereof. The estimated physicalquantity may also be a frequency, an amplitude, or a phase of anoscillation of the test mass. The estimated physical quantitymay also be related with said motional quantity of the test mass, such as an induced voltage or an induced current. It is also possible that the observer unit estimates multiple physical quantities of the test mass unit. The observer unit may comprisea linear or a non-linear observer, which may include a model ofthe test mass unit. The observer may comprise an error correc- tion term that minimizes the error between the estimated physi- cal quantity of the test mass unit and the corresponding physi-cal quantity in reality. In one embodiment of the invention, theobserver may be a Luenberger observer as described in D. G. Lu-enberger, "Observing the State of a Linear System," in IEEE Transac-tions on Military Electronics, vol. 8, no. 2, pp. 74-80,April 1964. In a preferred embodiment of the invention, theobserver comprises a Kalman- or Kalman-Bucy filter, as outlinedin S. Särkkä and L. Svensson, Bayesian filtering and smoothing,Vol. 17 (Cambridge university press, 2023) or in R. E. Kalmanand R. S. Bucy, New results in linear filtering and predictiontheory, Journal of Basic Engineering 1, 95 (1961). In this way,stochastic properties of measurement noise and disturbances mayadvantageously be systematically considered when estimating thephysical quantity of the test mass unit. The observer unit maybe implemented in a microprocessor or an FPGA. The observer unitand the feedback-controller unit may cooperate and form a Linear quadratic Gaussian regulator (LQG), which is the optimal con- troller for linear systems disturbed by Gaussian noise in the least square sense.In one embodiment of the invention, the observer unit may be fedwith the measurement signal, the controller output signal, and / or an actuator output signal. By means of the measurement signal, the controller output signal and / or an actuator output signal, the observer unit may reduce, in particular minimize, an error between the estimated physical quantity of the test mass unit and the corresponding physical quantity in reality. In order to control the physical quantity of the test mass unit, the observer unit may output the at least one estimated physical quantity to the feedback-controller unit. In a preferred embodiment, the measurement quantity and the estimated physical quantity of the test mass unit are fed into the feedback-controller unit. Based on the measurement quantity and theestimated physical quantity, the controller may output the controller output signal.As outlined above, the feedback-loop signals are a measure forthe energy required to actuate the test mass and thereby bring the physical quantity of the test mass that is being controlled in accordance with the reference value. In a favourable embodiment of the invention, the feedback-loop signal thatserves as a basis to determine the physical quantity of theparticle may be the controller output signal, an actuator outputsignal of the actuator unit, or the sensor output signal. Alsosignals that are related, in particular proportionally related, with said signals may be used to determine physical quantity of the particle. When an observer unit is included into the feedback-control- loop, the feedback-loop signal from which the physical quantity of the particle is determined may be an observer output signal which comprises the at least one physical quantity of the test mass unit estimated by the observer unit. In other words, the physical quantity of the particle does not have to be directly measured, but can be estimated. Based on the estimation, in which stochastic properties of measurement noise anddisturbances are systematically considered, the physicalquantity of the particle can be determined. In order to direct the particle towards the test mass unit, the particle may be accelerated towards the test mass unit. Theacceleration can be carried out with an electrical, magnetic, orelectromagnetic field. Preferably, the particle directed to thetest mass is charged, which enables the use of an electricalfield. The electrical field may be created through an electricpotential with a voltage between 100 V and 1*105 V. By means ofthe electrical field, particles may be accelerated such that particles may have a momentum between 1*10-22and 1*10-16kg*m / s.The particle may be charged by an ionization procedure.In order to achieve high velocities and to avoid collisions withother particles in the environment, the test mass unit is operated in vacuum. Also, a source unit, from where the particles originate, and the electrical field may be operated in vacuum. The vacuum may have a residual pressure lower than 10-2bar. The residual pressure may be, in another embodiment, lowerthan 10-3 bar or lower than 10-4 bar.In a preferred embodiment of the invention, the test mass unitcomprises an impact zone to which the particle is directed,wherein the impact zone has a diameter between 1 µm and 1000 µm. Preferably, the impact zone is between 40 µm and 100 µm. If the impact zone is essentially rectangular, the diameter refers tothe diagonal of the rectangle. If the impact zone is generally polygonal, the diameter refers to the largest diameter of the polygon. In one embodiment of the invention, the measurement unit maycomprise a capacitive sensor, an inductive sensor, and / or anoptical sensor that measures the measurement quantity. Asoptical sensor, an interferometer may be used. For example, aDoppler interferometer may be used. An interferometer maymeasure a motional quantity of the test mass, such as aposition, a velocity, or an acceleration. Capacitive orinductive sensors may measure changes in capacitance orinductance, respectively. From said changes in capacitance orinductance, motional quantities, such as a position, a velocity, or an acceleration, of the test mass may be derived. Themeasurement unit may be at least partially included into thetest mass unit or be separate from the test mass unit. Accordingto quantum mechanics, any measurement performed on the test mass implies a back-action on the test mass to ensure Heisenberg’s uncertainty relation. In one embodiment of the invention, the measurement unit is accurate enough to achieve the standard quantum limit of metrology, that is, it practically saturates the Heisenberg uncertainty relation. In order to control the physical quantity of the test mass unit, the actuator unit comprises an actuator that actuates the test mass unit on the basis of electrostatic forces, Lorentz forces, electromagnetic forces, and / or piezoelectric forces. The actuator may be at least partially included into the test mass unit or be separate from the test mass unit. In order to actuate the test mass unit with electrostatic forces, the test mass maybe charged, in one embodiment of the invention. The test massmay be pre-loaded with a charge. For the use of Lorentz forces,a magnetic field may be used. Magnetic fields may be generatedby permanent magnets or coils, for example. Electric currentswhich flow though the test mass, in particular a membrane, may be used to generate attracting or repelling forces, thereby altering the position of the test mass. Piezoelectric forces mayalso be used to actuate the test mass. In one embodiment, one ormore piezoelectric elements may be disposed in the holdingelement / s or frame that suspend / s a cantilever, a membrane or nanowire. In another embodiment, a cantilever may comprise a piezoelectric layer. In order to avoid that the deflection causes a non-linear behav- iour of the test mass, it is advantageous if the deflection of the test mass is limited, preferably by means of the feedback- control-loop. In one embodiment of the invention, the boundarydepends on the non-linearity of the test mass unit. Such non-linearity may be the non-linear relation between, for example, a voltage used to actuate the test mass and the position of thetest mass. The controller is designed such that the test massunit exhibits an essentially linear behavior. In the linearrange, preferably, a linear relationship between the physicalquantity of the test mass unit and the measurement quantity and between the physical quantity of the particle and the measure- ment quantity is given. The invention also relates to a method of performing a spectrom- etry, in particular mass spectrometry, comprising the following steps: Providing a specimen; Separating at least one particle from the specimen, prefera- bly wherein the at least one particle is ionized; Analysing the at least one particle by using a method of de- termining a physical quantity of a particle as described above. The specimen may, for example, be solid, liquid and / or gaseous. In particular in case of solid or liquid specimen, particles may be separated from the rest of the specimen by, for example, by nebulization by a jet or an electrospray. The particles may be ionized upon separation or thereafter, for example, by means ofa matrix-assisted laser desorption / ionization (MALDI) or elec-trospray ionization. The at least one particle separated fromthe rest of the specimen is then directed to a test mass unit asdescribed above. In order to evaluate multiple particles paral- lelly, the test mass unit may comprise multiple test masses con-trolled individually as described above, or multiple test massunits. The invention also relates to a system for determining a physi- cal quantity of a particle, which is preferably an atom or molecule, comprising a test mass unit having a test mass to which the particle is directable, characterized by a feedback-control-loop configured to control a physical quantity of the test mass unit according to a reference value, wherein the feedback-control-loop comprises: -a measurement unit configured to output a measurementsignal related to a measurement quantity of the test mass unit into the feedback-control-loop, -a feedback-controller unit configured to output a con-troller output signal and -an actuator unit, which is configured to actuate the testmass unit based on the controller output signal; and a determination unit configured to determine the physical quantity of the particle on the basis of a feedback-loop signal of the feedback-control-loop.The advantages, effects, and features described above in connec-tion with the inventive method of determining a physical quan- tity of a particle also apply to the inventive system for deter- mining a physical quantity of a particle. Thus, with respect tothe advantages, effects, and features, it is herewith referredto the above remarks. The feedback-controller unit may be imple-mented in a microprocessor, an FPGA, or a computer. Also, thedetermination unit may be implemented in a microprocessor, anFPGA, or a computer. The observer unit may also be implementedin a microprocessor or an FPGA.The invention also relates to a spectrometer, in particular massspectrometer, comprising the following:a source unit configured to accommodate a specimen; a separation unit, in particular an ionization unit, config- ured to separate individual particles from the specimen, thereby preferably ionizing the particles; optionally an acceleration unit configured to accelerate particles; and a system for determining a physical quantity of a particle as described above. The source unit is configured to accommodate solid, liquid and / or gaseous specimen. The separation unit may be configured to direct the particles towards the test mass unit. In a pre- ferred embodiment, the separation unit may also ionize the par- ticles. To this end, the separation unit may be, for example, a separation unit that applies a matrix-assisted laser desorp- tion / ionization (MALDI) procedure. The particles may addition- ally be accelerated towards the test mass unit, for example byelectrical, magnetic or electromagnetic fields. To this end, el-ements that generate electrical, magnetic or electromagnetic fields, may be provided in the spectrometer. Electric fields may be, in one embodiment, generated by plates to which a voltage is applied. Magnetic and electromagnetic fields may be generated by coils, for example. In the following, exemplary embodiments of the invention are described with reference to the drawings, which the invention shall not be restricted to, however.Fig. 1 schematically shows a system for determining a physicalquantity of a particle; Fig. 2 schematically shows a resonator. Fig. 3 shows a spectrometer with a block diagram of a control scheme according to a first embodiment; Fig. 4 shows a spectrometer with a block diagram of a control scheme according to a second embodiment; Fig. 5 a measurement signal and a velocity of the test mass; and Fig. 6 a controller output signal and a fitted curve Fig. 1 schematically shows a setup of a system 1 for determininga physical quantity QP of a particle 2, such as a momentum pP, avelocity vP and or a mass mP of the particle 2 (see also Fig. 3).The particle 2 is preferably a molecule or an atom. The system 1comprises a test mass unit 3 with a test mass 4, an actuator unit 5, a measurement unit 6, a feedback-controller unit 7 and adetermination unit 8 for determining the physical quantity QP ofthe particle. In the embodiment shown, the actuator unit 5 ispartially included into the test mass unit 3, as will bedescribed below. The test mass 4 is formed by a membrane 9, but may also be a nanowire, a cantilever or a test particle (not shown). The membrane 9 is suspended by a frame 10 and may swingupon impact of a particle 2 in an impact zone 11 of the membrane9. After impact, the particle 2 may remain disposed on themembrane 9, i.e., stick on the membrane 9. The impact zone 11has a size of, for example, 50 µm times 50 µm. The kineticenergy Ekin_Pof the particle 2 is thereby transferred into anoscillation O of the membrane 9 or disturbs an oscillation Omaintained by the feedback-controller unit 7. The movement of the membrane 9 or generally the test mass 4 is detected via the measurement unit 6, which, in the embodiment shown, is an optical sensor 6a in the form of a Laser Doppler interferometer. Alternatively, inductive or capacitive sensors may be used. Preferably, the measurement unit 6 provides a measurementresolution of at least 10 pm / Hz1 / 2, more preferably of at least 1pm / Hz1 / 2, or of at least 100 fm / Hz1 / 2. The optical sensor 6acomprises a Laser source 12 and multiple optical elements 13,such as beam splitters and lenses, and is configured to measurea movement of the membrane 9 at a predetermined spot 14 at themembrane 9. The spot 14 may be located inside or outside theimpact zone 11. The measurement unit 6 may measure a measurementquantity QMof the test mass unit 3 in the form of a motional quantity, in particular a position xT, a velocity vTor an acceleration aT of the test mass 4. The measurement unit 3outputs an analogue or digital measurement signal y(t) relatedto a measurement quantity QMto the feedback-controller unit 7or, in a preferred embodiment of the invention, to an observerunit 15, which will be described below.The feedback-controller unit 7 is preferably implementeddigitally in a microprocessor or an FPGA and is configured tooutput a controller output signal u(t) to the actuator unit 5for controlling a physical quantity QTof the test mass unit 3, in particular a motional quantity of the test mass 4, such as a position xT, a velocity vTor an acceleration aTof the test mass 4. To this end, the feedback-controller unit 7 may comprise anon-linear or a linear controller, such as a P-, a PI- or a PID-controller. However, any suitable controller design may be used. Preferably, an LQ-controller is used, which is particularly advantages with respect to the use of an observer unit 15, as will be described below. In one embodiment, the measurement quantity QMand the controlled physical quantity QTof the test mass unit 3 may be the same. The feedback-controller unit 7outputs an output signal u(t) to the actuator unit 5 such thatthe physical quantity QTof the test mass unit 3 corresponds to areference value R. The reference value R may be static or varywith time, which is favourable if an oscillation O of the testmass 4 is desired. Specifically, upon impact on of a particle onthe test mass 4 and hence deflection of the test mass 4, thefeedback-controller unit 7 provides a controller output signalu(t) that causes the actuator unit 5 to act on the test massunit 3 such that the physical quantity QTof the test mass unit 3is brought back to the reference value. In case the physicalquantity QTof the test mass unit 3 that is controlled is aposition xT, the reference value may also be a position R = xref.However, the physical quantity QTof the test mass unit 3 mayalternatively be, for example, also a velocity vT, anacceleration aTor a higher derivative of the test mass 4 as well. Thus, the reference value may also be a velocity, anacceleration or a higher derivative thereof. It shall be notedthat the invention is not restricted to motional quantities asphysical quantity QT of the test mass unit 3 or as themeasurement quantity QM. In alternative embodiments, electricalquantities, such as induced currents or voltages, may serve asphysical quantity QTof the test mass 4 or measurement quantity QMof the test mass unit 3, specifically when such electrical quantities are related to motional quantities of the test mass4. Also, the reference value R may an electrical quantity.The actuator unit 5 is, in the present embodiment, partially included into the test mass unit 3. The actuator unit 5comprises magnets 16 which generate a magnetic field B, forexample with a field strength of at least 1 T (see also Fig. 2).Magnets 16 may be permanent magnets. The membrane 9 comprises,in the embodiment shown, two wires 17 (see Fig. 2), which mayconduct electrical currents i1(t), i2(t) (see also Fig. 2). Dueto Lorentz forces F(t), the membrane 9 can be actuated by thecurrents i1(t), i2(t). To generate the currents i1(t), i2(t), anamplifier may be used. However, the amplifier is omitted in theshown embodiment. By regulating currents i1(t), i2(t), thephysical quantity QT, in particular a position xTof the testmass 4, of the test mass unit 3 may be controlled such that thephysical quantity QTcorresponds to the reference value R. The test mass unit 3, the actuator unit 5, the measurement unit 6 and the feedback-controller unit 7 form a feedback-control-loop 18 by means of which the physical quantity QT of the testmass unit 3 is controlled according to a reference value R. Uponimpact of a particle 2 on the membrane 9, the membrane 9 is deflected and causes the feedback-controller unit 7 to counteract and bring the physical quantity QTof the test mass unit 3 back to the reference value R.Fig. 2 shows a membrane 9 hinged to a frame (not shown) viaconnection elements 9a in the form of tethers. The membrane 9 isactuated via wires 17 attached to or included into the membrane9. The magnetic field B is directed in z-axis-direction. Thewires 17 are arranged at least partially obliquely to themagnetic field B. Currents i1(t), i2(t) flowing in the wires 17generate Lorentz forces F(t), which allow for actuating themembrane 9 into the direction of the x-axis. Such membranes asdescribed herein are also described in WO 2020 / 047572 A2, whichis incorporated into the present application herewith. In Fig. 2, also an impact zone 11 is indicated. In another, but not shown embodiment, the controlled physical quantity QTof the test mass unit 3 may also be an electricalquantity, such as a current iind(t) or a voltage uind(t) inducedinto the wires 17. These electrical quantities are induced dueto a movement of the membrane 9 in the magnetic field B. As aconsequence, said electrical quantities are related to amotional quantity of the test mass 4. Thus, the currents iind orvoltages Uindinduced into the wires 17 may be used as measurement quantities QMand / or as controlled physical quantity QTof the test mass unit 3. Referring to Fig. 1 again, the setup also comprisesdetermination unit 8 which is configured to determine thephysical quantity QP of the particle 2 on the basis of afeedback-loop signal 19 of the feedback-control-loop 18. Thefeedback-loop signal 19 may, for example, be the controller output signal u(t), an actuator output signal F(t) of the actuator unit 5 or the sensor output signal y(t). An outputsignal u(t) (thinner curve) is shown in Fig. 6 on the basis ofwhich the physical quantity QPof the particle 2, in particular the momentum pP, may be determined, preferably by fitting (thicker curve). Fig. 3 schematically shows a spectrometer 20 using a system 1 for determining a physical quantity QPof a particle 2 according to a first embodiment. The spectrometer 1 comprises a source unit 21 configured to accommodate a specimen 22. The specimen 22may be gaseous, liquid or solid. By means of a separation unit23, which is preferably an ionization unit 24, individual parti-cles 2 are separated from the specimen 22. Upon separation fromthe specimen, the particles 2 may be ionized. The separationunit 23 may use a laser 25 to separate and ionize the particles from the specimen 22. MALDI (Matrix-assisted Laser Desorp-tion / Ionization) may be used to this end. In order to direct theparticles 2 to a specific spot, an acceleration unit 26 may beused. Such a setup of spectrometers 20 is already known from theprior art and will thus not be explained in more detail.According to the invention, the spectrometer also comprises asystem 1 for determining a physical quantity QP of a particle 1as described above. Fig. 3 comprises a block diagram that illustrates a control scheme of the invention according to the first embodiment. The system 1 comprises a test mass unit 3 with a test mass 4, an actuator unit 5, a measurement unit 6, a feedback-controller unit 7 and a determination unit 8 for determining the physicalquantity QP of the particle 2. In the embodiment shown in Fig. 3,a position xTof the test mass 4 is measured by the measurement unit 6 as measurement quantity QMand provided to the controller unit 7, which processes the measurement signal y(t) and outputs a controller output signal u(t) to the actuator unit 5. On the basis of the output signal u(t), the actuator unit 5 actuates the test mass 4 so that a physical quantity QTof the test mass unit 3, for example the position xTof the test mass 4,corresponds to the reference value R. The controller unit maycomprise a controller which may be, for example, an LQ-controller (also referred to as Linear quadratic Regulator). The controller output signal u(t) is fed into the determination unit8 for determining the physical quantity QP of the particle 2. Thetime of the impact of the particle on the test mass 4 may be determined by detecting the passing particle 2 when leaving the accelerator unit 26 or by determining the impact from measurement data through event-detection methods.Since all components in the feedback-control-loop 18 includingthe controller are essentially linear or can be consideredlinear, the response of the closed-loop system to the impact of the particle 2 is also linear with a known impulse response function u^^(t), i.e., the response of the closed-loop system to agiven momentum kick δp. The impulse response function u^^(t) maybe determined by measurements or calculated from calibratedmathematical models of the test mass unit 3, the measurement unit 6, the actuator unit 5, and the known feedback algorithm in the control unit 7. Due to linearity, any observed response u(t)for t ≥ 0, whereby the particle impact is assumed to happen att = 0, is thus only a multiple of u^^(t). The momentum kick pP or(also denoted as) Δp^ provided by the impacting particle 2 canthus be determined by fitting u^^(t) to the recorded time signalu(t), e.g., if u(t) = α u^^(t) then Δp = α δp. α is a factor which maybe determined by a relation between u(t) and u^^(t). Since thisholds true at every point in time t, a very simple method is tomerely use the equations above at a single point in time t̅> 0.If a non-constant reference value R is used, then the sameprocedure can be used by correcting for the steady-state controller output signal required to follow reference value.For a known kinetic energy of the particle = p^^ / (2m^), e.g.,due to an acceleration unit 26 that yields = q^ U with apreferably known charge q^ of the particle 2 and the preferablyknown accelerator voltage U, the mass of the particle 2 is givenby m^ = Δp ^^ / (2E^^^) when the momentum of the particle istransferred to the test mass 4. For a known velocity v^ of theparticle 2, its mass is directly given by m^ = Δp^ / v^ . Fig. 6shows a fitting of u^^(t) to the recorded time signal u(t).Fig. 4 shows an embodiment of the invention with an alternativecontrol scheme. The spectrometer 20 is identical to thespectrometer 20 of Fig. 3. The system 1 comprises a test massunit 3 with a test mass 4, an actuator unit 5, a measurement unit 6, a feedback-controller unit 7, an observer unit 15 and a determination unit 8 for determining the physical quantity QPof the particle 2. The observer unit 15 comprises an observer 27 that estimates a physical quantity QTof the test mass unit 3. In a preferred embodiment, the observer 27 estimates a physical quantity QTof the test mass unit 3 which is not measured by themeasurement unit 6. To estimate a physical quantity QT of thetest mass unit 3, the observer 27 may comprise a mathematical model of the test mass unit 3 which is fed with the controlleroutput signal u(t). Further, the observer may comprise acorrection term (see the matrix K below) which is associatedwith the measurement signal y(t) and reduces, preferablyminimizes, an error between the output x^(t) of the mathematicalmodel, i.e., the estimated physical quantity QT of the test massunit 3, and the real physical quantity QT of the test mass unit3. In a preferred embodiment of the invention, the observer comprises a Kalman-Bucy-filter, which allows to systematically factor in stochastic properties of measurement noise anddisturbances. The use of a Kalman-Bucy filter is in particularadvantageous when used in combination with an LQ-controller. Thecombination of a Kalman-Bucy filter and an LQ-controller (or LQ-regulator) is known as LQG-Controller (LQG-Controller = Linear-Quadratic-Gaussian Controller). In Fig. 4, the measurement signal y(t) is fed into the observer unit 15. The measurementsignal y(t) may contain a position xT(t) of the test mass 4. Themeasurement signal y(t) containing the position xT(t) of the testmass 4 may be forwarded to the observer unit 15 and thus theobserver 27, which may estimate the velocity vT(t) of the testmass 4, for example. The observer unit 15 outputs the estimatedphysical quantity vT(t) as estimated output x^(t) to the feedback-controller unit 7 and to the determination unit 8 fordetermining the physical quantity QP of the particle 2. Estimatedvariables may be denoted with a hat. Thus, the estimatedphysical quantity vT(t) may be denoted as v^^(t). In the signalx^(t), also the measured position xT(t) may be contained. Based onthe output x^(t), the physical quantity QPof the particle 2 can be determined. Based on the output x^(t), the feedback-controller unit7, which may be a state controller, generates a controlleroutput u(t), which is forwarded to the actuation unit 5. In this way, the feedback-control-loop 18 controls the physical quantity of the test mass unit 3 such the physical quantity QTof the test mass 4, such as the position xT(t) or the velocity vT(t), corresponds to a reference value R. To obtain the momentum kick Δp^provided by the impacting particle 2 from the estimated state ^(t), one can proceed asoutlined above, by fitting a recorded time signal of ^(t) to theknown impulse response u^^(t). The advantage over the method aboveis that the observer can account systematically for stochastic and known disturbances and results is less noisy signals.A more advanced method aims directly to estimate thediscontinuity in the state due to the momentum kick, i.e., Δ^ =^(0 +) − ^(0 −), where ^(0 +) and ^(0 −) denotes the right-sided andleft-sided limit, respectively. Such a momentum kick is depictedin Fig. 5 for the signal vT, where a sudden change of velocity isshown. Velocity vT is measured in µm / s. y denotes the measurementsignal y(t). An optimal state observer such as the Kalman-Bucyfilter directly provides the optimal state estimate ^(t−), i.e.,before the impact of the particle 2. The recorded time signal of^(t) for t ≥ 0, i.e., after the impact of the particle 2, can beimproved by using a Rauch-Tung-Striebel (RTS) smoother, whichgives the optimal state estimate ^(t+) directly after the impactof the particle. As a result, one directly obtains the estimatedmomentum kick Δp from the estimated discontinuity in the stateΔ^ = ^(t +) − ^(t−) if position and momentum of the test mass areused as state variables, i.e., Δ^ = [Δz Δp^]^. Again, for a knownvelocity v^ of the particle 2, its mass mP is directly given bym^ = Δp^ / v^ and for known kinetic energy the mass follows as m^ =Δp^^ / ^2E^^^_^^. In the following, mechanical system of the test mass unit 3, the controller contained in the controller unit 7 and the observer27 contained in the container unit 15 will be described ingreater detail. In the present disclosure, bold letters denote matrices and vectors, while non-bold letters denote scalars. Letters with hat denote estimated variables.The state vector x ∈ Rn represents a variable constructed todescribe the future evolution of the system together withan external inputs u ∈ Rp. n and p are natural numbers. If thesystem of interest obeys linear dynamics, as assumed in thepresent case (please note that the controller operates the test mass unit 3 in a linear range), one obtains the system ofdifferential equationsd dt^ = ^^ + ^^ + ^^(1)whereby the derivative of the state x with respect to time isdetermined by the state x acting via the dynamic matrix A. Also,it is assumed that one can act on the system via the input u,i.e. the actuator unit 5, and some unknown input ξ act, via theinput matrix B and via the disturbance matrix G, respectively.x, u and ξ are vectors.If the state x is only accessible by a certain measurementprocedure, that is the measurement unit 6, which is alsoconsidered linear, a measurable quantity y ∈ Rm can beconstructed as (2)Here C describes the measurement matrix whichprojects the state vector x into the measurement space, thematrices D and H do the same for the known control input andpotentially an unknown external disturbancerespectively. Additionally, noise process ν isadded to account for noise arising from the measurementprocedure. It is assumed that the unknown disturbance ξ and themeasurement noise process ν are both white Gaussiannoise processes with mean and covariance according to Q and R are matrices and describe the covariances of theprocesses. δ is the Dirac delta defining white noise processes.To derive a model for the test mass unit 3 comprising the testmass 4, a single mode harmonic oscillator dynamics of the formm^ẍ^ + γ^x^̇ + k^x^ = F(t)(4)is assumed. Here, xT is the displacement of the test mass 4 andF(t) an external forcing term, which comprises for exampleforces exerted by the actuator unit 5 or by externaldisturbances. mT, γTand kTrepresent the effective mass, the effective vicious damping and the effective spring constant of the test mass unit 3. Equation (4) can beexpressed in the form of equation (1) with Ω = ^^^ / γ^ and Γ =γ^ / ^^as d x ^^dt v^ ^ = ^ 0 1 ^ ^x^ ^ ^−Ω^ −Γ v^ + where the state ^ = [x^ v^]^ with v^ = ẋ^ comprises the position xT,and velocity vT of the test mass 4. In equation 5b a purevelocity measurement vTof the test mass unit is assumed, for example, with the Laser-Doppler interferometer as depicted inFig. 1. It is assumed that the position cannot be measured. Asnanomechanical systems such as the test mass unit 3 often have amultitude of oscillation modes, equations (5a) and (5b) can be extended to multiple uncoupled multi-mode harmonic oscillatormodels, which may be controlled independently. To facilitateunderstanding, a single mode harmonic oscillator is assumed.In order to reconstruct, i.e., estimate, non-measured physicalquantities QTof the test mass unit 3, an optimal observer isdeveloped. If one assumes the unmeasured noise terms ξ and ν tobe Gaussian white noise as in equation (3) then the optimalestimator is given by the Kalman-Bucy filtering equations asexplained in S. Särkkä and L. Svensson, Bayesian filtering andsmoothing, Vol. 17 (Cambridge university press, 2023), or in R. E. Kalman and R. S. Bucy, New results in linear filtering andprediction theory, Journal of Basic Engineering 1, 95 (1961) orin A. Gelb, Applied Optimal Estimation. Cambridge, USA: MITPress, 1974. Based on the already obtained model and theaccessible measurements – in this case the velocity vT of thetest mass 4 – the dynamics can be described as (6)wherein ^ are the estimated states comprising the estimatedposition x^^ and the measured velocity vT. The weighting matrix Kdetermines how much the observer should consider the model orthe measurement. For optimal state observers such as the Kalman-Bucy filter, the weighting matrix K is chosen such that itminimizes the estimation error ‖^ − ^‖^ in the mean square sense.K may be determined by solving a differential Riccati equationas described in S. Särkkä and L. Svensson, Bayesian filteringand smoothing, Vol. 17 (Cambridge university press, 2023), or in R. E. Kalman and R. S. Bucy, New results in linear filtering andprediction theory, Journal of Basic Engineering 1, 95 (1961) orin A. Gelb, Applied Optimal Estimation. Cambridge, USA: MIT Press, 1974. In order to find an optimal feedback-law, the linear quadraticregulator (LQR) problem will be solved, as described in M.Athans and P.L. Falb, Optimal Control: An Introduction to theTheory and Its Applications, Dover Publications, 2007. indetail. The goal is to find an optimal feedback law ^ as afunction of the states of the system, such that a quadratic costterm (7)is minimized with N being symmetric and positive semidefinite and M being symmetric and positive definite. Theoptimal state feedback-law can be derived as ^= −^^^^^^^with ^ given by the algebraic Riccati equation^ = ^^ + ^^^ − ^^^^^^^^ + ^(8)The combination of Kalman filter and LQ-controller togetherforms the so called Linear quadratic Gaussian (LQG) regulator which is the optimal controller for linear systems disturbed byGaussian white noise in the least squares sense. This controlscheme is depicted in Fig. 4.

Claims

Claims:

1. Method of determining a physical quantity (QP) of a particle(2), which is preferably an atom or molecule, comprising thefollowing steps: Directing the particle (2) to a test mass unit (3), whereinan impact of the particle (2) on the test mass unit (3) causes atest mass (4) of the test mass unit (3) to deflect,characterized by Controlling a physical quantity (QT) of the test mass unit(3) according to a reference value (R) by means of a feedback-control-loop (18), the feedback-control-loop (18) comprising ameasurement unit (6) which outputs a measurement signal (y(t))related to a measurement quantity (QM) of the test mass unit (3)into the feedback-control-loop (18), a feedback-controller unit(7) which outputs a controller output signal (u(t)) for control-ling the physical quantity (QT) of the test mass unit (3) and anactuator unit (5) which actuates the test mass unit (3) based onthe controller output signal (u(t)); andDetermining the physical quantity (QP) of the particle (2)based on a feedback-loop signal (19) of the feedback-control-loop (18).

2. Method according to claim 1, characterized in that the physi-cal quantity (QP) of the particle (2) is a mass (mp) of the par-ticle (1), a velocity (vP) of the particle (2), a momentum (pP)of the particle (1) or an electrical charge of the particle (2).

3. Method according to claim 1 or 2, characterized in that thetest mass unit (3) comprises, as the test mass (4), a test par-ticle, which is preferably levitated, a membrane (9), in partic-ular a trampoline, a cantilever and / or a nanowire.

4. Method according to one of claims 1 to 3, characterized inthat the physical quantity (QT) of the test mass unit (3) is amotional quantity of the test mass (4), preferably a position(pT), a velocity (vT) or an acceleration (aT), or a physicalquantity which is preferably proportionally related with saidmotional quantity of the test mass (4).

5. Method according to one of claims 1 to 4, characterized inthat the measurement quantity (QM) of the test mass unit (3) is amotional quantity of the test mass (4), preferably a position(pT), a velocity (vT) or an acceleration (aT), or a physicalquantity which is preferably proportionally related with saidmotional quantity of the test mass (4).

6. Method according to one of claims 1 to 5, characterized inthat the reference value (R) is a motional quantity of the testmass (4), preferably a position (pT), a velocity (vT) or an ac-celeration (aT), or a physical quantity which is preferably pro-portionally related with said motional quantity of the test mass (4).

7. Method according one of claims 1 to 6, characterized in thatthe feedback-control-loop (18) comprises an observer unit (15)that estimates at least one physical quantity (QT) of the testmass unit (3), in particular at least one motional physicalquantity of the test mass (4) or a physical quantity which ispreferably proportionally related with said motional quantity ofthe test mass (4).

8. Method according to claim 7, characterized in that the ob-server unit (15) is fed with the measurement signal (y(t)), thecontroller output signal (u(t)) and / or an actuator output signal(F(t)).

9. Method according to one of claims 7 or 8, characterized inthat the observer unit (15) outputs the at least one estimatedphysical quantity (QT) to the feedback-controller unit (7).

10. Method according to one of claims 1 to 9, characterized inthat the feedback-loop signal (19) on the basis of which thephysical quantity (QP) of the particle (2) is determined is thecontroller output signal (u(t)), an actuator output signal(F(t)) of the actuator unit (6) or the sensor output signaly(t).

11. Method according to one of claims 7 to 9, characterized inthat the feedback-loop signal (19) from which the physical quan-tity (QP) of the particle (2) is determined is an observer outputsignal (^) which comprises the at least one physical quantity(QT) of the test mass unit (2) estimated by the observer unit(15).

12. Method according to one of claims 1 to 11, characterized in that the particle (2) is accelerated towards the test mass unit(3), in particular by means of an magnetic, electrical or elec-tromagnetic field.

13. Method according to one of claims 1 to 12, characterized inthat the test mass unit (3) is operated in vacuum.

14. Method according to one of claims 1 to 13, characterized inthat the test mass unit (3) comprises an impact zone (11) towhich the particle (2) is directed, wherein the impact zone (11)has a diameter between 1 µm and 1000 µm.

15. Method according to one of claims 1 to 14, characterized inthat the measurement unit (6) comprises a capacitive sensor, aninductive sensor and / or an optical sensor (6a) which measuresthe measurement quantity (QM).

16. Method according to one of claims 1 to 15, characterized inthat the actuator unit (5) comprises an actuator (5) that actu-ates the test mass unit (3) on the basis of electrostaticforces, Lorentz forces, electromagnetic forces, and / or piezoe-lectric forces.

17. Method according to one of claims 1 to 16, characterized inthat the deflection of the test mass (4) is limited to a prede-termined boundary, preferably by means of the feedback-control-loop (18).

18. Method of performing a spectrometry, in particular massspectrometry, comprising the following steps:Providing a specimen (22);Separating at least one particle (2) from the specimen (22),preferably wherein the at least one particle (2) is ionized;Analysing the at least one particle (2) by using a method ofdetermining a physical quantity (QP) of a particle according to one of claims 1 to 17.

19. System (1) for determining a physical quantity (QP) of a par-ticle (2), which is preferably an atom or molecule, comprising atest mass unit (3) having a test mass to which the particle (2)is directable, characterized by a feedback-control-loop (18) configured to control a physi- cal quantity (QT) of the test mass unit (3) according to a refer- ence value (R), wherein the feedback-control-loop (18) com- prises: -a measurement unit (6) configured to output a measurementsignal (y(t)) related to a measurement quantity (QM) of the test mass unit (3) into the feedback-control-loop (18), -a feedback-controller unit (7) configured to output acontroller output signal (u(t)) and -an actuator unit (5) which is configured to actuate thetest mass unit (3) based on the controller output signal (u(t)); and adetermination unit (8) configured to determine the physi-cal quantity (QP) of the particle (1) based on a feedback-loopsignal (19) of the feedback-control-loop (18).

20. Spectrometer (20), in particular mass spectrometer, compris-ing: asource unit (21) configured to accommodate a specimen(22); aseparation unit (23), in particular an ionization unit,configured to separate individual particles (2) from the speci-men (22), thereby preferably ionizing the particles (2);optionally an acceleration unit (26) configured to acceler-ate particles (1); and a system (1) for determining a physical quantity (QP) of a particle (2) according to claim 19.

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