WO2012149649A1

WO2012149649A1 - Apparatus and method for in situ impedance measurement of a piezoelectric actuator

Info

Publication number: WO2012149649A1
Application number: PCT/CA2012/050249
Authority: WO
Inventors: Rudolph SEETHALER; Mohammad Islam
Original assignee: The University Of British Columbia
Priority date: 2011-05-05
Filing date: 2012-04-19
Publication date: 2012-11-08

Abstract

An apparatus and method is disclosed for in situ impedance measurement of a piezoelectric actuator located in a mechanical system. There is a signal generator that generates a voltage signal having a frequency greater than a resonant frequency of the piezoelectric actuator in the mechanical system. The voltage signal is applied to the piezoelectric actuator thereby creating a current signal. The piezoelectric actuator is mechanically unresponsive to the voltage and current signals. There is also a voltage sensor, a current sensor and a computer. The voltage sensor is connected with the piezoelectric actuator for measuring a voltage representative of the voltage signal. The current sensor is connected with the piezoelectric actuator for measuring a current representative of the current signal. The computer is in communication with the voltage sensor and the current sensor and is programmed to compute an impedance value based on the voltage and the current.

Description

Apparatus and Method for In situ Impedance Measurement of a Piezoelectric

Actuator

Technical Field

[0001 ] An apparatus and method are disclosed for in situ impedance measurement of a piezoelectric actuator located in a mechanical system.

Background

[0002] Piezoelectric actuators have several advantages over magnetic devices which include compactness, resolution, reliability, speed and dynamics. As a result, piezoelectric actuators are usefully employed in various applications from scanning probe microscopy to automotive fuel injectors.

[0003] For example, fuel injectors with piezoelectric actuators are serviceable in a wide temperature range and over millions of cycles. However, both temperature and aging have a significant effect on the performance of the actuator. In particular, the capacitance of the actuator can change significantly under these influences. These actuators are usually driven in an open loop configuration with no position feedback, so inaccuracies in the amount of fuel injected are a common problem. In order to provide a means to compensate for these errors, the actuator needs to be characterized during normal operation.

[0004] Multilayered piezoelectric actuators are constructed by stacking thin layers (< 100μηι) of piezoelectric material with the electrodes packed in between the layers. The thin layered construction enables the actuators to produce high electric fields by applying low voltages in comparison to bulk construction of piezoelectric actuators. With reference to FIG. 1, the stroke length of a piezoelectric actuator caused by the expansion (or contraction) of the stack of piezoelectric layers is dependent upon the electric field, which results from the applied voltage across the actuator. Due to the relatively low driving voltage and large displacement characteristics as well as other unique properties such as high resolution, speed, compactness and dynamics, these multilayered piezoelectric actuators are widely used in various high speed applications such as fuel injector assemblies, vibration control, microrobotics, motors, acoustic-optic modulators, etc. [0005] Capacitance

[0006] Piezoelectric actuators are typically modeled as capacitive elements for control purposes. As mentioned previously, piezoelectric stack actuators are arranged in such a way that several hundred piezoelectric layers are sandwiched between electrodes. These layers are connected in parallel and create the capacitive load.

[0007] An important model parameter, clamped capacitance, is considered constant and obtained through offline measurements. However, the capacitance value changes with operating conditions such as electric fields, environmental temperatures, and aging. In addition, traditional capacitance measurements are not hysteresis free. [0008] Several models have been proposed for the control of piezoelectric actuators. One of the most widely used models for piezoelectric actuators was proposed in the mid- 1990's by Michael Goldfarb and Nikola Celanovic when both were at Vanderbilt University in the United States of America. This model describes the piezoelectric actuators as capacitive elements in their application frequency range. An important modeling parameter for the piezoelectric actuators is the clamped capacitance which corresponds to a measurement when the piezoelectric actuator is restrained from expanding. Traditionally, this parameter is obtained by using a bridge circuit with a known reference impedance in order to obtain an effective capacitance for the piezoelectric actuator by comparing the transfer function of input and output voltage to the bridge circuit.

[0009] It has been found that the capacitance value is dependent on different factors such as applied electric field, actuator temperature, and aging. So the assumption of a constant capacitance value in the model is not an accurate approximation when the actuator is operated in highly dynamic applications and when applied for the lifetime of the actuator. An example of an application where this can be a factor is a fuel injector used in internal combustion engines where the voltage amplitude is not constant and also the temperature around the piezoelectric actuator is not constant. Since the variable voltage and temperature changes the capacitance value, an on-line in situ capacitance measurement technique is required to measure the clamped capacitance to improve the modeling accuracy.

[0010] Temperature [001 1 ] The temperature of a piezoelectric actuator is generally affected by environmental conditions and self-heating effects due to hysteresis losses. For example, a piezoelectric actuator used in a fuel injector is subjected to elevated temperatures caused by its proximity to the engine's combustion chamber and the heat of combustion generated therein. Piezoelectric actuators are subjected to driving voltages of sufficient magnitude that hysteresis losses have a considerable effect on temperature rise of the actuator. Referring to FIG. 2, which is a plot of a piezoelectric actuator's capacitance versus its temperature, it shows that capacitance increases with increasing temperature. This data shows a substantially linear relationship with the slope being constant for rising and falling temperatures; that is, the capacitance for a given temperature is constant whether the temperature is rising or falling. As shown in FIG. 2, a piezoelectric actuator's capacitance changes with its temperature, so not accounting for changes in temperature can add to the variance between a commanded actuator displacement and the actual displacement. [001 2] Prior Art

[001 3] Conventional piezoelectric actuator capacitance measurement techniques took advantage of a basic theory of electric fields according the following relationship:

V = Ι / (2πΓ Ο) (Eq. 1)

[001 4] In Eq. 1, "V" is the RMS value of a sinusoidal driving voltage, "I" is the RMS value of the resulting current, "f" is the frequency of the sinusoidal driving voltage, and "C" is the measured capacitance. In its general form, this capacitance measurement has two limitations. Firstly, the applied voltage and resultant current include charge and voltage hysteresis that distorts the capacitance measurement. Secondly, the measured capacitance is the free capacitance and not the clamped capacitance, because the applied voltage activates the actuator to cause displacements by expanding or contracting the piezoelectric elements.

[001 5] In European Patent Specification EP 1 , 138,906B1 , published on August 10, 2003 to Rueger et al, there is disclosed a method and an apparatus for setting an activation voltage for charging a piezoelectric element while considering the temperature dependent hysteresis of the piezoelectric element. The piezoelectric element's capacitance is used to obtain its temperature.

[001 6] The piezoelectric element's capacitance is measured on a cylinder-by-cylinder basis during every drive signal. That is, the drive voltage and charge quantities flowing, or the average current, can be multiplied by the charging/discharging time to obtain the piezoelectric element's capacitance. Since the piezoelectric element's capacitance also exhibits a temperature response, the capacitance can be used to derive the piezoelectric element's temperature and in turn, the desired maximum displacement caused by the piezoelectric element. [001 7] The drive voltage is used to actuate the piezoelectric element. Using the drive voltage and charge quantities flowing therefrom results in measuring the free capacitance of the piezoelectric element, as opposed to its clamped capacitance. This measurement technique is hysteresis dependent and therefore not a good indication of the capacitance of the piezoelectric element. [001 8] Furthermore, the resulting current flowing through the piezoelectric actuator is a factor of the driving voltage and the external forces acting on the actuator, e.g. frictional forces and inertial forces. The external forces change the value of the measured current through the actuator leading to inaccurate measurements of the actual capacitance. [0019] There is a need for an improved real time impedance measurement technique of piezoelectric actuators. The piezoelectric actuator displacement, i.e. expansion and/or contraction can be controlled more precisely from these improved measurements.

Summary

[0020] An improved method is provided for in situ impedance measurement of a piezoelectric actuator located in a mechanical system. The method comprises the steps of generating a first voltage signal having a first frequency greater than a resonant frequency of the piezoelectric actuator in the mechanical system, applying the first voltage signal to the piezoelectric actuator thereby producing a first current signal, measuring a voltage value and a current value representative of the first voltage signal and the first current signal respectively, and determining an impedance of the piezoelectric actuator from the voltage value and the current value. The piezoelectric actuator is mechanically unresponsive to the first voltage signal and the first current signal in the provided method. In addition, the disclosed method can further comprise a step for determining the temperature of the piezoelectric actuator based on the impedance.

[0021 ] In a preferred embodiment the step of measuring further comprises sub-steps of filtering the first voltage signal and the first current signal, and sampling the first voltage signal and the first current signal thereby producing a discrete time-domain voltage signal and a discrete time-domain current signal respectively. A sampling frequency is selected whereby the first voltage signal and the first current signal are undersampled, and the discrete time-domain voltage signal and the discrete time- domain current signal have respective aliased frequency components at an alias frequency. The alias frequency is greater than the resonant frequency of the piezoelectric actuator in the mechanical system, and preferably the alias frequency is one quarter the sampling frequency.

[0022] A further sub-step of transforming the discrete time-domain voltage signal and the discrete time-domain current signal into a discrete frequency-domain voltage signal and a discrete frequency-domain current signal respectively, is provided. The sub-step of transforming comprises performing a Fourier analysis on the discrete time-domain voltage signal and the discrete time-domain current signal to thereby produce the discrete frequency-domain voltage signal and the discrete frequency- domain current signal respectively. In preferred embodiments, the Fourier analysis is a discrete Fourier transform and a number of cycles is selected over which the discrete Fourier transform is performed, whereby respective frequency components representative of the discrete time-domain voltage signal and the discrete time-domain current signal are substantially included in respective discrete Fourier transforms, and mechanical vibrations of the piezoelectric actuator are substantially excluded.

[0023] The step of computing further comprises the steps of extracting voltage coefficients and current coefficients from the discrete frequency-domain voltage signal and the discrete frequency-domain current signal respectively, and calculating the impedance as a ratio the voltage coefficients and the current coefficients. The voltage coefficients are representative of the voltage value and the current coefficients are representative of the current value. [0024] The method includes the steps of communicating any one of the voltage coefficients, the current coefficients, the impedance or the temperature of the piezoelectric actuator to a diagnostic system.

[0025] In another preferred embodiment, the step of determining the impedance of the piezoelectric actuator comprises the steps of determining a phase angle between the voltage value and the current value, determining a magnitude ratio between the voltage value and the current value, and determining model parameters based on the phase angle and the magnitude ratio.

[0026] In another preferred embodiment, the mechanical system comprises a fuel injector and a computer. The fuel injector comprises a valve member and the piezoelectric actuator is adapted to actuate the valve member in response to command signals from the computer. The method further comprises the step of modifying the command signals in response to the impedance of the piezoelectric actuator, or the temperature of the piezoelectric actuator.

[0027] In yet another preferred embodiment, the method further comprises steps of generating a second voltage signal having a second frequency less than a resonant frequency of the piezoelectric actuator in the mechanical system, and applying the second voltage signal to the piezoelectric actuator simultaneously with the first voltage signal. The second voltage signal produces a second current signal through the piezoelectric actuator. The first voltage signal can be a ripple voltage signal from a switch mode power supply, and the second voltage signal can be a driving voltage signal for the piezoelectric actuator. The ripple voltage signal is superimposed on the driving voltage signal and the driving voltage signal actuates the piezoelectric actuator.

[0028] In still a further embodiment there is provided an apparatus for in situ impedance measurement of a piezoelectric actuator located in a mechanical system. The apparatus comprises a first signal generator, a voltage sensor, a current sensor and a computer. The first signal generator generates a first voltage signal having a first frequency greater than a resonant frequency of the piezoelectric actuator in the mechanical system. The first voltage signal is applied to the piezoelectric actuator thereby creating a first current signal. The piezoelectric actuator is mechanically unresponsive to the first voltage signal and the first current signal. The voltage sensor is operatively connected with the piezoelectric actuator for measuring a voltage value representative of the first voltage signal. The current sensor is operatively connected with the piezoelectric actuator for measuring a current value representative of the first current signal. The computer is in communication with the voltage sensor and the current sensor and is programmed to compute an impedance value based on the voltage value and the current value. The computer is further programmed to determine the temperature of the piezoelectric actuator based on the impedance so computed.

[0029] The mechanical system comprises a fuel injector having a valve member. The piezoelectric actuator is adapted to actuate the valve member in response to command signals from the computer. The computer is further programmed to modify the command signals in order to modify an actuation of the valve member in response to the impedance and/or the temperature of the piezoelectric actuator.

[0030] The voltage sensor comprises a first analog to digital converter element responsive to the first voltage signal and provides a digital voltage signal representative of the voltage value. The current sensor comprises a second analog to digital converter element responsive to the first current signal and provides a digital current signal representative of the current value.

[0031 ] The computer is responsive to the digital voltage signal and the digital current signal and is further programmed to compute a Fourier transform voltage signal from the digital voltage signal and a Fourier transform current signal from the digital current signal. The Fourier transform voltage signal comprises voltage coefficients and the Fourier transform current signal comprises current coefficients. The computer is responsive to the Fourier transform voltage signal and the Fourier transform current signal to compute the impedance value based on the voltage coefficients and the current coefficients. In another embodiment the computer can be further programmed to determine a phase angle and a magnitude ratio between the voltage value and the current value, and to determine model parameters based on the phase angle and the magnitude ratio.

[0032] The first and second analog to digital converter elements undersample the first voltage signal and the first current signal respectively. The digital voltage signal and the digital current signal have an alias frequency. The computer is further programmed to compute a phase angle between and a magnitude ratio of the voltage value and the current value at the alias frequency based on the voltage coefficients and the current coefficients.

[0033] In one example of a preferred embodiment of the apparatus, the first signal generator can comprise a switch mode power supply having an output ripple voltage signal wherein the first voltage signal is the output ripple voltage signal. In further examples, the first signal generator can comprise a pulse width modulator, or an oscillator, or a multivibrator, whereby the first voltage signal is generated.

[0034] In another embodiment of the apparatus, the first signal generator further generates a second voltage signal having a second frequency less than the resonant frequency of the piezoelectric actuator in the mechanical system. The first voltage signal is superimposed on the second voltage signal. The second voltage signal is applied to the piezoelectric actuator simultaneously with the first voltage signal and the second voltage signal produces a second current signal. The piezoelectric actuator is mechanically responsive to the second voltage signal and the second current signal.

[0035] The current sensor comprises a current to voltage translation element, a first filter element and a first analog to digital converter. The current to voltage translation element is responsive to the first and second current signals and produces a third voltage signal representative of the first and second current signals. The first filter element is responsive to the third voltage signal and produces a first filtered voltage signal representative of the first current signal. The first analog to digital converter is responsive to the first filtered voltage signal and produces a digital current signal representative of the first current signal. The computer is responsive to the digital current signal. [0036] The voltage sensor comprises a second filter and a second analog to digital converter. The second filter is responsive to the first voltage signal and the second voltage signal and produces a second filtered voltage representative of the first voltage signal. The second analog to digital converter is responsive to the second filtered voltage signal and produces a digital voltage signal representative of the first voltage signal. The computer is responsive to the digital voltage signal. [0037] The mechanical system comprises a fuel injector having a valve member. The piezoelectric actuator is adapted to actuate the valve member in response to command signals from the computer. The computer is further programmed to modify the second voltage signal in response to the impedance value. The computer is further programmed to determine a temperature value based on the impedance value, and to modify the second voltage signal in response to the temperature value.

[0038] In yet another embodiment of the apparatus, the apparatus can further comprise a second signal generator and a multiplexor. The second signal generator generates a second voltage signal having a second frequency less than the resonant frequency of the piezoelectric actuator in the mechanical system. The multiplexor is responsive to the first voltage signal and the second voltage signal to provide a third voltage signal to the piezoelectric actuator.

[0039] In yet again another embodiment of the apparatus, the apparatus can further comprise a second signal generator and an adder. The second signal generator generates a second voltage signal having a second frequency less than the resonant frequency of the piezoelectric actuator in the mechanical system. The adder is responsive to the first voltage signal and the second voltage signal to provide a third voltage signal to the piezoelectric actuator. The third voltage signal is related to a sum of the first voltage signal and the second voltage signal.

Brief Description of the Drawings

[0040] The drawings illustrate specific preferred embodiments of the invention, but should not be considered as restricting the spirit or scope of the invention in any way.

[0041 ] FIG. 1 is a plot of a generalized relationship between piezoelectric expansion and contraction versus an applied electric field; [0042] FIG. 2 is a plot of capacitance versus temperature for a conventional piezoelectric actuator;

[0043] FIG. 3 is a schematic view of a model of an impedance of a piezoelectric actuator; [0044] FIG. 4 is a phasor diagram of the impedance of the model of FIG. 3;

[0045] FIG. 5 is a schematic view of one embodiment of the apparatus for in situ measurement of impedance of a piezoelectric actuator in a fuel injector;

[0046] FIG. 6 is a graphical view of components of a superimposed signal of the apparatus for in situ measurement of impedance of FIG. 5; [0047] FIG. 7 is a schematic view of another example of an embodiment of the apparatus for in situ measurement of impedance of a piezoelectric actuator in a fuel injector;

[0048] FIG. 8 is a flow chart of an impedance measurement algorithm for the apparatus of FIG. 7; and [0049] FIG. 9 is a schematic view of yet another example of an embodiment of the apparatus for in situ measurement of impedance of a piezoelectric actuator in a fuel injector.

Detailed Description [0050] Referring to the figures and first to the illustrated embodiment of FIG. 5, there is shown an in situ impedance measurement apparatus indicated generally by reference numeral 10 for measurement of impedance Z of piezoelectric actuator 12 located in mechanical system 14. Mechanical system 14 in this example is fuel injector 16. In other embodiments, mechanical system 14 could be a vibration or position control assembly, as well as other types of assemblies that employ a piezoelectric actuator. Piezoelectric actuator 12 is activated to selectively open and close valve member 18 of fuel injector 16 in order to deliver a predetermined quantity of fuel to a combustion chamber of an internal combustion engine (not shown) . [0051 ] Apparatus 10 includes conventional piezo amplifier 20, for example, the E- 617. OOF high power piezo amplifier from Physik Instrumente (PI) GmbH, that generates superimposed voltage signal 22 that is applied to piezoelectric actuator 12. With reference to FIGS. 5 and 6, piezo amplifier 20 comprises a conventional switched mode power supply (not shown) that generates a voltage of sufficient magnitude 24 to create driving voltage signal 26. Driving voltage signal 26 is applied to the piezoelectric actuator in order to effect displacement. In the disclosed example, driving voltage signal 26 has a driving frequency f_d of approximately 100Hz; however for other applications and other embodiments, it will be understood that other driving frequencies can be employed within the spirit of the claimed invention.

[0052] The switch mode power supply of piezo amplifier 20 is a boost converter having a fixed frequency and duty cycle in this embodiment. A characteristic of the boost converter, and switch mode power supplies in general, is that they also generate ripple voltage signal 28, which heretofore was an unwanted side-effect of dc-to-dc conversion. Superimposed voltage signal 22 includes the combination of driving voltage signal 26 and ripple voltage signal 28 superimposed thereon. In this embodiment, ripple voltage signal 28 has a ripple frequency f_r of 100kHz and magnitude of lOOmV, although persons skilled in this technology will understand that other values can be used in other embodiments without departing from the spirit of the claimed invention.

[0053] Referring again to FIG. 5, piezoelectric actuator 12 in fuel injector 16 has a mechanical resonant frequency of 4kHz. It will be understood that in other mechanical systems the resonant, or natural frequency could be different. A mechanical bandwidth of less than 4kHz of the combination of piezoelectric actuator 12 and fuel injector 16 is too low to respond to the ripple frequency f_r of 100kHz of ripple voltage signal 28. As a result piezoelectric actuator 12 does not displace, by way of expansion or contraction, due to ripple voltage signal 28. Nevertheless, ripple voltage signal 28 induces ripple current signal 29 through piezoelectric actuator 12. Similarly, driving voltage signal 26 induces driving current signal 25 through piezoelectric actuator 12. Superimposed current signal 27 comprises ripple current signal 29 and driving current signal 25. [0054] Apparatus 10 further comprises voltage sensor 30, current sensor 32, signal processor 34 and control voltage generator 36. Voltage sensor 30 is responsive to superimposed voltage signal 22 to provide signal processor 34 with a measured ripple voltage V_mr representative of ripple voltage signal 28. Current sensor 32 is responsive to superimposed current signal 27 to provide signal processor 34 with measured ripple current representative of ripple current signal 29. Note that piezoelectric actuator

12 is responsive to superimposed voltage signal 22 to provide superimposed current signal 27.

[0055] Signal processor 34 is responsive to measured ripple voltage V_mr and measured ripple current I_mr to generate command signal 31 that is received by control voltage generator 36. Signal processor 34 can be implemented using analog components, digital components, or a combination of analog and digital components. Control voltage generator 36 is responsive to command signal 31 to generate control voltage signal 33 that is received by piezo amplifier 20. Piezo amplifer 20 amplifies control voltage signal 33 to generate superimposed voltage signal 22.

[0056] The relationship between ripple voltage signal 28 and ripple current signal 29 can be used to measure impedance Z of piezoelectric actuator 12. Referring to FIG. 3, there is illustrated a parametric model for impedance Z of the piezoelectric actuator that includes resistor R in series with capacitor C_c . Note that there are other possible models for piezoelectric actuator 12, for example one such model includes a resistor in series with a capacitor in series with an inductor.

[0057] With reference to Eq. l above and to FIG. 3, impedance Z is defined as:

^Z = T (Eq- ²)

^Lm^Lr ^{= R}-T^li^trc

Measured ripple voltage and measured ripple current I_mr are measured at ripple frequency f_r . Signal processor 34 calculates impedance Z upon receiving V_mr and l_mr values according to Eq. 2. Based on impedance Z , signal processor 34 modifies command signal 31 in order to adjust control voltage signal 33 such that driving voltage signal 26 actuates piezoelectric actuator 12 to a predetermined position. [0058] Referring now to FIG. 7 there is shown another embodiment of the disclosed apparatus wherein like parts to the embodiment of FIG. 5 have like reference numerals. For example, FIG. 7 shows mechanical system 14 comprising piezoelectric actuator 12, for actuating valve member 18 within fuel injecto 16. This embodiment is similar to the embodiment of FIG. 5 and like parts are not described in detail, if at all.

[0059] Referring within FIG. 7 to the in situ impedance measurement apparatus, hereinafter referred to as apparatus 10, current sensor 32 comprises shunt resistor 40, filter 42 and first analog-to-digital converter 44. Superimposed current signal 27 flows through shunt resistor 40 and produces a shunt voltage at node 46. The shunt voltage at node 46 comprises a component responsive to driving current signal 25 and another component responsive to ripple current signal 29. Conductor 47 provides a return path for superimposed current signal 27 to piezo amplifier 20. Note that shunt resistor 40 is illustrated in FIG. 7 as a low-side current sensing resistor. In other embodiments it is possible to have a high-side current sensing resistor instead.

[0060] First filter 42 is responsive to the shunt voltage at node 46 to filter the component that is responsive to driving current signal 25 and to pass through the component that is responsive to ripple current signal 29, thereby providing filtered ripple current signal 45. In the illustrated preferred embodiment first filter 42 is a band pass filter, however other filter types are possible in other embodiments, such as a high pass filter. First analog-to-digital converter 44 samples filtered ripple current signal 45 and provides digital current signal 48 to signal processor 34. Note that digital current signal 48 is a discrete time-domain ripple current signal.

[0061 ] Voltage sensor 30 includes second filter 50 and second analog-to-digital converter 52. Second filter 50 is responsive to superimposed voltage signal 22 to filter driving voltage signal 26 and to pass ripple voltage signal 28, thereby providing filtered ripple voltage signal 51. In this embodiment second filter 50 is another band pass filter, however other filter types are possible in other embodiments, such as another high pass filter Second analog-to-digital converter 52 samples filtered ripple voltage signal 51 and provides digital voltage signal 54 to signal processor 34. Note that digital voltage signal 54 is a discrete time-domain voltage signal. [0062] Signal processor 34 is a computer and in preferred embodiments it is a general purpose computer comprising CPU 60 and memory 62. Memory 62 is encoded with instructions that execute on CPU 60 that enables signal processor 34 to be responsive to digital current signal 48 and digital voltage signal 54 in order to calculate impedance Z of piezoelectric actuator 12, and to modify command signal 31 in response to the impedance so calculated. The instructions stored in memory 62 are representative of an algorithm for computing the impedance that will be described in more detail below.

[0063] Control voltage generator 36 includes digital to analog converter 70 responsive to command signal 31 to generate control voltage signal 33 received by piezo amplifier 20. In the disclosed example, control voltage signal 33 is an analog signal that is amplified by piezo amplifer 20. In other examples the piezo amplifier can be responsive directly from command signal 31 from signal processor 34. In other embodiments digital-to-analog converter 70 can be a pulse width modulator followed by a low pass filter.

[0064] Apparatus 10 further comprises conventional microcontroller 80 comprising signal processor 34. As can be seen by the dashed lines around voltage sensor 30, current sensor 32 and control voltage generator 36, portions of these components are contained within microcontroller 80. In other embodiments it is possible to have additional memory, for example, SRAM or FLASH, external to microcontroller 80. In still further embodiments, it is possible to have analog-to-digital converters and/or digital-to-analog converters external to microcontroller 80.

[0065] With reference to FIG. 7 and algorithm 82 shown in FIG.8, the steps for computing the impedance are now described in more detail. Signal processor 34 selects a sampling frequency f_s used by first and second analog-to-digital converters

44 and 52 respectively in step 84. Algorithm 82 takes advantage of symmetry in Fourier coefficient calculations, which is described in more detail below, that is obtained when sampling frequency f_s is exactly four times the frequency of interest, that is ripple frequency f_r . [0066] Sampling at four times ripple frequency f_r , however, would be computationally expensive for signal processor 34 since the ripple frequency is very high, namely 100kHz in this example. Instead, sampling is performed at a frequency lower than ripple frequency f_r in order to avoid excessive sampling. Sampling frequency f_s is then selected such that the ripple frequency folds to folded ripple frequency f_{r folded} exactly one quarter of the sampling frequency. In addition, folded ripple frequency f_{r folded} should be beyond the mechanical bandwidth of piezoelectric actuator 12 in fuel injector 16 in order to ensure that the measurements are not affected by expansion or contraction of the actuator.

[0067] There is a multitude of possible sampling frequencies. In the disclosed example, sampling frequency _sis selected to be 80kHz whereby ripple frequency f_r folds onto 20kHz. This selection has been determined to be a good compromise between lowering the sampling rate and allowing for highly dynamic actuation, since the mechanical bandwidth of mechanical system 14 is approximately 4kHz. However, if piezoelectric actuator 12 in fuel injector 16 has a lower resonant frequency, then much lower sampling frequencies can be employed. [0068] Referring still to FIGS. 7 & 8, in step 86 filtered ripple current signal 45 and filtered ripple voltage signal 51 are sampled at sampling frequency f_s to obtain digital current signal 48, and digital voltage ripple signal 54, respectively. Filtered ripple current signal 45 and filtered ripple voltage signal 51 each having ripple frequency f_r of 100kHz are undersampled by sampling frequency f_s of 80kHz in the described example. This results in digital current signal 48 and digital voltage signal 54 having aliased frequency components at an alias frequency of 20kHz. The alias frequency being equivalent to folded ripple frequency f_{r folded} .

[0069] In step 88 a Fourier analysis is performed in real-time on digital current signal 48 and digital voltage signal 54. In the described embodiment the Fourier analysis is a discrete Fourier transform (DFT) , however in other embodiments other types of transforms could be used, for example, a discrete time Fourier transform (DTFT) or a fast Fourier transform (FFT).

[0070] The DFT is performed on digital current signal 48 and digital voltage signal 54 in order to obtain a discrete frequency-domain current ripple signal and a discrete frequency-domain voltage ripple signal, respectively, which are Fourier transform signals. A magnitude ratio and phase angle relationship is determined between the discrete frequency-domain voltage ripple signal and the discrete frequency-domain current ripple signal.

[0071 ] The real time implementation of the DFT transform is very efficient because the frequency of interest is at exactly one quarter of sampling frequency f_s . Real current-ripple Fourier coefficient At and imaginary current-ripple Fourier coefficient B_r are obtained from the discrete frequency-domain current ripple signal. Real voltage-ripple Fourier coefficient Αγ_Γ, and imaginary voltage-ripple Fourier coefficient Βγ_Γ are obtained from the discrete frequency-domain voltage ripple signal. Fourier coefficients Αγ_Γ, By_r, A _r and B_r, can be obtained using the following discrete transfer functions that employ simple additions of the measured voltage and current values only:

1=1

[0072] In Eqs. 3 and 4, "n" is the number of cycles of folded frequency f_{T olded} (the alias frequency) the discrete Fourier transform is performed across. Note that the division by 2n does not actually have to be performed since the impedance of piezoelectric actuator 12 is determined from ratios of Fourier coefficients Av_r, Bv_r, At and B_r which are independent of n, as will be described in more detail below.

[0073] Choosing a larger number of cycles, n, has two effects. First, the frequency is filtered around a narrower band around folded ripple frequency f_{r folded} . Second, the bandwidth of the impedance measurement is reduced when more cycles, n, are employed. Note that in step 88 Fourier coefficients Αγ_Γ, By_r, A _r and B_r can be communicated to a diagnostic system running on the CPU 60, or they can be communicated to an external diagnostic system over a conventional communications bus, such as but not limited to a CAN bus or TCP/IP bus.

[0074] In step 90, model parameters of the parameteric model of piezoelectric actuator 12 are determined. Ideally, the piezoelectric actuator should be a purely capacitive element. However, by inspecting Fourier coefficients Αγ_Γ, By_r, A _r and B_r, the measurements at 100kHz indicate that a phase angle between ripple voltage signal 28 and ripple current signal 29 is not exactly 90°, but closer to 60° for the disclosed embodiment. [0075] Referring to FIG. 3, impedance Z modeling piezoelectric actuator 12 is shown. Impedance Z includes resistor R in series with capacitance C_c . Resistor R models resistive losses in the conductors feeding piezoelectric actuator 12. A phasor diagram of impedance Z is shown in FIG. 4. The phasor diagram includes voltage phasor 93 and current phasor 95. Components of the voltage phasor 93 include resistive voltage phasor 97 and reactive voltage phasor 98.

[0076] Magnitude |Z| and phase angle Θ of impedance Z are respectively defined with respect to Fourier coefficients Αγ_Γ, By_r, A _r and B_r as:

[0077] With reference to the phasor diagram in FIG. 4, the components of voltage and current in the real and imaginary directions are summed according to Ohm's law resulting in:

B

A 'ir

Vr (Eq. 7)

wC ^',C

(Eq. 8) [0078] These equations can then be solved for R and C_c yielding:

1 _r ² + B_Ir ²

C, c ^~ (Eq. 10) ω_Γ A_IrB_Vr - B_IrA_Vr [0079] Referring again to FIGS. 7 and 8, in step 92 the impedance is calculated by substituting Fourier coefficients Αγ_Γ, By_r, A _r and B_r into Equations 9 and 10 and substituting the resulting R and C_c values into Equation 2. Impedance Z can be communicated to the diagnostic system running on CPU 60, or can be communicated to the external diagnostic system over the conventional communications bus, such as but not limited to the CAN bus or the TCP/IP bus.

[0080] In step 94 a temperature of piezoelectric actuator 12 is obtained from a lookup table relating the capacitance with the temperature. In other embodiments a multidimensional lookup table can be employed relating the capacitance with the temperature and other variables, such as dc offset voltages and frequencies. The temperature of the piezoelectric actuator 12 can be communicated to the diagnostic system running on the CPU 60, or can be communicated to the external diagnostic system over the conventional communications bus, such as but not limited to the CAN bus or the TCP/IP bus.

[0081 ] In step 96 impedance Z , or the temperature obtained therefrom can be used to modify command signal 31 in order to bring piezoelectric actuator 12 to a predetermined position. Similarly, command signal 31 can be modified based on the impedance and/or temperature in order to maintain a predetermined flow rate through valve member 18. Providing such precise control over the displacement, or stroke, of the piezoelectric actuator is an improvement over conventional control methods because it allows a more precise quantity of fuel to be delivered to the combustion chamber of the internal combustion engine. Moreover, more precise control of the displacements caused by a piezoelectric actuator is an advantage for any mechanical system that benefits from more accurate movements of the system being actuated.

[0082] Referring now to FIG. 9, yet another embodiment of the disclosed apparatus is schematically depicted wherein like parts to the previous embodiment have like reference numerals. This embodiment is similar to the embodiments of FIGS. 5 and 7, and like parts are not described in detail, if at all. The in situ impedance measurement apparatus is referred to hereinafter as apparatus 10, which further comprises signal generator 100 and multiplexor-adder component 102.

[0083] Signal generator 100 operates stand alone and provides ripple voltage signal 28. For example, in stand alone operation the signal generator can be a clock oscillator, a crystal or a multivibrator circuit, in addition to other types of stand alone conventional signal generators. In other embodiments signal generator 100 can be responsive to a second command signal from signal processor 34 in order to provide ripple voltage signal 28. For example, the signal generator can comprise a pulse width modulator circuit that is responsive to signal processor 34 to define a frequency, duty cycle and magnitude of the generated waveform.

[0084] Multiplexor-adder component 102 is responsive to second command signal 104 from signal processor 34, driving voltage signal 26 and ripple voltage signal 28 to provide composite signal 106. Composite signal 106 can be any one of the following three combinations:

1. ripple voltage signal 28

2. driving voltage signal 26

3. ripple voltage signal 28 and driving voltage signal 26

Multiplexor-adder component 102 is responsive to second command signal 104 to multiplex ripple voltage signal 28 with driving voltage signal 26, or to add them together. In other embodiments multiplexor-adder component 102 could also scale the signals it multiplexes and adds.

[0085] In the embodiment of FIG. 9, piezo amplifier 20 is not used to provide ripple voltage 28. The piezo amplifier 20 either does not generate a ripple voltage superimposed on the driving voltage signal 26, or it sufficiently attenuates any such ripple voltage.

[0086] Several illustrative embodiments of the apparatus and associated method have been described in this disclosure. However, it will be apparent to persons skilled in the art that a number of variations and modifications can be made without departing from the scope of the invention as defined in the claims.

Claims

We Claim:

1. A method of in situ impedance measurement of a piezoelectric actuator located in a mechanical system, the method comprising steps of: generating a first voltage signal having a first frequency greater than a resonant frequency of the piezoelectric actuator in the mechanical system; applying the first voltage signal to the piezoelectric actuator thereby producing a first current signal, the piezoelectric actuator being mechanically unresponsive to the first voltage signal and the first current signal; measuring a voltage value and a current value representative of the first voltage signal and the first current signal respectively; and determining an impedance of the piezoelectric actuator from the voltage value and the current value.

2. The method of claim 1 , wherein the step of measuring further comprises a sub- step of sampling the first voltage signal and the first current signal thereby producing a discrete time-domain voltage signal and a discrete time-domain current signal respectively.

3. The method of claim 2, wherein the step of measuring further comprises a step of transforming the discrete time-domain voltage signal and the discrete time-domain current signal into a discrete frequency-domain voltage signal and a discrete frequency-domain current signal respectively.

4. The method of claim 3, wherein the step of transforming comprises performing a Fourier analysis on the discrete time-domain voltage signal and the discrete time-domain current signal to thereby produce the discrete frequency-domain voltage signal and the discrete frequency-domain current signal respectively.

5. The method of claim 4, wherein the step of transforming comprises a sub-step of computing a discrete Fourier transform on the discrete time-domain voltage signal and the discrete time-domain current signal.

6. The method of claim 5, wherein the sub-step of computing comprises selecting a number of cycles over which the discrete Fourier transform is performed whereby respective frequency components representative of the discrete time-domain voltage signal and the discrete time-domain current signal are substantially included in respective discrete Fourier transforms, and mechanical vibrations of the piezoelectric actuator are substantially excluded.

7. The method of claim 5, wherein the step of computing comprises the steps of: extracting voltage coefficients and current coefficients from the discrete frequency-domain voltage signal and the discrete frequency-domain current signal respectively, the voltage coefficients being representative of the voltage value and the current coefficients being representative of the current value; and calculating the impedance using the voltage coefficients and the current coefficients.

8. The method of claim 7, wherein the step of calculating the impedance using the voltage coefficients and the current coefficients comprises the step of calculating the impedance as a ratio of the voltage coefficients and the current coefficients.

9. The method of claim 1 , wherein the step of determining includes the steps of: determining a phase angle between the voltage value and the current value; determining a magnitude ratio between the voltage value and the current value; and determining model parameters based on the phase angle and the magnitude ratio.

10. The method of claim 2, wherein the sub-step of sampling comprises the step of selecting a sampling frequency whereby the discrete time-domain voltage signal and the discrete time-domain current signal have respective aliased frequency components at an alias frequency.

1 1. The method of claim 10, wherein the alias frequency is greater than the resonant frequency of the piezoelectric actuator in the mechanical system.

12. The method of claim 10, wherein the alias frequency is one quarter the sampling frequency.

13. The method of claim 10, further comprising a sub-step of computing respective discrete Fourier transforms on the discrete time-domain voltage signal and the discrete time-domain current signal, respectively providing a discrete frequency- domain voltage signal and a discrete frequency-domain current signal.

14. The method of claim 13, wherein the sub-step of computing comprises selecting a number of cycles of the alias frequency over which the respective discrete

Fourier transforms are performed whereby the respective aliased frequency components of the discrete time-domain voltage signal and the discrete time-domain current signal are substantially included in the respective discrete Fourier transforms and mechanical vibrations from the piezoelectric actuator in the mechanical system are substantially excluded.

15. The method of claim 2, wherein the sub-step of sampling further comprises selecting a sampling frequency whereby the first voltage signal and the first current signal are undersampled.

16. The method of claim 2, wherein the step of measuring further comprises filtering the first voltage signal and the first current signal prior to the sub-step of sampling.

17. The method of claim 16, wherein the step of filtering comprises bandpass filtering.

18. The method of claim 1, wherein the mechanical system comprises a fuel injector and a computer, the fuel injector comprising a valve member, the piezoelectric actuator being adapted to actuate the valve member in response to command signals from the computer, the method further comprising the step of modifying the command signals in response to the impedance of the piezoelectric actuator.

19. The method of claim 1 , the method further comprising the step of determining a temperature of the piezoelectric actuator based on the impedance.

20. The method of claim 19, wherein the mechanical system comprises a fuel injector and a computer, the fuel injector comprising a valve member, the piezoelectric actuator being adapted to actuate the valve member in response to command signals from the computer, the method further comprising the step of modifying the command signals in response to the temperature.

21. The method of claim 19, the method further comprising the step of communicating the temperature of the piezoelectric actuator to a diagnostic system.

22. The method of claim 1 , the method further comprising the steps of: generating a second voltage signal having a second frequency less than a resonant frequency of the piezoelectric actuator in the mechanical system; and applying the second voltage signal to the piezoelectric actuator simultaneously with the first voltage signal, the second voltage signal producing a second current signal.

23. The method of claim 22, wherein the first voltage signal is a ripple voltage signal and the second voltage signal is a driving voltage signal, the ripple voltage signal being superimposed on the driving voltage signal, the driving voltage signal actuating the piezoelectric actuator.

24. The method of claim 22, wherein the step of measuring comprises the sub-step of filtering out the second voltage signal and the second current signal.

25. The method of claim 1 , the method further comprising communicating the impedance of the piezoelectric actuator to a diagnostic system.

26. The method of claim 5, the method further comprising the steps of: extracting voltage coefficients and current coefficients from the discrete frequency-domain voltage signal and the discrete frequency-domain current signal respectively, the voltage coefficients being representative of the voltage value and the current coefficients being representative of the current value; and communicating the voltage coefficients and the current coefficients to a diagnostic system.

27. An apparatus for in situ impedance measurement of a piezoelectric actuator located in a mechanical system comprising: a first signal generator generating a first voltage signal having a first frequency greater than a resonant frequency of the piezoelectric actuator in the mechanical system, the first voltage signal being applied to the piezoelectric actuator thereby creating a first current signal, the piezoelectric actuator being mechanically unresponsive to the first voltage signal and the first current signal; a voltage sensor being operatively connected with the piezoelectric actuator for measuring a voltage value representative of the first voltage signal; a current sensor being operatively connected with the piezoelectric actuator for measuring a current value representative of the first current signal; and a computer programmed to compute an impedance value and being in communication with the voltage sensor and the current sensor; whereby the computer receives the voltage value and the current value and computes the impedance value of the piezoelectric actuator therefrom.

28. The apparatus of claim 27, wherein the voltage sensor comprises an analog to digital converter responsive to the first voltage signal and providing a digital voltage signal representative of the voltage value, the computer being responsive to the digital voltage signal.

29. The apparatus of claim 28, wherein the mechanical system comprises a fuel injector having a valve member, the piezoelectric actuator being adapted to actuate the valve member in response to command signals from the computer.

30. The apparatus of claim 29, wherein the computer is further programmed to modify command signals in order to modify an actuation of the valve member in response to the impedance value.

31. The apparatus of claim 27, wherein the current sensor comprises an analog to digital converter element responsive to the first current signal and providing a digital current signal representative of the current value, the computer being responsive to the digital current signal.

32. The apparatus of claim 27, wherein the voltage sensor comprises a first analog to digital converter element responsive to the first voltage signal and providing a digital voltage signal representative of the voltage value, and the current sensor comprises a second analog to digital converter element responsive to the first current signal and providing a digital current signal representative of the current value, the computer being responsive to the digital voltage signal and the digital current signal.

33. The apparatus of claim 32, wherein the computer is further programmed to compute a Fourier transform voltage signal from the digital voltage signal and a

Fourier transform current signal from the digital current signal, the Fourier transform voltage signal comprising voltage coefficients, the Fourier transform current signal comprising current coefficients, the computer being responsive to the Fourier transform voltage signal and the Fourier transform current signal to compute the impedance value.

34. The apparatus of claim 33, wherein the first and second analog to digital converter elements undersample the first voltage signal and the first current signal respectively, the digital voltage signal and the digital current signal having an alias frequency, the computer is further programmed to compute a phase angle between and a magnitude ratio of the voltage value and the current value at the alias frequency based on the voltage coefficients and the current coefficients.

35. The apparatus of claim 27, wherein the first signal generator comprises a switch mode power supply having an output ripple voltage signal, the first voltage signal being the output ripple voltage signal.

36. The apparatus of claim 27, wherein the first signal generator comprises a pulse width modulator whereby the pulse width modulator generates the first voltage signal.

37. The apparatus of claim 36, wherein the pulse width modulator is responsive to command signals from the computer.

38. The apparatus of claim 27, wherein the first signal generator comprises an oscillator whereby the oscillator generates the first voltage signal.

39. The apparatus of claim 27, wherein the computer is further programmed to determine a temperature of the piezoelectric actuator based on the impedance value.

40. The apparatus of claim 39, wherein the mechanical system comprises a fuel injector having a valve member, the piezoelectric actuator being adapted to actuate the valve member in response to command signals from the computer.

41. The apparatus of claim 40, wherein the computer is further programmed to modify the command signals in order to modify an actuation of the valve member in response to the temperature of the piezoelectric actuator.

42. The apparatus of claim 27, wherein the first signal generator further generates a second voltage signal having a second frequency less than the resonant frequency of the piezoelectric actuator in the mechanical system, the first voltage signal being superimposed on the second voltage signal.

43. The apparatus of claim 42, wherein the second voltage signal is applied to the piezoelectric actuator simultaneously with the first voltage signal, the second voltage signal producing a second current signal, the piezoelectric actuator being mechanically responsive to the second voltage signal and the second current signal.

44. The apparatus of claim 43, wherein the current sensor comprises: a current to voltage translation element responsive to the first and second current signals and producing a third voltage signal representative of the first and second current signals; a filter element responsive to the third voltage signal and producing a filtered voltage signal representative of the first current signal; and an analog to digital converter responsive to the filtered voltage signal and producing a digital signal representative of the first current signal; wherein the computer is responsive to the digital signal.

45. The apparatus of claim 44, wherein the current to voltage translation element comprises a resistor connected between the first signal generator and the piezoelectric actuator, the first and second current signals flowing through the resistor.

46. The apparatus of claim 43, wherein the mechanical system comprises a fuel injector having a valve member, the piezoelectric actuator being adapted to actuate the valve member in response to command signals from the computer.

47. The apparatus of claim 46, wherein the computer is further programmed to modify the second voltage signal in response to the impedance value.

48. The apparatus of claim 46, wherein the computer is further programmed to determine a temperature value based on the impedance value, and to modify the second voltage signal in response to the temperature value.

49. The apparatus of claim 42, wherein the voltage sensor comprises: a filter responsive to the first voltage signal and the second voltage signal and producing a filtered voltage representative of the first voltage signal; and an analog to digital converter responsive to the filtered voltage signal and producing a digital voltage signal representative of the first voltage signal; wherein the computer is responsive to the digital voltage signal.

50. The apparatus of claim 27, the apparatus further comprising: a second signal generator generating a second voltage signal having a second frequency less than the resonant frequency of the piezoelectric actuator in the mechanical system; and a multiplexor being responsive to the first voltage signal and the second voltage signal to provide a third voltage signal to the piezoelectric actuator.

51. The apparatus of claim 27, the apparatus further comprising: a second signal generator generating a second voltage signal having a second frequency less than the resonant frequency of the piezoelectric actuator in the mechanical system; and an adder being responsive to the first voltage signal and the second voltage signal to provide a third voltage signal to the piezoelectric actuator, the third voltage signal being related to a sum of the first voltage signal and the second voltage signal.

52. The apparatus of claim 33, wherein the computer is further programmed to calculate the impedance value based on the voltage coefficients and the current coefficients.

53. The method of claim 52, wherein the computer is further programmed to determine a phase angle and a magnitude ratio between the voltage value and the current value, and to determine model parameters based on the phase angle and the magnitude ratio.

54. An apparatus for in situ impedance measurement of a piezoelectric actuator located in a mechanical system comprising: means for generating a first voltage signal having a first frequency greater than a resonant frequency of the piezoelectric actuator in the mechanical system, the first voltage signal being applied to the piezoelectric actuator thereby creating a first current signal, the piezoelectric actuator being mechanically unresponsive to the first voltage signal and the first current signal; means for measuring a voltage value representative of the first voltage signal; means for measuring a current value representative of the first current signal; and means for determining an impedance value based on the voltage value and the current value.