Fast non-ringing dynamic system transient

Abstract

A method of control avoids inducing undesired oscillations, harmonics, and ringing during the energization or de-energization transients of a dynamic system. The same control method can deliberately induce desired oscillations, harmonics, or ringing during the energization or de-energization transients of a dynamic system. The control method accounts for energy inflows and outflows. The free response of the dynamic system is not affected but the forcing function that stimulates the dynamic system can be exactly tailored to suit the desired response throughout the entire duration of each transient response. Continuous control over the forcing function yields continuous control over the transient response, where undesired dynamics are not stimulated instead of being suppressed.

Description

TITLE: FAST NON-RINGING DYNAMIC SYSTEM TRANSIENTCROSS REFERENCE TO RELATED APPLICATIONS

[0001] This application relates to provisional patent application U.S. Serial No. 63 / 364,580, filed May 12, 2022, titled “Fast Non-Ringing Dynamic System Transient”, which is herein incorporated by reference in its entirety, including without limitation, the specification, claims, and abstract, as well as any figures, tables, appendices, or drawings thereof.FIELD OF THE DISCLOSURE

[0002] The present disclosure relates generally to devices or systems within which energy increases or decreases with respect to time. More particularly, but not exclusively, the present disclosure defines a dynamic system as a device or system that has at least one input port for energy and at least one output port for energy and to an improved method for operating a dynamic system with no undesired outputs such as unwanted oscillations, harmonics, ringing, and / or the like.BACKGROUND

[0003] Dynamic systems are dynamic because of the energy they contain. In the present disclosure, the time rate at which the energy contained within a dynamic system is increased or decreased is called a forcing function. Application of the forcing function occurs for a time duration referred to as a transient. Each rate at which energy is increased or decreased may have deleterious or even harmful effects. If the forcing function does not match the natural, free response characteristics of the dynamic system, the result is undesirable dynamics akin to, for example, a bell ringing after being struck. While it is purposefully desirable for a bell or a guitar string to resonate or ring, that is not true of other dynamic systems. Inducing undesired oscillations, harmonics, and ringing is not the primary reason for existence of many dynamic systems. It is undesirable for oscillations, harmonics, and / or ringing to be induced in structures such as bridges and railways that are not intended to be dynamic systems.

[0004] For example, the rotor in an electric power plant steam turbine-generator weighs many tons and rotates at speeds such as 60 complete revolutions per minute (“RPM”). With that much rotating kinetic energy and with the presence or absence of a significant quantity of high energy steam at the turbine inlet, connecting and disconnecting the generator from the power grid must be done precisely to avoid causing forcing function transients that can induce dynamics that may cause widespread power outages or catastrophic failures.

[0005] In another example, digital electronic communications exist in an analog world. A 1 or 0 digit is typically represented by the presence or absence of a voltage. Information is communicated by a sequential stream of such digits or bits. A voltage that suddenly rises or falls causes unwanted oscillations, harmonics, and / or ringing. The deleterious effect is that the means of measuring the presence or absence of this voltage waits for this ringing to decay sufficiently, slowing the rate at which information can be transmitted.

[0006] In yet another example, variable frequency drives (“VFDs”) use pulse-width modulation (“PWM”) to vary the rotational speed of electric motors in certain industrial applications. Employing the technique of the presence or absence of a voltage, PWM in an electric motor is much harsher than digital electronic communications because of the industrial voltages used and because of the length of the wiring between the motor and its VFD. PWM induces unwanted oscillations, harmonics, and / or ringing in the electric supply lines to the VFD, in the lines to the motor, and within the motor itself. The deleterious effects include higher heat losses in conductors, poor start-ups and abnormally high slip in induction motors, pulsating torque causing losses and mechanical oscillations with harmful heat, higher eddy losses, higher winding losses, electrical noise, the cost of mitigating the external effects of that noise, and the extra cost to design and build components rugged enough to tolerate the high energy contained in these oscillations.

[0007] In yet another example analogous to the long lines between the VFD and the motor it controls, rapid closure of a hydraulically-actuated load on an airplane can induce a pressure wave in the hydraulic supply line that rings back and forth between the hydraulic actuator and, say, the source of pressure and flow. If rapid closure is truly required, a solution is to install an accumulator in the supply line. The pressure wave is still generated but the accumulator snubs its magnitude to a tolerable level. Instead of mitigating the cause of the pressure wave, one deleterious effect is that the added accumulator weight will cost extra fuel over the life of the airframe.

[0008] In yet another example, diesel fuel injectors are commanded to be open or closed by a solenoid valve that controls the balance of high-pressure fuel across the main valve or needle. Like the ringing airplane hydraulic system, needle opening and closing transients induce pressure waves traveling upstream in the fuel supply system. The deleterious effects include lack of high speed and continuous control over the fuel flow rate which lessens engine performance. In addition, the induced pressure wave transients may affect other injectors in the same system. Finally, impact fatigue is caused by the needle slamming shut on its seat, a design limit factor.

[0009] In yet another example, consider motion controllers. A common motion control profile is a trapezoid, a shape featuring non-smooth discontinuities, the sharp corners of the shape. However, both speed and accurate positioning are crucial in some applications like 3D printers for such thingsas television screens. Assessing structural integrity in aircraft components requires accurate control to detect the presence and dimensions of small cracks. A partial solution details specifics for one case. In particular, while one prior art reference discusses the cause of “impact loading, residual vibration, and possibly audible noise,” the reference settles for iteration and rapid, finite changes in the time rate of change of acceleration. In contrast, the method of the present disclosure reveals how to calculate the complete solution without iteration or compromise.

[0010] Further examples include single pulse sonar projectors, seismic imagers, medical imagers, non-destructive evaluation methods, and other devices where unwanted post-pulse oscillations, harmonics, and / or ringing may limit or interfere with results.

[0011] Undesirable phenomena generally labeled as noise may be more effectively and economically suppressed by application of the method of the present disclosure. Because of the physical insight perspective the method uses, it may well apply to suppressing the creation of undesirable electromagnetic interference, acoustic emissions such as audibly clicking fuel cell fuel injectors, and / or annoying vibrations.

[0012] State-of-the-art analyses typically, but not necessarily always, use sinusoidal dynamics and methods such as Kirchoff s voltage and current laws. The method of the present disclosure can account for such things as the back EMF in a motor.

[0013] Mirroring physical dynamic systems, attempting to mathematically represent a non-smooth discontinuity with infinite slope such as PWM or a sudden jump between 0 and 1 or between 1 and 0 causes ringing. Known as Gibbs phenomenon, as the number of terms in the mathematical description increases, the slope does increase toward vertical but ringing appears at both the beginning and end of the transition. The computational effort to more closely approach a perfect square wave increases until economics provide the limit. Failure to eliminate undesired oscillations, harmonics, and / or ringing during a transient reveal the limitations of the prior art.SUMMARY

[0014] A dynamic system may be described by what can be measured at its ports. The best solution to undesired oscillations, harmonics, and / or ringing in such dynamic systems during a transient is to not induce them. Serious efforts for at least decades have, at best, only mitigated induction of this ringing but tend to not eliminate it. The present disclosure advances the art by providing a complete and general method to avoid inducing any ringing during a transient or to intentionally induce ringing as desired. Alternatively, a device can be used to help reduce and / or eliminate undesired oscillations, harmonics, ringing, or resonance in the device or the system when energizing or de-energizing. For example, where such oscillations, harmonics, ringing, or resonance in the device are already presentin the device, the methods and apparatus of the present disclosure can reduce the amount of oscillations, harmonics, ringing, or resonance in the device to asymptotically approach zero. For example, continued operation of the device over time can preferably reduce an amount of oscillations, harmonics, ringing, or resonance originally present in a device to less than 5%, more preferably less than 1%, and even more preferably less than 0.1%.

[0015] Instead of first selecting the mathematical method which then limits the permissible boundary conditions, the present disclosure starts with the complete set of desired boundary conditions and then matches the mathematics to that set. The method is a closed-form analytical solution that combines the desired dynamic system output with the mathematical description of the physics of the dynamic system. The solution predicts the exact energy with respect to time input requirement into or out of the dynamic system, the forcing function profile for the entire transient duration, where the word “exact” as used in the present disclosure reflects the accuracy of the mathematical description for that particular dynamic system.

[0016] The method of the present disclosure beneficially accounts for energy inflows and outflows. The free response of the dynamic system is not affected but the forcing function that stimulates the dynamic system can be exactly tailored to suit the desired response throughout the entire duration of each transient response. Continuous control over the forcing function yields continuous control over the transient response, where undesired dynamics are not stimulated instead of being suppressed.

[0017] In a first embodiment, experimental tests using a readily available magnetostrictive actuator that converts electrical input into mechanical output prove that the method of the present disclosure indeed prevents unwanted oscillations, harmonics, and / or ringing from being generated by the forcing function during transients. In a second embodiment, the tests prove that ringing can be intentionally induced in the very same device a short while after the non-ringing transient. These test results predict that there can be zero delay between pulses, provided the forcing functions are exact. Figures 5A and 5B compare the predicted displacement of the method of the present disclosure to experimental test data.

[0018] In particular, both the first embodiment of the present disclosure and the second embodiment of the present disclosure relate to a magnetostrictive device that is a durable, continuously controllable, fast, compact, and powerful source of vibration. An alloy offers a unique combination of inherent properties that enable a durable electromechanical actuator with high mechanical power density. Terbium (element number 65 on the periodic chart of the elements) inseparably couples magnetic with mechanical effects. This unusual phenomenon, called magnetostriction, is indestructible; it cannot be permanently degraded because it originates from quantum mechanics within the terbium atom itself. Terbium is combined with dysprosium (element number 66) and ironto package this effect into a useful actuator alloy. This terbium alloy is among the best known couplers of magnetic input to mechanical output. The mechanical expansion of the terbium alloy is a nearly linear scale of the strength of the applied magnetic field. Within the operating range of a single actuator, it enables both fast and small mechanical outputs as well as slow and large mechanical outputs and anything in between as desired and as continuously controlled by continuously controlling its electrical input. Besides continuous control, the quantum mechanical origin of its magnetostrictive effect endows the terbium alloy with the inherent durability to survive demanding environments. Magnetostriction has not been observed to fatigue the terbium alloy and non-melting temperatures do not permanently degrade it.

[0019] The forcing functions for energization and de-energization need not be symmetrical or mirror images of each other. That is, if the time allotted for energization is different than the time allotted for de-energization, the forcing functions will reflect that. Variations in the solution produce variations in the desired output such as the two illustrated embodiments. Besides these two embodiments illustrated in the present disclosure, a wide variety of other intentional transient behaviors is possible by customizing the solution to match a desired set of boundary conditions.

[0020] The following objects, features, advantages, aspects, and / or embodiments, are not exhaustive and do not limit the overall disclosure. No single embodiment need provide each and every object, feature, or advantage. Any of the objects, features, advantages, aspects, and / or embodiments disclosed herein can be integrated with one another, either in full or in part.

[0021] A primary object, feature, and / or advantage of the present disclosure is to improve upon or overcome the deficiencies in the art.

[0022] Another object, feature, and / or advantage of the present disclosure is to precisely control the entry or exit of energy into a device or system used as a dynamic system to prevent unwanted oscillations, harmonics, ringing, and the like. For example, said control can rely on calculations regarding how best to inject energy into a dynamic system during a transient. In one embodiment, this can be accomplished without making the dynamic system ring. In yet another embodiment, this can be accomplished by making the dynamic system ring deliberately.

[0023] Still another object, feature, and / or advantage of the present disclosure is to precisely control the entry or exit of energy into a device or system used as a dynamic system to intentionally induce oscillations, harmonics, ringing, and the like.

[0024] Still yet another object, feature, and / or advantage of the present disclosure is to provide an exact analytical method that may be used to optimize the design and operation of a device or system used as a dynamic system.

[0025] Yet another object, feature, and / or advantage of the present disclosure is to provide an exact analytical method that may be used to compensate for and maintain the best operation of a device or system used as a dynamic system as a component(s) deteriorates or its behavior is otherwise altered during its service life.

[0026] Still yet another object, feature, and / or advantage of the present disclosure is to improve energy efficiency; to reduce size, weight and cost; to quiet; and to lengthen the service life of many kinds and classes of devices or systems used as dynamic systems.

[0027] Still yet another object, feature, and / or advantage of the present invention is to detect frequency content and / or a lack thereof. The non-ringing nature of the waveforms resulting from the dynamic system transients described herein show up as a substantial (near-zero) lack of frequencies in Fourier spectra. It should be appreciated that a physically-realizable object is generally imperfect, and a very small amount of frequency content is therefore expected. Recording the Fourier Transform spectra to quantify the frequency content of the magnetostrictive actuator can be used to collect nonringing and ringing data.

[0028] Still yet another object, feature, and / or advantage of the present invention is to provide a practical means for distinguishing whether the motion of a dynamic device or system is ringing or non-ringing. Motions such as ringing occur in many dynamic systems, such motions occurring with respect to, for example, time in the time domain. A fast Fourier transform (FFT) can convert a time domain function or signal into the frequency domain for analysis. The lack of frequency content in the FFT of a dynamic device or system signal indicates it is non-ringing. Many suitable commercially available computer programs exist that use the Fourier Transform method to analyze a signal to determine its frequency content. Because no physical device or system can ever be perfect, impurities known as noise will distort the signal. However, at least one effective method of reducing noise to insignificance is to apply a Gaussian smoothing function. For each finite data point in a set of data points for a signal, the Gaussian smoothing function takes its neighboring points and applies the familiar Gaussian statistical bell curve to them, where those points nearer to the point of interest are weighted higher while the farther points are weighted lower. Thus, a Fourier Transform of a dynamic signal from a device or system can prove that undesired oscillations, harmonics, ringing, or resonance in the device or system have been eliminated. The commercially available computer programs typically label the method as a Fast Fourier Transform or a Digital Fourier Transform.

[0029] These and / or other objects, features, and advantages of the present disclosure will be apparent to those skilled in the art. The present disclosure is not to be limited to or by these objects, features and advantages. No single embodiment need provide each and every object, feature, or advantage.BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Several embodiments in which the present invention can be practiced are illustrated and described in detail, wherein like reference characters represent like components throughout the several views. The drawings are presented for exemplary purposes and may not be to scale unless otherwise indicated.

[0031] Figure 1 plots the sinusoidal functions sin(ωt), first derivative ωcos(ωt) / ω, second derivative −ω2sin(ωt) / ω2, and third derivative −ω3cos(ωt) / ω3.

[0032] To compare and contrast with Figure 1, Figure 2 plots polynomial x(T), first derivative xT / (2.1875×ttr), second derivative xTT / (7.5107× ttr2), and third derivative xTTT / (52.5× ttr3), all calculated below in accordance with a first illustrative embodiment of the present disclosure that is intended to not ring.

[0033] To again compare and contrast with Figure 1, Figure 3 plots polynomial u(T), first derivative uT / 1 / .9694×t ), second derivative uTT / (−9.8696× ten2), and third derivative uTTT / (−38.733×ten3)), all calculated below in accordance with a second illustrative embodiment of the present disclosure that is intended to ring.

[0034] Figure 4 is a cross-sectional view of an underdamped magnetostrictive actuator used to collect embodiment 1 and embodiment 2 data for Figures 5A-B.

[0035] Figure 5A plots three traces and shows the end-to-end test of both embodiments.

[0036] Figure 5B provides detailed clarity for second embodiment data.

[0037] Figure 5C shows two traces, where the upper trace is the non-ringing displacement data between approximately 0.1 and 0.2 of Figure 5A and the lower trace is its corresponding Fourier Transform with Gaussian smoothing.

[0038] Figure 5D shows two traces, where the upper trace is the ringing displacement from approximately 0.35 to 0.363 seconds of Figure 5B and the lower trace is its corresponding Fourier Transform with Gaussian smoothing.

[0039] Figure 6 shows averaged data of 99 sample runs identical to Figures 5A and 5B, wherein “identical” in this instance means the Matlab script generated the exact same digital voltage output to the DT9836 for every run.

[0040] Figure 7 shows the same data as Figure 6 with added ±3σ envelope.

[0041] Figure 8 shows FFT of the non-ringing expansion displacement portion. The data is unprocessed.

[0042] Figure 9 shows the same data as Figure 8 except the y axis has been normalized.

[0043] Figure 10 shows normalized plot of the data of Figure 9 with minimized spectral leakage.

[0044] Figure 11 shows normalized, minimal spectral leakage data of Figure 10 that has had Gaussian smoothing applied.

[0045] Figure 12 shows FFT of the ringing displacement portion. This data is unprocessed.

[0046] Figure 13 shows the same data as Figure 12 except the y axis has been normalized.

[0047] Figure 14 shows a normalized plot of the data of Figure 13 with minimized spectral leakage.

[0048] Figure 15 shows normalized, minimal spectral leakage data of Figure 14 that has had Gaussian smoothing applied.

[0049] An artisan of ordinary skill in the art need not view, within isolated figure(s), the near infinite number of distinct permutations of features described in the following detailed description to facilitate an understanding of the present invention.DETAILED DESCRIPTION

[0050] The present disclosure is not to be limited to that described herein. Mechanical, electrical, chemical, procedural, and / or other changes can be made without departing from the spirit and scope of the present invention. No features shown or described are essential to permit basic operation of the present invention unless otherwise indicated.

[0051] Figure 1 is prior art that plots the sinusoidal functions sin(fflt) 10, first derivative ωcos(ωt) / co11, second derivative -ω2sin(ωt)lω212, and third derivative -ω3cos(ωt) / ω313. The derivatives are all normalized for clarity. If they were not normalized, magnitude of the last derivative would be increased by co or 8π3, a factor of about 248. Accordingly, comparing and contrasting the traces on one plot is less subject to printing limitations.

[0052] The key characteristic of a sinusoid is that it describes the free response of a system but not necessarily the forced response. The key detriment is that its shape is fixed. With respect to generating undesired oscillations, harmonics, ringing, and / or the like over a defined transient time interval, the magnitude of the derivatives of a fixed-shape sinusoid are also fixed shapes at fixed multiples of a base frequency, a derivative may or may not start or stop at zero, and adverse polarity may be present. In addition, the defined transient time interval may or may not match the free response of the system.

[0053] To compare and contrast with Figure 1, Figure 2 plots polynomial x(T) 20, first derivative2 3 xT / (2.1875xttr) 21, second derivative xTT / (7.5107 x tt) 22, and third derivative xTTT / (52.5 x tt) 23, all calculated below in accordance with a first illustrative embodiment of the present disclosure that is intended to not ring. Like Figure 1, each derivative is normalized by its peak magnitude factor. Unlike Figure 1, both these magnitudes and their polarities may be defined as desired, a key advantage of the present disclosure. The shapes of x(T) and its derivatives match the natural, key characteristics of the load.

[0054] To again compare and contrast with Figure 1, Figure 3 plots polynomial w(T) 30, first derivative uT / (1.9694x ten) 31, second derivative uT T / (-9.8696x ten2)32, and third derivative wTTT / (-38.733x ten3)33, all calculated below in accordance with a second illustrative embodiment of the present disclosure that is intended to ring. Like Figure 1, each derivative is normalized by the peak magnitude factor indicated in their labels. Unlike Figure 1, both these magnitudes and their polarities may be defined as desired, a key advantage of the present disclosure. The shape of u(T) and its derivatives match the natural, key characteristics of the load.

[0055] Figure 4 is a cross-sectional view of an underdamped magnetostrictive actuator 100 used to collect embodiment 1 and embodiment 2 data for Figures 5A-B. In accordance with the descriptions of the present disclosure, actuator 100 has an input port 110 for electrical energy and an output port 120 for mechanical energy. The main features of interest are the mass 130 accelerated by the actuator 100, the preload spring 140, the solenoid coil 150 that converts electrical input from electrical input port 110 into a magnetic field, and magnetostrictive rod 160 that converts magnetic field input into mechanical displacement output at mechanical port 120.

[0056] Figure 5A plots three traces. The upper trace is the predicted, normalized voltage with respect to time calculated according to the method of the present disclosure for the first embodiment of not ringing, with different rise and fall rates, soon followed by the second embodiment that intentionally induces ringing. This predicted voltage trace was fed into the test article actuator to produce the measured displacement trace shown. That is, the cause calculated in accordance with the method of the present disclosure produced the desired effect. The lower two traces are the normalized defined and measured displacement traces for both embodiments, where the defined output is the dotted line and measured test data is the solid line. Figure 5A shows the end-to-end test of both embodiments whereas Figure 5B provides detailed clarity for second embodiment data.

[0057] It is therefore to be appreciated that one can set a frequency content threshold of approximately zero for cases of non-ringing. Moreover, the graphs of Figures 5C-5D further exemplify some of the many benefits of using the control algorithms and control devices described. The graphs provide greater a threshold of confidence for establishing use of the control algorithms and devices described herein, which will substantially advance the art.

[0058] Forms of energy considered in the present disclosure include mechanical, electrical, magnetic, hydraulic (fluidic), and heat. Energy is always a positive quantity that can be neither created nor destroyed. Therefore, for a dynamic system, energy output equals energy input minus any internal storage. Energy output includes the heat irreversibly dissipated whenever energy is transferred.

[0059] Energy affects and is affected by a dynamic system and its constitutive elements. Reactive elements store energy without dissipating it. Transducing elements convert energy from one form to another. Resistive elements dissipate energy without storing it. The illustrative embodiments of the method of the present disclosure are of dynamic systems of lumped parameters. A lumped parameter dynamic system consists of discrete, finite elements such as masses, springs, dampers, inductances, capacitances, resistors, and / or the like. The method may be extended to dynamic systems of distributed parameters. A distributed parameter dynamic system consists of vanishingly small but non-zero versions of these same elements and considers waves traveling within the distributed parameter system.

[0060] The time rate of change of energy in a dynamic system, the forcing function acting over a defined transient duration, may be thought of as a combined cause and effect. For example, voltage causes current, magnetic field causes magnetic flux, pressure causes fluid flow, and force causes velocity. In the present disclosure the cause of a time rate of change of energy in a dynamic system is referred to as an across variable, abbreviated AV, and the effect of a time rate of change of energy in a dynamic system is referred to in the present disclosure as a through variable, abbreviated TV. Both are referred to as state variables. At any instant in time, these quantities are distinguished as follows: AV magnitude varies smoothly from one side of the dynamic system port upon which it acts to the other side of that port while the magnitude of its corresponding TV remains uniform from one side of that same dynamic system port to the other side of that port. As used here, the word smooth means no sudden changes or discontinuities. The instantaneous time rate of change of an AV multiplied by its corresponding TV yields the instantaneous time rate of change of energy flowing through that port into or out of the dynamic system. In a dynamic system, these state variables change with respect to time and therefore so does the energy state of the dynamic system.

[0061] Now consider a dynamic system that converts energy from one form to another, where conversion may include the scaling of state variable magnitudes only. Examples include electric motors, electric transformers, a hydraulic cylinder moving an aircraft flight control surface, magnetostrictive actuators, piezoelectric actuators, sonar sources, seismic imaging sources, or semiconductors. In each case, the time rate of energy input may almost equal the time rate of energy output, where the word almost is used here to mean that any internal storage and the inevitable dissipated heat must be subtracted from the output. An authoritative mathematical description is typical of what may be found in the vast literature in which coupling between the input energy port and the output energy port as a function of time tends to be modeled asInd. AVl(t) = dep. TVl(t) + coupled dep. TV2(t) (or AV2(t))Ind. AV2(t) = dep. TV2(t) + coupled dep. TV1(t) (or AV1(t))

[0062] where there are only two dependent variables per equation. Each equation is independent and represents inflow of energy into one port or the other. For modeling forcing function transients, the approach is unsatisfactory because the third dependent variables are missing. Adding them in to complete each equation as a function of timeInd. AVl(t) = dep. TVl(t) + coupled dep. TV2(t) + coupled dep. AV2(t) Ind. AV2(t) = dep. TV2(t) + coupled dep. TV1(t) + coupled dep. AV1(t)

[0063] Scaling the variables with non-zero material-, device-, and / or system-specific coefficients Cn or Dn completes the equations:AV1(t) = C 1TV1)I + C2 AV2(t) + C3 TV2(t)AV2(t) = D1 TV2(t) + D2 AV1(t) + D3 TV1(t)

[0064] Each equation may be re-cast with any one of the other three variables as the independent variable.

[0065] For the first preferred embodiment of no ringing during an energization forcing function transient, solution is as follows. Suppose it is desired that the dynamic system start from a first rest position and quickly move to stop at a second rest position, without ringing. Define displacement x first and second rest positions as, say, -x0and xx- x0. Normalize time by defining T = t / ttrwhere t is time and ttris the defined duration of the transient. It is to be observed that the method of the present disclosure does not limit how short the transient time can be defined. Limits are provided by material, design, operational constraints, and / or the like.Refer to Figure 2. If the dynamic system is at first rest position -x0and at T= 0, then velocity xT, acceleration xTT, and the derivative of acceleration xTTTare all zero. When T= 1 at the end of the transient, x has moved to second rest position x1- x0while the condition of no ringing requires xT, xTT, and xTTTto have all returned to zero. The role of the third derivative xTTTis to control the approach of the second derivative to zero or other point.

[0066] For a polynomial, each specified boundary condition adds a degree. Therefore, for a polynomial and its three derivatives with eight specified boundary conditions, the order must be not less than eight. Unlike sinusoids, polynomial derivatives need not suffer adverse polarity or scaling. Since higher orders yield more than one solution, the unique solution being sought is of order eight x(T) = AT7+ BT6+ CT5+ DT4+ ET3+ FT2+ GT1+ HT0where A through H are coefficients and exponents 1 and 0 are usually implied but are explicitly included in the present disclosure to ensure only one meaning. The first three derivatives are xT= [7 AT6+ 6BT5+ 5CT4+ 4DT3+ 3ET2+ 2FT + G] / ttrxTT= [42AT5+ 30BT4+ 20CT3+ 12DT2+ GET + 2F] / xTTT= [210AT4+ 120BT3+ 60CT2+ 24DT +

[0067] Solve for coefficients A through H by substituting the specified boundary conditions. At T= 0, the unenergized dynamic system is at rest and xTTT= 0, xTT= 0, xT= 0, and first rest position x = - x0. At T= 1, xTTT= 0, xTT= 0, xT= 0, and the dynamic system has returned to rest at second rest position x = x1- x0. Therefore

[0068] One of the four state variables has now been defined as desired, in this case the mechanical output across variable, AV2(T), in the Independent AVI (T) equation. The other mechanical output state variable that completes the energy state at the mechanical port is force, TV2(T). Force can be found by knowledge of the external load that the dynamic system is intended to operate, a load such as a spring, mass, and damper. The appearance of velocity xT, the time rate of change of displacement at the output port of the dynamic system from energy input into its input port, requires a time rate of change of force FTat the output portFT= mxTTT+ bxTT+ kxT

[0069] where discrete lumped load parameters are m for accelerated mass, b for damping coefficient, and k for the spring constant. Substituting and integrating

[0070] where Fois the constant of integration. The cause-and-effect state variables for the output are now known. Their product F(T) xTis the time rate of change of dynamic system energy output from its mechanical port, WT. Multiplying

[0071] Integrating yields W(T), the total mechanical energy output from this port with respect to timewhere Wois the constant of integration. The change in mechanical energy, APT, during the transient is the difference between W(0) and W(1).where the first term is the inevitable heat loss and the second term is energy stored outside of the actuator, in the spring of the load driven by the actuator.

[0072] Displacement and force are two of the four state variables in either of the coupling equations for the method of the first preferred embodiment, which combine to quantify the mechanical energy side of the actuator. Since solving either coupling equation requires knowing one more state variable, consider assuming a definition for AVI (T) or TV1(T) as follows: for a transducing element either AV2(T) or TV2(T) is very likely to be close to a proportional scale of either input state variable with respect to time AVI (T) or TV1(T). This means that the form of expression with respect to time for the third state variable will be the same as the state variable it is scaling. Test shows this assumption to be true for at least one kind of dynamic system, the magnetostrictive actuator of Figure 4. The simple and flexible magnetostrictive actuator used for this testing scales current to displacement in a nearly proportional manner. (However, the method of the present disclosure could be improved by “pre-warping” the input to more nearly approach complete proportionality.) Adopting the position and velocity polynomials and scaling them for currentwhere 7pkis the peak current magnitude found below.

[0073] Substitute the three known state variables into the first coupling equation to find an expression for the fourth state variable, in this case magnetic flux Φ(T) as a function of current, displacement, and force

[0074] As with the mechanical output, form the product of the time rate of change of the input AV with its corresponding input TV. This product is the time rate of change of the input energy, ET.

[0075] where the first term is the time rate of change of energy stored within the actuator. Integrate Erto find the total input energy, E(T). Solve for the difference between E(0) and E( 1 ) to find AE.

[0076] To find the magnitude of form a quadratic equation in by setting the sum of AE andAW to zero and solve for By conservation of energy, this sum is set to zero and already includesenergy storage and any dissipated heat from the actuator output port.

[0077] To find actuator input voltage V(T), note that A, is also the product of V(T) and / (T). Add in the inevitable heat dissipation from the energy input port to complete the customized forcing function for a specified non-ringing transient durationwhere R is ohmic resistance.

[0078] Figure 5A plots test data confirming that the set of eight specified boundary conditions yields a particular, exact solution for V(T). The profile of voltage input with respect to time, K(T), is the forcing function that acts to energize the actuator over a defined transient period, with no ringing. The absence of ringing is illustrated by the steady-state current to hold position xx- x0inserted between actuator energization and de-energization. A separate forcing function is calculated for deenergizing.

[0079] The first embodiment of the method of the present disclosure predicts the exact forcing function with respect to time needed to energize or de-energize a dynamic system without undesired oscillations, harmonics, ringing, and / or the like. Transient duration is only limited by materials of construction, their configuration, their operation, and / or the like in the dynamic system, not the method of the present disclosure.

[0080] Just as non-ringing is one set of boundary conditions for a first preferred embodiment, the specified boundary conditions can be altered to deliberately create ringing or any other operational characteristic as desired. For a second preferred embodiment that intentionally induces only resonant ringing in the same dynamic system, consider the following revised boundary conditions. The same magnetostrictive actuator in Figure 4 used to provide test data for the first preferred embodiment of the present disclosure was re-used to provide data for the second preferred embodiment.

[0081] Again normalize time by defining T = t / tenwhere t is time and tenis the duration of energization. If the dynamic system is to ring at its sinusoidal free response resonant frequency, duration of energization is defined as one-half of the period of a complete sinusoidal cycle at the sinusoidal free response resonant frequency, the expansion time of the test actuator. A key characteristic of this particular actuator is that it only expands when electrically energized, regardless of the polarity of the electrical input. Therefore, the compression time is the other half of a complete sinusoidal cycle, which is left unenergized. This permits an increase in magnitude of vibrations by superposition of energization / expansion periods.

[0082] At T= 0, the unenergized dynamic system is at rest and wTTT= 0, uTT= 0, uT= 0, and u = - and the dynamic system is at first displacement u = u1- u0. That is, acceleration wTTis not zero at T= 1 so that the dynamic system will be excited into and stay in resonance. Then

[0083] The actuator and load exchange equal amounts of kinetic and potential energy at resonance. It is to be observed that this stored energy is treated separately — the coupling equation does not apply to it. That is, while state variable u(T) includes stored energy terms, in this case stored energy is not part of the coupling equation. By superposition, the coupled energy can add to or subtract from the total stored energy, but the stored energy itself is not part of the coupling calculations.

[0084] From this different starting point, the method of solution is similar to that of the first embodiment above, forming WTand W(T). The difference is that re-employing x(T) of the first embodiment is not recommended in this second embodiment since u(T) includes the consequences of stored energy on displacement. That is, the required set of boundary conditions for I(T) are not the same as u(T) because the actuator can store mechanical energy but cannot store electrical energy.

[0085] To solve this, consider defining a pseudo-displacement v(T) that mirrors the zero boundary conditions for I(T) and its derivatives. That is, set the form of pseudo-displacement v(T) and current 7(T) to mimic velocity uTinstead of displacementu u(T) since velocity uTis zero at each end of each expansion. Function v(T) and its three derivatives require eight boundary conditions of zero each to induce only the desired resonance, the stored energy represented within w(T), while avoiding induction of unwanted oscillations, ringing, harmonics, and / or the like.

[0086] Finding peak current magnitude 7pkin the second embodiment requires solving for the coupled part of output energy W at an intermediate T between 0 and 1 to find ΔW since there can be no coupling if the specified boundary conditions are zero current at T(0) and T(1). A convenient intermediate T is½. Correspondingly, set v = u(½), to calculate a non-zero boundary condition. To clarify, quantity u(½) is actually 14 of a complete resonant cycle in which half of the cycle is energized and the other half is not. For a polynomial with nine boundary conditions, the unique solution being sought is then of order nine. ThereforeSolving by substitution

[0087] And the matching pseudo-displacement used only in the electrical section because this is all that can be coupled

[0088] As in the first embodiment, substitute the expressions for v(T) and I(T) into the coupling equation to find remaining state variable Φ(T), product ET, integral E, the magnitude of Tk, and finally the forcing function voltage with respect to time V(T) .

[0089] To increase vibration magnitude, sequential displacement strokes may be super-posed to increase the quantity of stored energy, where this stored energy manifests as the kinetic and potential energies being exchanged between the actuator and its load.

[0090] Because test proves that the method of the present disclosure accurately predicts dynamic system operation, the method of the present disclosure provides physical insights to further predict the effects of improvements in material properties, geometry, and every other element of dynamic system design, fabrication, and operation. For example, the well-known performance deterioration of piezoelectric ceramics with use may be lessened by the physical insights provided by this method. For a second example, the PWM wave forms used to obtain variable electric motor speeds may use the non-ringing transient method of the present disclosure to improve efficiency, heat loss, and component stress.

[0091] In the same manner, if the method of the present disclosure is used within an adaptive motion controller, variable frequency drive (“VFD”), soft starter (e.g., in applications where there is a large inrush of current that could damage a motor while a VFD controls and can vary the speed of a motor), digital communication device, aircraft hydraulic system, internal combustion engine fuel injector, piezoelectric actuator, and / or the like, it can alter the predictions for energy control based on wear or other variations to maintain the desired motion with respect to time over the service life of the dynamic system. The required number of calculations will be minimized. The present disclosureprovides mathematics that are simple and compact enough for a computer to quickly calculate and update during dynamic system operation.

[0092] As would be expected, the desirable behavior of a magnetostrictive actuator cannot be without limit. For example, a limit is imposed by the mechanical strength of the terbium alloy. No matter how it is operated, the mechanical limit of the actuator is simply the mechanical strength of the terbium alloy. When operated inside this one limit, performance has not been observed to degrade over time. Within its destructive limits, terbium alloy performance has never been observed to be degraded by any known combination of high stress, high strain, high field, and / or high temperature. Because at least high stress and high strain are required, it is theorized that the upper limit of mechanical power density for the terbium alloy occurs very close to its mechanical strength limit. In other words, this mechanical power density limit coincides with maximum compressive stress and / or minimum displacement amplitude. The elastic modulus of the terbium alloy is relatively soft. This can be of great advantage for both power density and flexible operation, key features of a durable actuator intended to provide powerful and precisely controllable vibration. The soft elastic modulus permits superposition to be used to obtain larger displacement magnitudes from smaller electrical inputs. The durable nature of the terbium alloy permits long life to be expected with larger displacement magnitudes.

[0093] Similar to other materials such as steel, another limit may be found to be the time rate at which stress and / or strain can be applied. For example, it is known that in its unmagnetized and motionless state, the terbium alloy stress and strain will asymptotically decay with time to a small degree, presumably due to the spontaneous realignment of magnetic domains. The method of the present disclosure enables all magnetostrictive actuator phenomena to be accounted for in order to operate it at its maximum permissible power density.

[0094] The non-ringing first embodiment method of the present disclosure is able to suppress undesired ringing by supplying a countermeasure to an existing system. That is, the output from a separate dynamic system would be calculated to absorb an undesired dynamic using knowledge of energy with respect to time.

[0095] The method of the present disclosure can be used, for example, in a diesel fuel injector to control its orifice size as it injects fuel into the combustion chamber. That is, the injection orifice can open in the desired amount of time, it can open partially, it can oscillate once fuel is being injected to both steer the fuel direction and / or help with atomization, and it can close quickly without causing impact fatigue on the valve seat. Engine power and economy are thus increased while reducing the in-cylinder generation of emissions. Different injection profiles can be used to accommodate different fuels without losing performance.

[0096] The method of the present disclosure is not to be limited to the two particular embodiments described herein. In particular, the disclosure contemplates numerous variations in which the load consists of any combination of discrete energy storage and dissipation elements in mechanical, electrical, magnetic, and hydraulic systems. Further, the disclosure contemplates a load consisting of distributed parameters characterized by wave mechanics.

[0097] The foregoing description has been presented for purposes of illustration and description. It is not intended to be an exhaustive list or limit any of the disclosure to the precise forms disclosed. It is contemplated that other alternatives or exemplary aspects are considered included in the disclosure. The description is merely examples of embodiments, processes or methods of the disclosure. It is understood that any other modifications, substitutions, and / or additions can be made, which are within the intended spirit and scope of the disclosure. From the foregoing, it can be seen that the present invention accomplishes at least all of the stated objectives.EXAMPLES

[0098] Embodiments of the present invention are further defined in the following non-limiting Examples. It should be understood that these Examples, while indicating certain embodiments of the invention, are given by way of illustration only. From the above discussion and these Examples, one skilled in the art can ascertain the essential characteristics of this invention, and without departing from the spirit and scope thereof, can make various changes and modifications of the embodiments of the invention to adapt it to various usages and conditions. Thus, various modifications of the embodiments of the invention, in addition to those shown and described herein, will be apparent to those skilled in the art from the foregoing description. Such modifications are also intended to fall within the scope of the appended claims.

[0099] Energizing or de-energizing a dynamic system need not cause undesired ringing. An automated method for control was written and tested to prove this. Fourier transform of dynamic data can be used to quantify frequency content, a means of detecting whether the automated method for control has been effectively employed.

[0100] There exists no perfect physical object. Therefore, even small imperfections in the test article or test instrumentation will cause noise to appear.

[0101] The test specimen was the first TdVib, LLC industrial vibrator, serial number 5135. The test specimen vertically accelerated a steel mass of 9.830 kilograms. The test specimen and mass were rigidly fixed to a granite block weighing approximately two tons.

[0102] For this testing, one signal was output and three signals were input. The output signal is voltage and the input signals are a monitor of this output voltage plus the resulting test specimen current and displacement.

[0103] The control law predicts the test specimen input voltage required to obtain a desired output displacement. Computer output is digital. Control law output and data collection were controlled by a Matlab script. The computer operated and recorded the data transmitted to it.

[0104] Data Translation model DT9836 serial number 00645986, offers two analog outputs and twelve analog inputs. That is, it converts the computerized digital signal into an analog output. Its twelve analog inputs digitize the analog inputs. The analog voltage output signal is sent to both the amplifier input and one of the DT9836 input channels to monitor. Matlab in the computer operated this device at 100,000 samples per second, or every ten microseconds.

[0105] The amplifier was an A. E. Techron model 7782, serial number 194970. It has a signal available that is a scale of its output current.

[0106] Test specimen displacement was measured by an MTI Instruments Fotonic Sensor, serial number 1604. This instrument was selected due to its -3 dB response at 161 kHz. Range 1 was selected and the bandpass filter set to DC to 1 kHz. The Fotonic Sensor is fixtured to a Melies Griot stage slidably adjustable by a micrometer. In turn, the stage is rigidly affixed to the granite block.

[0107] The electronic instrumentation for this test was allowed to warm up before use.

[0108] Once launched, the Matlab script generates the voltage output, sends it to the DT9836, and records the data from the DT9836.

[0109] The Fotonic displacement sensor had been mounted on a separate granite plate of substantially less mass. It was determined that this arrangement was sensitive to seismic motions. Re-mounting the sensor on the two-ton granite block alleviated much data contamination, but not all. For example, nearby footsteps could be detected. The solution was to wait until output was motionless and then run a test.

[0110] One hundred (100) sample runs were recorded. Each run is identical to Figures 5A and 5B, z.e., the Matlab script generated the exact same digital voltage output to the DT9836 for every run. One run was eliminated due to unusual and excessive noise, leaving 99 good data sets.[OHl] The test specimen performed as expected. It was of no other concern during this test series.

[0112] The instrumentation performed as expected. It was of no other concern during this test series.

[0113] There were no known instrumentation malfunctions. Post-test averaging of the raw data is helpful. Separate grounding wires were run from all instruments to a structural beam. This reduced some electronic noise.

[0114] There was noise in the raw data. Shielding of all instrumentation wiring does not appear to be an issue.

[0115] The DT9836 suffers two defects. First, the start of a signal rarely coincides from one test to another. Particularly, time zero does not match time zero of the calculated input voltage analog signal,forcing post-processing to align prediction with data to see delays between cause and effect. The data time zero can be plus or minus a random amount from prediction time zero. Therefore, the zeroes of all data sets were aligned manually, it being easy to find the offset and subtract it by graphing the data. Second, sample intervals cannot be set to such amounts as a power of 2 within one second. That is, for FFT it is desirable to set the number of samples per second to a power of 2 such as 131,072. However, this testing simply set it to 100,000.

[0116] Data correction was limited to the time zero alignment of prediction with data, to be able to more accurately observe delay between cause and effect.

[0117] The 99 Fotonic sensor displacement data sets were zero-aligned and then averaged to produce the graphs of Figures 6-7. Correction is limited to aligning prediction and data zeroes. Displacement was small (see Figure 7).

[0118] Matlab version 2021a with the optional Signal Analyzer Toolbox, a product of The MathWorks, Inc., was used to produce the following graphs. The graphs of Figures 8-15 are presented in the sequence in which they were processed to produce the final results. The sequences of Figures 8-11 and Figures 12-15 are separated into the sequence for the non-ringing embodiment 1 of U.S. Serial No. 63 / 364,580, filed May 12, 2022, titled “Fast Non-Ringing Dynamic System Transient” followed by the sequence for the ringing embodiment 2 of same.EXAMPLE 1 : FFT OF THE NON-RINIGING EXPANSION DISPLACEMENT PORTION

[0119] The 99-average non-ringing displacement visible from 0.00 to 0.08 seconds, 8,001 data points in each set, was subject to FFT by Matlab’s Signal Analyzer Toolbox with the results shown in Figures 8-11.EXAMPLE 2: FFT OF THE RINIGING DISPLACEMENT PORTION

[0120] The 99-average ringing displacement visible from 0.15500 to 0.17472 seconds, 1,973 data points in each set, was subject to FFT by Matlab’s Signal Analyzer Toolbox with the results shown in Figures 12-15.

[0121] Figure 6 (EXAMPLE 1) and Figure 10 (EXAMPLE 2) show the stark, obvious difference between the non-ringing and ringing embodiments of the present disclosure. The difference shows that infringement of the non-ringing intellectual property is readily identifiable.

[0122] All post-processing steps were identical. Gaussian smoothing was chosen due to its production of significantly different results than the other available smoothing algorithms. While the signals above are displacement, the same post-processing techniques apply to any and all dynamic signals such as electrical, hydraulic, pneumatic, and so forth.GLOSSARY

[0123] Unless defined otherwise, all technical and scientific terms used above have the same meaning as commonly understood by one of ordinary skill in the art to which embodiments of the present disclosure pertain.

[0124] The terms “a,” “an,” and “the” include both singular and plural referents.

[0125] The term “or” is synonymous with “and / or” and means any one member or combination of members of a particular list.

[0126] As used herein, the term “exemplary” refers to an example, an instance, or an illustration, and does not indicate a most preferred embodiment unless otherwise stated.

[0127] The term “about” as used herein refer to slight variations in numerical quantities with respect to any quantifiable variable. Inadvertent error can occur, for example, through use of typical measuring techniques or equipment or from differences in the manufacture, source, or purity of components.

[0128] The term “substantially” refers to a great or significant extent. “Substantially” can thus refer to a plurality, majority, and / or a supermajority of said quantifiable variable, given proper context.

[0129] The term “generally” encompasses both “about” and “substantially.”

[0130] The term “configured” describes structure capable of performing a task or adopting a particular configuration. The term “configured” can be used interchangeably with other similar phrases, such as constructed, arranged, adapted, manufactured, and the like.

[0131] Terms characterizing sequential order, a position, and / or an orientation are not limiting and are only referenced according to the views presented.

[0132] “Reasonable” data will appear both plausible and truthful to one skilled in the art.

[0133] “Ringing” describes the natural, free response of a dynamic system that has been stimulated. For example, a bell “rings” after being struck.

[0134] The “invention” is not intended to refer to any single embodiment of the particular invention but encompass all possible embodiments as described in the specification and the claims. The “scope” of the present disclosure is defined by the appended claims, along with the full scope of equivalents to which such claims are entitled. The scope of the disclosure is further qualified as including any possible modification to any of the aspects and / or embodiments disclosed herein which would result in other embodiments, combinations, subcombinations, or the like that would be obvious to those skilled in the art.

Claims

CLAIMSWhat is claimed is:

1. A method for operating a device or a system comprising: combining, in a combination, a time rate of change of a cause of energy flow out of the device or the system with an effect of the time rate of change of the cause of energy flow out of the device or the system; and using the combination to define the time rate of change of a cause of energy flow into the device or the system; combining the cause of energy flow into the device or the system with an effect of the time rate of change of the cause of energy flow into the device or the system, thereby yielding a time rate or a frequency at which energy enters or exits the device or the system, said time rate or said frequency yielding approximately no spectral content.

2. The method of claim 1 wherein the combination is a smooth, continuously differentiable function.

3. The method of claim 2 wherein the smooth, continuously differentiable function is a polynomial.

4. The method of any one of claims 1-3 further comprising: reducing undesired oscillations, harmonics, ringing, or resonance in the device or the system when energizing or de-energizing.

5. The method of any one of claims 1-3 further comprising: intentionally not inducing any undesired oscillations, harmonics, ringing, or resonance in the device or the system when energizing or de-energizing.

6. The method of any one of claims 1-5 further comprising: intentionally inducing desirable oscillations, harmonics, ringing, or resonance in a device or a system when energizing or de-energizing.

7. The method of any one of claims 1-6 wherein the device or the system transmits or receives information as a sequence of digits.

8. The method of claim 6 wherein there are only two possible digit values that are represented by a higher voltage and a lower voltage.

9. The method of any one of claims 1-8 wherein the device or the system controls a load by controlling an energy supply in pulses.

10. The method of claim 9 wherein the pulses have only two possible values of a higher cause of energy flow and a lower cause of energy flow.

11. The method of claim 10 wherein a time width of each pulse can be varied and a time width between pulses can be varied.

12. The method of claim 9 wherein the device or the system is a variable frequency drive or a soft starter that supplies an electric motor.

13. The method of any one of claims 1-12 wherein the device or the system is selected from the group consisting of: internal combustion engine fuel injectors; and fuel cell fuel injectors.

14. The method of any one of claims 1-13 further comprising non-destructively evaluating an object using the device or the system, wherein the device or the system is selected from the group consisting of: medical imaging devices; and seismic imaging devices.

15. The method of any one of claims 1-14 wherein the device or the system is selected from the group consisting of: sonar projectors; noise-cancelling devices; and devices that avoid creating noise.

16. The method of any one of claims 1-15 further comprising cancelling vibrations or preventing vibrations from occurring in an object.

17. The method of any one of claims 1-16 wherein the device or the system is selected from the group consisting of: piezoelectric devices; and magnetostrictive devices.

18. The method of any one of claims 1-17 wherein the device or the system is selected from the group consisting of: magnetostrictive devices with preload greater than 10,000 psi.

19. A device or a system comprising: a first combination comprising: a time rate of change of a cause of energy flow out of the device or the system; and an effect of the time rate of change of the cause of energy flow out of the device or the system; a second combination comprising: a cause of energy flow into the device or the system; an effect of the time rate of change of the cause of energy flow into the device or the system; wherein the first combination and the second combination yield a time rate or a frequency at which energy enters or exits the device or the system, wherein said time rate or said frequency yields approximately no spectral content, and wherein operation of said device allows contact with an object at a near-zero contact velocity.

20. An integrated microchip compiled and / or programmed to perform the method of any one of claims 1-18.

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