Fast non-ringing dynamic system transients

Abstract

The control method avoids inducing undesired oscillations, harmonics, and ringing during energization or de-energization transients of a dynamic system. The same control method can deliberately induce desired oscillations, harmonics, or ringing during energization or de-energization transients of a dynamic system. The control method takes into account energy inflow and outflow. The free response of the dynamic system is not affected, but the forcing function that stimulates the dynamic system can be precisely adjusted to match the desired response throughout the duration of each transient response. Continuous control over the forcing function results in continuous control over the transient response, and undesired dynamics are not stimulated instead they are suppressed.

Description

[Technical field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This application is related to U.S. Provisional Patent Application No. 63 / 364,580, entitled "Fast Non-Ringing Dynamic System Transient," filed May 12, 2022, which is incorporated by reference in its entirety, including but not limited to the specification, claims, and abstract, and any figures, tables, appendices, or drawings thereof.

[0002] The present disclosure generally relates to devices or systems in which energy increases or decreases over time. More specifically, but not exclusively, the present disclosure defines a dynamic system as a device or system having at least one input port for energy and at least one output port for energy, and an improved method for operating the dynamic system without undesirable outputs such as unwanted oscillations, harmonics, ringing, and / or the like. [Background technology]

[0003] A dynamic system is dynamic due to the energy it contains. In this disclosure, the time rate at which the energy contained within the dynamic system increases or decreases is referred to as the forcing function. The application of the forcing function occurs over a period of time called a transient. Each rate at which the energy increases or decreases can have deleterious or even adverse effects. If the forcing function does not match the natural free response characteristics of the dynamic system, the result is undesirable dynamics, similar to, for example, a bell ringing after being struck. While it is intentionally desired for a bell or guitar string to resonate or ring, that is not true for other dynamic systems. Inducing undesirable oscillations, harmonics, and ringing is not the primary reason many dynamic systems exist. It is undesirable to induce oscillations, harmonics, and / or ringing in structures such as bridges and railroads that are not intended to be dynamic systems.

[0004] For example, the rotor of a power plant steam turbine generator can weigh many tons and rotate at speeds such as 60 complete revolutions per minute ("RPM"). With such a large amount of rotational kinetic energy and the presence of large amounts of high-energy steam at the turbine inlet, connecting and disconnecting the generator from the power grid must be done precisely to avoid causing forced function transients that could induce dynamics that could cause widespread power outages or catastrophic failures.

[0005] In another example, digital electronic communication exists in an analog world. The digits 1 or 0 are 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 detrimental effect is that the means to measure the presence or absence of this voltage slows down the rate at which information can be transmitted while waiting for this ringing to sufficiently decay.

[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. Using a voltage present technique, PWM of an electric motor is much more demanding than digital electronic communication because of the industrial voltages used and the length of wiring between the motor and its VFD. PWM induces unwanted oscillations, harmonics, and / or rumble in the power supply lines to the VFD, in the lines to the motor, and in the motor itself. Detrimental effects include increased conductor heat losses, poor starting and abnormally high slip in induction motors, pulsating torques that cause losses and mechanical oscillations with harmful heat, increased eddy losses, increased winding losses, electrical noise, the cost of mitigating the external effects of that noise, and the extra cost of designing and building components robust enough to withstand the high energy contained in these oscillations.

[0007] In yet another example, similar to the long lines between a VFD and the motor it controls, rapid closure of a hydraulically operated load on an airplane may induce pressure waves in the hydraulic supply lines that ring back and forth between the hydraulic actuator and, say, a pressure and flow source. If rapid closure is truly necessary, the solution is to install an accumulator in the supply line. A pressure wave is still created, but the accumulator suppresses its magnitude to an acceptable level. Instead of mitigating the cause of the pressure wave, one detrimental effect is that the weight of the added accumulator consumes extra fuel over the life of the aircraft.

[0008] In yet another example, diesel fuel injectors are commanded to open and close by a solenoid valve that controls the balance of high pressure fuel across a main valve or needle. Like a ringing airplane hydraulic system, the needle opening and closing transients induce pressure waves that travel upstream in the fuel delivery system. Detrimental effects include a lack of fast and continuous control over fuel flow rate that reduces engine performance. In addition, the induced pressure wave transients can affect other injectors in the same system. Finally, impact fatigue is caused by design limiting factors that cause the needle to slam shut on its seat.

[0009] In yet another example, consider a motion controller. A typical motion control profile is trapezoidal, a shape characterized by non-smooth discontinuities, sharp corners in the shape. However, both speed and precise positioning are important in some applications, such as 3D printers for television screens and the like. Evaluating the structural integrity of aircraft components requires precise control to detect the presence and size of small cracks. A partial solution details one case. Specifically, one prior art reference discusses the causes of "shock loads, residual vibrations, and possible audible noise," but the reference compromises with respect to iterative and rapid, finite changes in the time rate of change of acceleration. In contrast, the method of the present disclosure reveals how to compute a complete solution without iterations or compromises.

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

[0011] Undesirable phenomena commonly labeled as noise may be more effectively and economically suppressed by application of the disclosed method, which, due to the perspective of physical insight it employs, may be well-suited to suppressing unwanted electromagnetic interference, acoustic emissions such as fuel cell fuel injectors making audible clicking noises, and / or the generation of objectionable vibrations.

[0012] State-of-the-art analysis typically, but not always, uses sinusoidal dynamics and methods such as Kirchhoff's voltage and current laws. The methods of the present disclosure can account for back EMF in motors, etc.

[0013] When one tries to mirror a physical dynamic system and mathematically represent a non-smooth discontinuity with infinite slope, such as PWM, or an abrupt jump between 0 and 1 or 1 and 0, ringing occurs. Known as the Gibbs phenomenon, as the number of terms in the mathematical description increases, the slope increases towards vertical, but ringing appears at both the beginning and end of the transition. The amount of computation to get closer to a perfect square wave increases until economy brings a limit. The inability to eliminate undesirable oscillations, harmonics, and / or ringing during a transient reveals limitations of the prior art. Summary of the Invention

[0014] A dynamic system may be described by what can be measured at its ports. The best solution to undesirable oscillations, harmonics, and / or ringing in such dynamic systems during transients is not to induce them. Serious efforts over at least several decades have at best only mitigated the induction of this ringing, but have no tendency to eliminate it. The present disclosure advances the art by providing a complete and general method to avoid inducing any ringing during transients, or to intentionally induce ringing as desired. Alternatively, the device may be used to help reduce and / or eliminate undesirable oscillations, harmonics, ringing, or resonances in a device or system upon energization or de-energization. For example, if such oscillations, harmonics, ringing, or resonances in a device are already present in the device, the method and apparatus of the present disclosure may reduce the amount of oscillations, harmonics, ringing, or resonances in the device to asymptotically approach zero. For example, continued operation of the device over an extended period of time can preferably reduce the amount of oscillations, harmonics, ringing, or resonance inherently present in the device to less than 5%, more preferably less than 1%, and even more preferably less than 0.1%.

[0015] Instead of first choosing a mathematical method and thereby restricting the boundary conditions allowed, the present disclosure starts with a complete set of desired boundary conditions and then fits the mathematics to that set. The method is a closed-form analytical solution that combines the desired dynamic system output with a mathematical description of the physics of the dynamic system. The solution predicts accurate energy with respect to time input requirements to and from the dynamic system, the forcing function profile for the entire transient period, where the word "accurate" as used in this disclosure reflects the accuracy of the mathematical description for that particular dynamic system.

[0016] The disclosed method beneficially accounts for energy inflows and outflows. The free response of the dynamic system is unaffected, but the forcing function that stimulates the dynamic system can be precisely tuned to match the desired response throughout the entire duration of each transient response. Continuous control over the forcing function results in continuous control over the transient response, and undesirable dynamics are not stimulated instead they are suppressed.

[0017] In a first embodiment, experimental testing using readily available magnetostrictive actuators that convert electrical input to mechanical output proves that the disclosed method does indeed prevent unwanted oscillations, harmonics, and / or ringing from being generated by the forcing function during a transient. In a second embodiment, testing proves that in the very same device, ringing can be intentionally induced for a short period of time after a non-ringing transient. These test results predict that if the forcing function is correct, the delay between pulses can be zero. Figures 5A and 5B compare the predicted displacement of the disclosed method with experimental test data.

[0018] Specifically, both the first embodiment of the present disclosure and the second embodiment of the present disclosure relate to magnetostrictive devices that are durable, continuously controllable, fast, compact, and powerful sources of vibration. The alloy offers a unique combination of intrinsic properties that enable durable electromechanical actuators with high mechanical power density. Terbium (element number 65 on the periodic table of elements) inseparably couples magnetic and mechanical effects. This extraordinary phenomenon, called magnetostriction, is robust and cannot degrade forever because it originates from the quantum mechanics of the terbium atom itself. Terbium is combined with dysprosium (element number 66) and iron to encapsulate this effect into a useful actuator alloy. This terbium alloy is one of the best known to couple magnetic input to mechanical output. The mechanical expansion of the terbium alloy scales nearly linearly with the strength of the applied magnetic field. Within the operating range of a single actuator, it allows both fast and small mechanical outputs and slow and large mechanical outputs, as well as everything in between, to be controlled as desired and continuously by continuously controlling its electrical input. In addition to continuous control, the quantum mechanical origin of the magnetostrictive effect gives terbium alloys the inherent durability to withstand demanding environments. Magnetostriction has not been observed to fatigue terbium alloys, and they are not permanently degraded by non-melting temperatures.

[0019] The forcing functions for energization and deenergization do not have to be symmetric or mirror images of each other. That is, if the time allocated for energization is different from the time allocated for deenergization, the forcing functions will reflect that. Variations in the solution will result in variations in the desired output such as the two embodiments shown. In addition to these two embodiments shown in this disclosure, a wide variety of other intentional transient behaviors are 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 is required to provide every object, feature, or advantage. Any of the objects, features, advantages, aspects, and / or embodiments disclosed herein may be integrated with one another, either fully or partially.

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

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

[0023] Yet another object, feature, and / or advantage of the present disclosure is to precisely control energy entering or leaving a device or system used as a dynamic system to purposefully induce oscillations, harmonics, rumbles, and the like.

[0024] Yet another object, feature, and / or advantage of the present disclosure is to provide an accurate 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 accurate analysis method that may be used to compensate for and maintain optimal operation of a device or system used as a dynamic system when components degrade or their behavior is otherwise altered during its life.

[0026] Still further objects, features, and / or advantages of the present disclosure are to improve energy efficiency, reduce size, weight, and cost, quieten, and extend the lifespan of many types and classes of devices or systems used as dynamic systems.

[0027] Yet another object, feature, and / or advantage of the present invention is to detect frequency content and / or lack thereof. The non-ringing nature of the waveform resulting from the dynamic system transients described herein is manifested as a substantial (close to zero) lack of frequency in the Fourier spectrum. It should be understood that physically realizable objects are generally imperfect and therefore a very small amount of frequency content is expected. Non-ringing and ringing data can be collected using recording Fourier transform spectra to quantify the frequency content of the magnetostrictive actuator.

[0028] 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, and such motions occur with respect to time, for example, in the time domain. A Fast Fourier Transform (FFT) can convert a time domain function or signal into the frequency domain for analysis. A lack of frequency content in the FFT of a dynamic device or system signal indicates non-ringing. There are many suitable commercially available computer programs that use Fourier transform methods to analyze a signal to determine its frequency content. Because physical devices or systems are never perfect, impurities known as noise distort the signal. However, at least one effective way to reduce noise to an unproblematic level is to apply a Gaussian smoothing function. For each finite data point in a set of data points of a signal, the Gaussian smoothing function takes its neighbors and applies the well-known Gaussian statistical bell curve to them, such that points closer to the point of interest are weighted more highly and points further away are weighted less highly. Thus, a Fourier transform of a dynamic signal from a device or system can prove that undesirable oscillations, harmonics, ringing, or resonances in the device or system have been eliminated. Commercially available computer programs typically label the method as a Fast Fourier Transform or Digital Fourier Transform.

[0029] These and / or other objects, features, and advantages of the present disclosure will be apparent to those of ordinary skill in the art. The present disclosure should not be limited to or by these objects, features, and advantages. No single embodiment is required to provide every object, feature, or advantage.

[0030] Certain embodiments in which the present disclosure may be practiced are illustrated and described in detail, where like reference characters represent like components throughout the several views. The drawings are presented for illustrative purposes and may not be drawn to scale unless otherwise indicated. [Brief description of the drawings]

[0031] [Figure 1] Plot the sine function sin(ωt), the first derivative ωcos(ωt) / ω, the second derivative -ω2sin(ωt) / ω2, and the third derivative -ω3cos(ωt) / ω3. [Diagram 2] For comparison and contrast with FIG. 1 , we plot the polynomial x(T), the first derivative xT / (2.1875×ttr), the second derivative xTT / (7.5107×ttr 2), and the third derivative xTTT / (52.5×ttr 3), all calculated below according to a first exemplary embodiment of the present disclosure that is intended to be non-ringing. [Diagram 3] Also for comparison and contrast with FIG. 1 , we plot the polynomial u(T), the first derivative uT / (1.9694×ten), the second derivative uTT / (−9.8696×ten 2), and the third derivative uTTT / (−38.733×ten 3), all calculated below according to a second exemplary embodiment of the present disclosure that is intended to ring. [Figure 4] FIG. 5C is a cross-sectional view of an underdamped magnetostrictive actuator used to collect data of embodiments 1 and 2 for FIGS. 5A-5B. [Figure 5A] Three traces are plotted showing end-to-end testing of both embodiments. [Figure 5B] Provide detailed clarification of the data of the second embodiment. [Figure 5C] Two traces are shown, where the top trace is the unruffled displacement data from about 0.1 to 0.2 in FIG. 5A, and the bottom trace is the corresponding Fourier transform with Gaussian smoothing. [Figure 5D] Two traces are shown: the top trace is the ringing displacement from approximately 0.35 to 0.363 seconds in FIG. 5B, and the bottom trace is its corresponding Fourier transform with Gaussian smoothing. [Figure 6]Averaged data from the same 99 sample runs as in Figures 5A and 5B is shown, where "identical" in this example means that the Matlab® script produced the exact same digital voltage output to the DT9836 for each run. [Figure 7] The same data as in Figure 6 with the addition of a ±3σ envelope. [Figure 8] The FFT of the non-ringing expansion displacement portion is shown. The data is unprocessed. [Figure 9] The same data as in FIG. 8 are shown, except that the y-axis is normalized. [Figure 10] FIG. 10 shows a normalized plot of the data of FIG. 9 with minimized spectral leakage. [Figure 11] The normalized minimum spectral leakage data in FIG. 10 is shown with Gaussian smoothing applied. [Figure 12] The FFT of the rumble displacement portion is shown. This data is unprocessed. [Figure 13] The same data as in FIG. 12 is shown, except that the y-axis is normalized. [Figure 14] FIG. 14 shows a normalized plot of the data of FIG. 13 with minimized spectral leakage. [Figure 15] Normalized minimum spectral leakage data from FIG. 14 with Gaussian smoothing applied.

[0032] Those skilled in the art need not view the nearly infinite number of different permutations of the features described in the following detailed description in isolated drawings to facilitate understanding of the present disclosure. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0033] The present disclosure is not limited to what is described herein. Mechanical, electrical, chemical, procedural, and / or other changes may be made without departing from the spirit or scope of the invention. Unless otherwise indicated, no feature shown or described is essential to enable basic operation of the invention.

[0034] Figure 1 shows the sine function sin(ωt) 10, the first derivative ωcos(ωt) / ω 11, and the second derivative -ω 2 sin(ωt) / ω 2 12, and the third derivative -ω 3 cos(ωt) / ω 3 13. For clarity, the derivatives have all been normalized. If they were not normalized, the magnitude of the last derivative would be approximately a factor of 248, ω 3 or 8π 3 Thus, comparison and contrast of traces on one plot is less affected by printing limitations.

[0035] The main property of a sine wave is that it describes the free response of a system, but not necessarily a forced response. The main disadvantage is that its shape is fixed. With respect to generating undesirable oscillations, harmonics, ringing, and / or the like over a defined transient time interval, the magnitude of the derivative of a fixed shape sine wave is also a fixed shape at a fixed multiple of the base frequency, the derivative may or may not start or stop at zero, and may have opposite polarity. Additionally, the defined transient time interval may or may not coincide with the free response of the system.

[0036] For comparison and contrast with FIG. 1, FIG. 2 shows the polynomial x(T) 20, the first derivative x T / (2.1875×t tr ) 21, second derivative x TT / (7.5107×t tr 2 ) 22, and the third derivative x TTT / (52.5×t tr 3 ) 23, all of which are calculated below according to the first exemplary embodiment of the present disclosure, which is intended to be non-ringing. As in FIG. 1, each derivative is normalized by its peak magnitude factor. Unlike FIG. 1, both these magnitudes and their polarities may be defined as desired, which is a major advantage of the present disclosure. The shapes of x(T) and its derivatives match the natural main characteristics of the load.

[0037] Also for comparison and contrast with FIG. 1, FIG. 3 shows a polynomial u(T) 30, the first derivative u T / (1.9694×t en ) 31, second derivative u TT / (-9.8696×t en 2 ) 32, and the third derivative u TTT / (-38.733×t en 3 ) 33, all of which are calculated below according to the second exemplary embodiment of the present disclosure that is intended to ring. As in FIG. 1, each derivative is normalized by the peak magnitude factor indicated in their label. Unlike FIG. 1, both these magnitudes and their polarities may be defined as desired, which is a major advantage of the present disclosure. The shapes of u(T) and its derivatives match the main characteristics of the load's nature.

[0038] 4 is a cross-sectional view of an underdamped magnetostrictive actuator 100 used to collect data for embodiments 1 and 2 for FIGS. 5A-5B. In accordance with the teachings of this disclosure, the actuator 100 has an input port 110 for electrical energy and an output port 120 for mechanical energy. The main features of interest are a mass 130 that is accelerated by the actuator 100, a preload spring 140, a solenoid coil 150 that converts an electrical input from the electrical input port 110 into a magnetic field, and a magnetostrictive rod 160 that converts a magnetic field input into a mechanical displacement output at the mechanical port 120.

[0039] FIG. 5A plots three traces. The top trace is the predicted normalized voltage over time calculated according to the disclosed method for a first non-ringing embodiment, with different rise and fall rates, followed immediately by a second embodiment that intentionally induces ringing. This predicted voltage trace was fed to a test article actuator to produce the measured displacement trace shown. That is, the cause calculated according to the disclosed method produced the desired effect. The bottom two traces are the normalized defined and measured displacement traces for both embodiments, with the defined output being the dotted line and the measured test data being the solid line. FIG. 5A shows end-to-end testing of both embodiments, while FIG. 5B provides detailed clarity of the data for the second embodiment.

[0040] It should be appreciated that in the case of no ringing, the frequency content threshold can therefore be set near zero. Additionally, the graphs of Figures 5C-5D further illustrate some of the many benefits of using the described control algorithms and control devices. The graphs provide a greater confidence threshold for establishing the use of the control algorithms and devices described herein, which would substantially advance the art.

[0041] Forms of energy considered in this disclosure include mechanical, electrical, magnetic, hydraulic (fluid), and thermal. Energy is always a positive quantity and cannot be created or destroyed. Thus, for a dynamic system, energy output is the energy input minus any internal storage. Energy output includes heat, which is irreversibly dissipated whenever energy is transferred.

[0042] Energy affects and is affected by dynamic systems and their components. Reactive elements store energy without dissipating it. Transducing elements convert energy from one form to another. Resistive elements dissipate energy without storing it. An exemplary embodiment of the method of the present disclosure is that of lumped parameter dynamic systems. Lumped parameter dynamic systems consist of discrete finite elements such as masses, springs, dampers, inductances, capacitances, resistors, and / or the like. The method may be extended to distributed parameter dynamic systems. Distributed parameter dynamic systems consist of very small but non-zero versions of these same elements and consider waves moving through the distributed parameter system.

[0043] The time rate of change of energy in a dynamic system, a forcing function acting over a defined transient period, may be thought of as a combination of cause and effect. For example, voltage causes current, magnetic field causes magnetic flux, pressure causes fluid flow, and force causes velocity. In this disclosure, the cause of the time rate of change of energy in a dynamic system is called a cross variable, or AV for short, and the effect of the time rate of change of energy in a dynamic system is called a through variable, or TV for short, in this disclosure. Both are called state variables. At any instant in time, these quantities are distinguished as follows: the magnitude of an AV varies smoothly from one side of the dynamic system port it acts on 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 herein, the word "smooth" means free of abrupt changes or discontinuities. Multiplying the instantaneous time rate of change of an AV by its corresponding TV gives the instantaneous time rate of change of energy flowing into or out of the dynamic system through that port. In a dynamic system, these state variables change with respect to time, and therefore the energy state of the dynamic system also changes.

[0044] Now consider dynamical systems that convert energy from one form to another, where the conversion may involve scaling of state variables only in magnitude. Examples include electric motors, electric transformers, hydraulic cylinders that move flight control surfaces of aircraft, magnetostrictive actuators, piezoelectric actuators, sonar sources, seismic imaging sources, or semiconductors. In any case, the time rate of energy input may be approximately equal to the time rate of energy output, where the word approximately is used to mean that any internal storage and necessarily dissipated heat must be subtracted from the output. A reliable mathematical description is typical, which can be found in a voluminous literature, where the coupling between the input and output energy ports as a function of time tends to be modeled as follows: Ind.AV1(t) = dep.TV1(t) + coupled dep.TV2(t) (or AV2(t)) Ind.AV2(t) = dep.TV2(t) + coupled dep.TV1(t) (or AV1(t))

[0045] where there are only two dependent variables per equation. Each equation is independent and represents the inflow of energy to one port or the other. For modeling forced function transients, the approach is insufficient because a third dependent variable is missing. Add it to complete each equation as a function of time. Ind.AV1(t)=dep.TV1(t)+coupled dep.TV2(t)+coupled dep.AV2(t) Ind.AV2(t)=dep.TV2(t)+coupled dep.TV1(t)+coupled dep.AV1(t)

[0046] Scaling the variables by non-zero material-, device-, and / or system-specific coefficients Cn or Dn completes the equation. AV1(t)=C1 TV1(t)+C2 AV2(t)+C3 TV2(t) AV2(t)=D1 TV2(t)+D2 AV1(t)+D3 TV1(t)

[0047] Each equation can be recast using any one of the other three variables as the independent variable.

[0048] For the first preferred embodiment, where there is no ringing during the energized forcing function transient, the solution is as follows: Assume that it is desired for a dynamic system to start from a first rest position, move quickly and stop at a second rest position, without ringing. Let the first and second rest positions of displacement x be, for example, -x 0 and x 1 -x 0 Define T ≡ t / t tr (where t is time, t tr where is the defined duration of the transient. It should be observed that the method of the present disclosure does not limit how short the transient time can be defined. Limitations may be provided by materials, design, operational constraints, and / or the like. Referring to FIG. 2, the dynamic system is in a first rest position -x 0 If T=0, then the velocity x T , acceleration x TT , and the derivative of acceleration x TTT are all zero. At the end of the transient, when T=1, x is the second rest position x 1 -x 0 The condition for no alarm is x T , x TT , and x TTT We need to set all of the third derivatives x back to zero. TTT The role of is to control the approach of the second derivative to zero or other point.

[0049] For polynomials, the order is added for each specified boundary condition. Thus, for a polynomial with eight specified boundary conditions and its three derivatives, the order must be eight or greater. Unlike sine waves, polynomial derivatives do not need to undergo inverse polarity or scaling. Higher orders result in more than one solution, so the unique solution sought is of order eight. x(T)=AT7 +BT 6 +CT 5 +DT 4 +ET 3 +FT 2 +GT 1 +HT 0 where A through H are coefficients, and the indices 1 and 0 are normally implied but are explicitly included in this disclosure to ensure only one meaning. The first three derivatives are

number

[0050] Solve for the coefficients A through H by substituting the specified boundary conditions. At T=0, the unenergized dynamic system is at rest, and x TTT ≡0, x TT ≡0, x T ≡0, and the first rest position x ≡ -x 0 At T=1, x TTT ≡0, x TT ≡0, x T ≡0, and the dynamic system reverts to the second rest position x ≡ x 1 -x 0 It is paused at . Therefore,

number

[0051] One of the four state variables is now defined as desired, in this case the mechanical output over variable AV2(T) in the independent AV1(T) equation. The other mechanical output state variable that completes the energy state at the mechanical port is the force TV2(T). The force can be found by knowledge of the external loads against which the dynamic system is intended to operate, i.e. loads such as springs, masses, and dampers. The velocity x, which is the time rate of change of displacement at the output port of the dynamic system from the energy input to that input port, is T The appearance of the force F at the output port T A time rate of change of FT =mx TTT bx TT +kx T

[0052] where the discrete aggregate load parameters are m for the accelerating mass, b for the damping coefficient, and k for the spring constant. Substitution and Integration

number

[0053] In the formula, F 0 is the integral constant. Now we know the state variables that are the causes and effects of the output. Their product F(T) x T is the time rate of change of the dynamic system energy output from the mechanical port, W T Multiplication

number

[0054] W T Integrating gives the total mechanical energy output from this port versus time, W(T).

number

number

[0055] Displacement and force are two of the four state variables in either of the coupled equations for the method of the first preferred embodiment, and combine to quantify the mechanical energy side of the actuator. Since solving either of the coupled equations requires knowing one more state variable, consider assuming the following definition of AV1(T) or TV1(T): For a transducing element, either AV2(T) or TV2(T) is very likely to be close to a proportional scale of either of the input state variables with respect to time AV1(T) or TV1(T). This means that the form of the expression with respect to time for the third state variable will be the same as the state variable it is scaling. Testing has shown that this assumption is true for at least one type of dynamic system, the magnetostrictive actuator of FIG. 4. The simple and flexible magnetostrictive actuator used in this testing scales current to displacement in a nearly proportional manner. (However, the method of the present disclosure can be improved by "pre-distorting" the input to more closely approximate perfect proportionality.) Take the position polynomial and the velocity polynomial and scale them to the current. I(T)=I pk [-20T 7 +70T 6 -84T 5 +35T 4 ] I T= 140 I pk [-T 6 +3T 5 -3T 4 +T 3 ] / t tr In the formula, I pk is the magnitude of the peak current shown below.

[0056] The three known state variables are substituted into the first coupled equation to obtain an expression for the fourth state variable, in this case magnetic flux φ(T) as a function of current, displacement, and force. φ(T)=(1 / C1)I(T)-(C2 / C1)x(T)-(C3 / C1)F(T)

[0057] As with mechanical outputs, we form a product of the time rate of change of an input, AV, and the corresponding input, TV. This product is the time rate of change of the input energy, E T It is. E T= φ(T)I T= (1 / C1)I(T)I T -(C2 / C1) x (T)I T -(C3 / C1)F(T)I T

[0058] where the first term is the time rate of change of the energy stored in the actuator. E T Integrate to find the total input energy E(T). Solve the difference between E(0) and E(1) to find ΔE.

[0059] I pk To find the magnitude of I, set the sum of ΔE and ΔW to zero. pk Form a quadratic equation of I pk Due to conservation of energy, this sum is set to zero and already includes energy storage and any dissipated heat from the actuator output ports.

[0060] To calculate the actuator input voltage V(T), E T Note that V(T) is also the product of V(T) and I(T). Add the inevitable heat dissipation from the energy input port to complete the customized forcing function for the specified non-ringing transient period. V(T)=E T / I(T)+RI(T) 2 where R is the ohmic resistance.

[0061] FIG. 5A plots test data that confirms that the set of eight specified boundary conditions results in a specific and accurate solution for V(T). The profile of the voltage input with respect to time, V(T), is a forcing function that acts to energize the actuator for a defined transient period without ringing. The absence of ringing is observed at a position x inserted between energizing and de-energizing the actuator. 1 -x0 A separate forcing function is calculated for de-energization.

[0062] A first embodiment of the method of the present disclosure predicts an accurate forcing function for the time required to energize or de-energize a dynamic system without undesirable oscillations, harmonics, ringing, and / or the like. The transient period is limited only by the materials of structure in the dynamic system, their configuration, their operation, and / or the like, and not by the method of the present disclosure.

[0063] While no ringing is one set of boundary conditions for the first preferred embodiment, the specified boundary conditions may be altered to intentionally create ringing or any other operating characteristic, as desired. For the second preferred embodiment, which intentionally induces only resonant ringing in the same dynamic system, consider the following revised boundary conditions: The same magnetostrictive actuator of FIG. 4 used to provide the test data for the first preferred embodiment of the present disclosure was reused to provide the data for the second preferred embodiment.

[0064] T≡t / t en (where t is time, t en We again normalize time by defining ω = ω (where ω is the period of energization). When the dynamic system is vibrating at its sinusoidal free response resonant frequency, the period of energization is defined as half the period of a complete sinusoidal cycle at the sinusoidal free response resonant frequency, i.e., the expansion time of the test actuator. The main property of this particular actuator is that it only expands when electrically energized, regardless of the polarity of the electrical input. Thus, the compression time is the remaining half of a complete sinusoidal cycle, which remains unenergized. This allows for an increase in the amplitude of vibration due to the superposition of the energization / expansion periods.

[0065] At T=0, the unenergized dynamic system is at rest, and u TTT ≡0, u TT ≡0, u T ≡0, and u ≡ -u 0T=1, u TTT ≡0, u TT ≡-π 2 u 1 / t en 2 , u T At ≡0, the dynamic system undergoes a first displacement u ≡ u 1 -u 0 That is, at T=1, the acceleration u TT Since is nonzero, the dynamic system is excited to resonance and remains at resonance. Then

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[0066] The actuator and the load exchange equal amounts of kinetic and potential energy at resonance. It should be observed that this stored energy is treated separately, and the coupling equations do not apply to it. That is, although the state variable u(T) contains a stored energy term, the stored energy is not part of the coupling equations in this case. By superposition, the coupling energy can be added to or subtracted from the total stored energy, but the stored energy itself is not part of the coupling calculation.

[0067] From this different starting point, the solution method is similar to that of the first embodiment described above, with W T and form W(T). The difference is that re-adopting x(T) of the first embodiment is not recommended in this second embodiment, since u(T) contains the result of stored energy versus displacement, i.e. the set of necessary boundary conditions for I(T) is not the same as for u(T), since the actuator can store mechanical energy but not electrical energy.

[0068] To solve this, consider defining a pseudo-displacement v(T) that mirrors the zero boundary conditions on I(T) and its derivatives. That is, the velocity u Tis zero at the end of each expansion, we can use the form of the pseudo-displacement v(T) and current I(T) as velocity u(T) instead of displacement u(T). T The function v(T) and its three derivatives each require eight boundary conditions of zero in order to induce only the desired resonance, the stored energy represented in u(T), while avoiding inducing unwanted oscillations, ringing, harmonics, and / or the like.

[0069] The magnitude of the peak current in the second embodiment I pk Solving for v requires the solution of the coupled portion of the output energy W at an intermediate T between 0 and 1 to solve for ΔW, since there can be no coupling if the specified boundary condition is zero current at T(0) and T(1). A convenient intermediate T is 1 / 2. Correspondingly, we set v=u(1 / 2) to calculate the non-zero boundary conditions. For clarity, the quantity u(1 / 2) is actually 1 / 4 of a complete resonant cycle, with half the cycle energized and the other half not. For a polynomial with nine boundary conditions, the unique solution sought is of order 9. Thus

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[0070] Also, the matching pseudo-displacement is only used in the electrical section since this is all that can be combined.

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[0071] As in the first embodiment, the equations for v(T) and I(T) are substituted into the coupled equations to obtain the remaining state variables φ(T), the product E T , integral E, I pk and finally, the forcing function voltage versus time V(T).

[0072] To increase the magnitude of vibration, successive displacement strokes may be superimposed to increase the amount of stored energy, which appears as kinetic and potential energy exchanged between the actuator and its load.

[0073] Because testing proves that the disclosed method accurately predicts dynamic system behavior, the disclosed method provides physical insight to further predict the effects of improvements in material properties, geometry, and all other elements of the design, manufacture, and operation of dynamic systems. For example, the well-known performance degradation of piezoelectric ceramics with use may be mitigated by the physical insight provided by this method. In a second example, PWM waveforms used to achieve variable electric motor speeds may use the disclosed non-rumble transient method to improve efficiency, heat losses, and component stresses.

[0074] In a similar manner, when the methods of the present disclosure are used in adaptive motion controllers, variable frequency drives ("VFDs"), soft starters (e.g., in applications where there is a large inrush of current that can damage the motor while the VFD controls the motor and can vary the speed of the motor), digital communication devices, aircraft hydraulic systems, internal combustion engine fuel injectors, piezoelectric actuators, and / or the like, energy control predictions can be altered based on wear or other variations to maintain the desired motion versus time over the life of the dynamic system. The number of required calculations is minimized. The present disclosure provides mathematics that is simple and compact enough for a computer to quickly calculate and update during dynamic system operation.

[0075] As expected, the desired behavior of magnetostrictive actuators cannot be without limitations. For example, limitations are imposed by the mechanical strength of terbium alloys. Regardless of how they are operated, the mechanical limit of the actuator is simply the mechanical strength of the terbium alloy. When operated within this limit, no degradation in performance over time has been observed. Within its destructive limits, terbium alloy performance has not been observed to degrade at all with any known combination of high stress, high strain, high magnetic field, and / or high temperature. Due to the need for at least high stress and high strain, it is theorized that the upper limit of the mechanical power density of terbium alloys occurs very close to its mechanical strength limit. In other words, this mechanical power density limit coincides with the maximum compressive stress and / or minimum displacement amplitude. The elastic modulus of terbium alloys is relatively soft. This can be a great advantage for both power density and flexible operation, which are the main features of durable actuators intended to provide powerful and precisely controllable vibrations. The soft elastic modulus allows the use of superposition to obtain larger displacements from smaller electrical inputs. The durability of terbium alloys allows for greater displacements to be expected with longer life.

[0076] As with other materials such as steel, another limitation may be found to be the time rate at which stress and / or strain can be applied. For example, in its unmagnetized and immobile state, it is known that the stress and strain of terbium alloys decay slightly asymptotically with time, likely due to spontaneous rearrangement of magnetic domains. The method of the present disclosure allows for the consideration of all magnetostrictive actuator phenomena in order to operate them at their maximum allowable power density.

[0077] The method of the first embodiment of the present disclosure of anti-rumble can suppress undesired rumble by providing a countermeasure to the existing system: the output from a separate dynamic system will be calculated to absorb the undesired dynamics using knowledge of the energy over time.

[0078] The disclosed method can be used, for example, in diesel fuel injectors to control the orifice size when injecting fuel into the combustion chamber. That is, the injection orifice can be open for a desired amount of time, can be partially open, can oscillate as fuel is being injected to both steer fuel direction and / or aid atomization, and can close quickly without causing shock fatigue to the valve seat. Thus, engine power and economy are improved while reducing in-cylinder emissions. Different injection profiles can be used to accommodate different fuels without compromising performance.

[0079] The methods of the present disclosure should not be limited to the two particular embodiments described herein. In particular, the present 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. Additionally, the present disclosure contemplates loads consisting of distributed parameters characterized by wave mechanics.

[0080] The foregoing description has been presented for purposes of illustration and description. It is not intended to be an exhaustive list or to limit any of the present disclosure to the precise form disclosed. It is contemplated that other alternatives or exemplary aspects are included in the present disclosure. The description is merely an example of an embodiment, process, or method of the present disclosure. It is understood that any other modifications, substitutions, and / or additions may be made that are within the intended spirit and scope of the present disclosure. From the foregoing, it can be seen that the present invention accomplishes at least all of the objectives set forth. EXAMPLES

[0081] The embodiments of the present invention are further defined by the following non-limiting examples. These examples, while showing certain embodiments of the present invention, should be understood to be given by way of illustration only. From the above discussion and these examples, those skilled in the art can ascertain the essential characteristics of the present invention, and can make various changes and modifications of the embodiments of the present invention to adapt them to various applications and conditions without departing from the spirit and scope thereof. Thus, in addition to those shown and described herein, various modifications of the embodiments of the present invention 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.

[0082] Energizing or de-energizing a dynamic system does not necessarily cause undesired ringing. To prove this, an automated method for control was written and tested. Using a Fourier transform of the dynamic data, one can quantify the frequency content, which is a means of detecting whether the automated method for control has been effectively employed.

[0083] No physical object is perfect, so even small imperfections in the test item or test equipment will manifest as noise.

[0084] The test specimen was a No. 1 TdVib, LLC industrial vibrator, serial number 5135. The test specimen was a 9.830 kilogram steel mass accelerated vertically. The specimen and mass were rigidly fixed to a granite block weighing approximately 2 tons.

[0085] In this test, one signal was output and three signals were input. The output signal was a voltage and the input signals were a monitor that measured this output voltage plus the resulting specimen current and displacement.

[0086] The control law predicts the specimen input voltage required to obtain the desired output displacement. The computer output is digital. The control law output and data collection were controlled by a Matlab script. The computer manipulated and recorded the data transmitted to it.

[0087] The Data Translation model DT9836, serial number 00645986, provides two analog outputs and twelve analog inputs; that is, it converts computerized digital signals into analog outputs. The 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 for monitoring. A Matlab® computer operated the device at 100,000 samples per second, or every 10 microseconds.

[0088] The amplifier was an AETechron model 7782, serial number 194970. It has an available signal that is a scale of its output current.

[0089] The specimen displacement was measured by an MTI Instruments Fotonic Sensor, serial number 1604. This instrument was selected with a response of -3 dB at 161 kHz. Range 1 was selected and the bandpass filter was set to DC for 1 kHz. The Fotonic Sensor is fixed to a Melles Griot stage that is slidably adjustable in 1 micrometer increments. The stage is then rigidly affixed to a granite block.

[0090] The electronics for this test were allowed to warm up before use.

[0091] Once launched, the Matlab® script generates a voltage output, sends it to the DT9836, and records the data from the DT9836.

[0092] The Fotonic displacement sensor was mounted on a separate granite plate of substantially less mass. This arrangement was determined to be sensitive to seismic motion. Remounting the sensor on a 2-ton granite block mitigated much, but not all, of the contamination of the data. For example, nearby footsteps were sometimes detected. The solution was to wait until the output was stationary and then run the test.

[0093] 100 sample runs were recorded. Each run was identical to Figure 5A and Figure 5B, i.e., the Matlab script generated the exact same digital voltage output to the DT9836 for each run. One run was eliminated due to anomalous excessive noise, leaving 99 good data sets.

[0094] The specimens performed as expected and there were no other concerns during this test series.

[0095] The device performed as expected and no other concerns were noted during this test series.

[0096] There were no known equipment malfunctions. Post-test averaging of raw data is useful. Separate ground wires were run from all equipment to the structural beams. This reduced some electronic noise.

[0097] There was noise in the raw data. Shielding of all the equipment wiring is not an issue.

[0098] The DT9836 has two defects. First, the start of the signal rarely matches from one test to another. In particular, the time zero does not match the time zero of the calculated input voltage analog signal, so post-processing is forced to align the prediction with the data in order to see the delay between cause and effect. The data time zero can be plus or minus a random amount from the predicted time zero. Therefore, the zeros of all data sets are manually aligned, and it is easy to find and subtract the offset by graphing the data. Second, the sample interval cannot be set to an amount like a power of two within one second. That is, for the FFT, it is desirable to set the number of samples per second to a power of two such as 131,072. However, in this test, it was simply set to 100,000.

[0099] Data correction was limited to time zero alignment of the prediction and the data so that the delay between cause and effect could be observed more accurately.

[0100] 99 Fotonic sensor displacement data sets were zero-aligned and then averaged to create the graphs in Figures 6 - 7. The correction is limited to aligning the prediction and the data zero. The displacement was small (see Figure 7).

[0101] The following graphs were generated using Matlab® version 2021a with the optional Signal Analyzer Toolbox, a product of The MathWorks, Inc. The graphs in Figures 8 - 15 are presented in the order in which they were processed to produce the final results. The order of Figures 8 - 11 and Figures 12 - 15 is separated into the order of Non-Ringing Embodiment 1 and the subsequent Ringing Embodiment 2 of U.S. Provisional Patent Application No. 63 / 364,580, titled "Fast Non-Ringing Dynamic System Transient", filed on May 12, 2022.

[0102] Example 1: FFT of the Non-Ringing Extended Displacement Portion The 99 average non-ringing displacements visible from 0.00 to 0.08 seconds, each set of 8,001 data points, were subjected to FFT with the Signal Analyzer Toolbox in Matlab®, and the results are shown in Figures 8 to 11.

[0103] Example 2: FFT of the rumbling displacement part The 99 average visible rumble displacements from 0.15500 to 0.17472 seconds, each set of 1,973 data points, were subjected to FFT with the Signal Analyzer Toolbox in Matlab®, and the results are shown in Figures 12 to 15.

[0104] Figures 6 (Example 1) and 10 (Example 2) show the clear and obvious difference between the non-ringing and ringing embodiments of the present disclosure, which shows that non-ringing intellectual property infringement is easily identifiable.

[0105] All post-processing steps were identical. Gaussian smoothing was chosen because it produces significantly different results than other available smoothing algorithms. Although the signals shown above are displacements, the same post-processing techniques apply to any and all dynamic signals, including electrical, hydraulic, pneumatic, etc.

[0106] Glossary Unless otherwise defined, all technical and scientific terms used above have the same meaning as commonly understood by one of ordinary skill in the art to which the embodiments of the present disclosure pertain.

[0107] The terms "a," "an," and "the" include both singular and plural referents.

[0108] The term "or" is synonymous with "and / or" and means any one member or combination of members of a particular list.

[0109] As used herein, the word "exemplary" refers to an example, instance, or illustration, and does not refer to a most preferred embodiment, unless specifically stated otherwise.

[0110] The term "about" as used herein refers to slight variations in a quantity for any quantifiable variable. Unintentional errors may occur, for example, from the use of typical measuring techniques or equipment, or from differences in manufacture, source, or purity of the components.

[0111] The term "substantially" refers to a large or significant degree. Thus, given the appropriate context, "substantially" can refer to a plurality, a majority, and / or a vast majority of the quantifiable variables in question.

[0112] The term "generally" encompasses both "about" and "substantially."

[0113] The term "configured" describes a structure that is capable of performing a task or adopting a particular configuration. The term "configured" may be used interchangeably with other similar phrases such as built, arranged, adapted, manufactured, etc.

[0114] Terms characterizing sequential order, position, and / or orientation are not limiting and are merely referred to according to the figures presented.

[0115] "Reasonable" data is deemed reasonable and true by those of ordinary skill in the art.

[0116] "Ringing" describes the natural free response of a dynamical system that is stimulated. For example, a bell "rings" after it has been struck.

[0117] "The present invention" is not intended to refer to any single embodiment of a particular invention, but rather encompasses all possible embodiments described in the specification and 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 present disclosure is further limited as including any possible modifications to any of the aspects and / or embodiments disclosed herein that result in other embodiments, combinations, subcombinations, etc. that will be apparent to those skilled in the art.

Claims

1. A method for operating a device or system, Combining the time rate of change of the cause of energy leakage from the device or system with the influence of the time rate of change of the cause of energy leakage from the device or system, Using the above combination, define the time rate of change of the cause of energy inflow into the device or the system, A method comprising combining the cause of energy inflow into the device or system with the effect of the rate of change of time of the cause of energy inflow into the device or system, thereby resulting in a time velocity or frequency at which energy enters or leaves the device or system, which yields virtually no spectral content.

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

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

4. The method according to claim 1, further comprising reducing undesirable oscillations, harmonics, buzzing, or resonances in the device or system when power is applied or de-powered.

5. The method according to claim 1, further comprising not intentionally inducing any undesirable oscillation, harmonics, buzzing, or resonance in the device or system when power is applied or de-powered.

6. The method according to claim 1, further comprising intentionally inducing a desired oscillation, harmonic, hum, or resonance in the device or system when power is applied or de-powered.

7. The method according to claim 1, wherein the device or system transmits or receives information as an array of numbers.

8. The method according to claim 6, wherein there are only two possible numerical values, represented by a higher voltage and a lower voltage.

9. The method according to claim 1, wherein the device or system controls the load by controlling the energy supply with pulses.

10. The method according to claim 9, wherein the pulse has only two possible values: a higher energy flow cause and a lower energy flow cause.

11. The method according to claim 10, wherein the time width of each pulse can be changed and the time width between pulses can be changed.

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

13. The device or the system Internal combustion engine fuel injector, The method according to claim 1, selected from the group consisting of a fuel cell fuel injector and

14. The further includes non-destructively evaluating an object using the device or system, and the device or system Medical imaging devices and The method according to claim 1, selected from the group consisting of an earthquake imaging device and

15. The device or the system Sonar projector and, Noise-canceling devices and, The method according to claim 1, selected from the group consisting of a device for avoiding noise generation.

16. The method according to claim 1, further comprising canceling out vibrations in an object or preventing the occurrence of vibrations.

17. The device or the system Piezoelectric devices and The method according to claim 1, selected from the group consisting of a magnetostrictive device and a magnetostrictive device.

18. The device or the system The method according to claim 1, selected from the group consisting of magnetostrictive devices having a preload exceeding 10,000 psi.

19. A device or system, The first combination, The time rate of change of the cause of energy leakage from the device or system, and A first combination including the effect of the time rate of change of the cause of energy leakage from the device or the system, The second combination is, The cause of energy inflow into the aforementioned device or system, and A second combination including the effect of the time rate of change of the cause of energy inflow into the device or system, The first combination and the second combination result in a time velocity or frequency at which energy enters or leaves the device or system. The aforementioned time speed or frequency yields virtually no spectral content. The operation of the device enables contact with an object at near zero contact speed.

20. An integrated microchip compiled and / or programmed to carry out the method according to any one of claims 1 to 18.

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