Patent Application: US-201113186459-A

Abstract:
a method for synthesis of a hysteresis function of a plurality of inputs is described . the method includes receiving and processing of a plurality of input signals with at least a parameterized multivariable nonlinearity , the parameterized multivariable nonlinearity serving as a parameterized hysteron , to produce at least one output signal . the plurality of input signals is also processed by at least a controller function , the controller function comprising memory and producing at least one control signal responsive to at least one of the plurality of input signals , the at least once control signal for controlling the parameterized hysteron . the at least one control signal is used to control the parameterized hysteron so as to create a hysteretic response to at least one of the plurality of input signals .

Description:
in the following , numerous specific details are set forth to provide a thorough description of various embodiments . certain embodiments may be practiced without these specific details or with some variations in detail . in some instances , certain features are described in less detail so as not to obscure other aspects . the level of detail associated with each of the elements or features should not be construed to qualify the novelty or importance of one feature over the others . in the following description , reference is made to the accompanying drawing figures which form a part hereof , and which show by way of illustration specific embodiments of the invention . it is to be understood by those of ordinary skill in this technological field that other embodiments may be utilized , and structural , electrical , as well as procedural changes may be made without departing from the scope of the present invention . those of ordinary skill in this technological field will understand that other embodiments may be utilized , and structural , electrical , as well as procedural changes may be made without departing from the scope of the present invention . wherever possible , the same reference numbers will be used throughout the drawings to refer to the same or similar parts . traditional hysteresis curves for transformers , gears , pseudo - elastic deformation , etc . are well known ( see for example [ r ]). most such hysteresis curves are at least piecewise continuous although they typically have discontinuities in at least the first derivative . many such hysteresis curves do not include “ dead - zones ,” but notable exceptions to this are mechanical toothed - gear hysteresis under rotational direction reversal and “ schmitt trigger ” electrical circuits . although there are many types and variations of hysteresis curves , fig1 a depicts a commonly rendered representation of a closed hysteresis curve (“ loop ”). more specifically , fig1 a depicts a representation of an example typical hysteresis trajectory curve “ loop ” representing phenomenon present , for example , in magnetic systems subjected to a periodic input . these types of curves are sometimes referred to as a “ limiting loop ” or related terminology . fig1 b depicts a representation of a more general example of a hysteresis trajectory curve for a hysteretic system , such as that producing the hysteresis trajectory curve depicted in fig1 a , resulting from an input that repeatedly reverses direction over an interval of time with monotonically increasing peak - to - peak amplitude . these types of open ( nonclosed or “ non - loop ”) curves , regardless of direction of travel over time , are sometimes referred to as a “ reversal curve ” or related terminology . fig1 c depicts an analogous “ reversal curve ” representation of a more general example of a hysteresis trajectory curve for a hysteretic system , such as that producing the hysteresis trajectory curve depicted in fig1 a , resulting from an input that repeatedly reverses direction over an interval of time with monotonically decreasing peak - to - peak amplitude . fig1 d depicts a representation of an example hysteresis trajectory resulting from an input that repeatedly reverses direction over an interval of time but with irregularly - varying peak - to - peak amplitude . fig1 e depicts how the hysteresis process such as that associated with fig1 d transforms the input signal into an output signal . fig1 f and fig1 g , reproduced from [ e ], depict representations of an example “ butterfly - shaped ” hysteresis loops that occur in quantum - level optical mixing phenomena . fig1 h depicts a representation of an example “ pinched ” hysteresis loop that occur in memristor implementations [ p ]. the hysteresis modeling literature is immense [ a - x ] and continuing to expand . much of this has to with analysis efforts , the modeling of properties of materials , systems , and processes , and to some extent the design of control systems . the mathematics is rich , inviting , and as deep and intricate as a thinking mathematician or physicist would happily and stridently seek . the present invention is directed in part to the synthesis of hysteresis processes and their use in real - time systems , control systems , numerical simulations of system , signal processing , music audio , and other applications . although all of the mathematical machinery and empirical observation behind it are extensively informative to the background of the invention , only a few selected aspects of this extensive mathematics are leveraged in the present invention . some of the scalar hysteresis modeling concepts useful to the present invention include but are not limited to : informal interpretations of scalar hysteresis as nonlinearities with memory attributes that invoke branching [ s ]; hysterons which are the individual branches ( typically nonlinear , but for the purposes of the present invention will include linear and piecewise - linear ) of a hysteresis curve or trajectory rate - independent aspects of a hysteresis process ; rate - dependent aspects of a hysteresis process ; “ selector ” and “ almost selector ” aspects adapted from representations of multi - valued functions [ l ]— other names and variations of these exist , for example “ switch function ,” “ switching - function ,” and in some terminologies “ branch condition ,” “ branching condition ,” etc . ; local memory aspects wherein future - time values of such aspects a hysteresis process output are uniquely determined by the present - time value of that output and future - time behavior of the input . in somewhat deeper mathematical formulations , local memory aspects of a hysteresis process are “ play ” and “ stop ” operators [ l ]. in a differential model , each point in the input - output graph of a local - memory aspect of a hysteresis process can only lead to only two possible future paths . a schmitt trigger electrical circuit is an example of a local memory aspect of a hysteresis process ; non - local memory aspects wherein future - time values and future - time paths of such aspects a hysteresis process output depend on more than the current output value . two important examples are : values of the most recent input extrema , values of the two most recent input extrema , values of “ all ” ( perhaps asymptotically suppressed ) input extrema , the entire history of input values overtime , rate - of - change over time of the input . in a differential model , each point in the input - output graph of a local - memory aspect of a hysteresis process can only lead to many ( or an infinite number ) of possible future paths . an electrical transformer is an example of a non - local memory aspect of a hysteresis process . it is with regards to non - local memory aspects a hysteresis process that additional mathematical hysteresis models ( such as prieisach , stoner - wohlfarth [ s ], differential [ u ], automata [ r ]) and aspects of multi - valued functions [ l ] can be further employed in the implementation of hysteresis synthesis as provided for by the present invention . example scalar hysteresis synthesis such as that taught in u . s . pat . no . 7 , 309 , 828 scalar hysteresis is the form of hysteresis wherein there is a single input variable and a single output variable . scalar hysteresis is the form of hysteresis that is most discussed , taught , and studied . figs . x1i , x1j , and x1k , reproduced from fig6 of the inventor &# 39 ; s previous patent u . s . pat . no . 7 , 309 , 828 relating to hysteresis synthesis , shows aspects of hysteresis synthesis as provided for by that patented invention . these aspects of hysteresis synthesis pertain to at least scalar a brief review is provided here : the input / output graph depicted in fig1 i shows example symmetric curves that are linear 102 , superlinear 103 , and sub - linear 104 along with the time / amplitude oscillograph of an example applied waveform 110 depicted in fig1 j . other types of symmetric or non - symmetric nonlinearities can also be used . a time - derivative operation on the applied signal waveform 110 followed by sign detection reveals whether the applied signal waveform is at any instant increasing or decreasing . as an example , the applied signal waveform 110 would be applied to one nonlinear warping function such as 103 , 104 when increasing and the other when decreasing , resulting in the waveform depicted in fig1 k comprised of solid - line curve segments 113 ( thin - line ) and 114 ( bold - line ) rather than the dashed - line waveform 112 that would have been created by the linear curve 102 . the nonlinear branch segments 113 , 114 serve here as hysterons . in order to allow the applied input signal to vary in amplitude and still maintain piecewise - continuity of the waveform , the invention of u . s . pat . no . 7 , 309 , 828 provides for the warping nonlinearities to be themselves adaptively scaled or otherwise altered based on amplitude information from the current and previous direction reversals , moving average of waveform area or waveform power , etc . these aspects address at least local memory , non - local memory , selector , and rate - independent aspects of various types of hysteresis processes . the invention of u . s . pat . no . 7 , 309 , 828 also provides for aspects of the hysteresis synthesis process , such as curve shapes and degrees of dependency on waveform history , to be varied in real - time by control parameters . the invention of u . s . pat . no . 7 , 309 , 828 allows for such control parameters to be used for the modulation of synthesized hysteresis processes , for example in the production of electronic music signal processing and electric guitar distortion . the invention of u . s . pat . no . 7 , 309 , 828 also allows for such control parameters to be used for the adjustment of synthesized hysteresis processes , for example under control parameter recall in the context of stored program control . the present invention provides for such control parameters to be used for the tuning , adaptation , etc . of synthesized hysteresis processes . the present invention further provides for such control parameters to be used as an element and / or method in the synthesis of more complex synthesized hysteresis processes . for example , synthesized hysterons can be parameterized in this fashion and control signals can be used to adjust synthesized hysteron parameters . the control signals can , for example , be produced by a controller function according to the outputs of selectors , signal time - derivative sign detectors , integrators , fractional dynamical processors , control systems , system measurement sensors , etc . fig2 depicts an input - output representation that is applicable to the hysteresis synthesis arrangements of fig1 i through 1k as well as other types of hysteresis discussed herein and elsewhere . here the input signal g ( x ) is operated on by the hysteretic synthesis element to create an output signal h ( x ). in an embodiment of the invention , the characteristics of the type and character of the hysteresis operation invoked by the hysteretic synthesis element can be parameterized , i . e ., determined by the value of one or more parameter ( s ). in an embodiment of the invention , the value of one or more of these parameter ( s ) can be used as a control input , here designated as the quantity c . if there are a plurality of such parameters structured as a control input , c is a vector . if there is only a single such parameter structured as a control input , c is a scalar . the present invention provides additional and more advanced types of synthesized hysteresis for use in applications including signal processing , controllers , music , and computer simulations in physics , engineering , and economics . in particular , the present invention provides for , among other things , the following types of advanced hysteresis which can be used individually or in combination : multi - variable hysteresis synthesis ; phase hysteresis synthesis ; frequency - dependent hysteresis synthesis ; dynamical variation of hysteresis parameters for hysteresis synthesis . each of these is considered in more detail in the sections to follow . additionally , the present invention provides for the use of synthesized hysteresis of the types described in u . s . pat . no . 7 , 309 , 828 , and / or the types of advanced hysteresis listed above , in control systems , computer simulation , and as a component in the advanced hysteresis synthesis systems and methods to be presented . for scalar hysteresis synthesis , the control signals produced by a controller function can accordingly be hysteretic ally responsive to the input signal . for multi - variable ( vector ) hysteresis synthesis , the control signals produced by a controller function can accordingly be hysteretic ally responsive to at least one of a plurality of input signals . in an example implementation the controller function is responsive to at least one extremal value of the phase of at least one of the plurality of input signals . in another implementation the controller function is responsive to at least an integration of the phase of at least one of the plurality of input signals . in another implementation the controller function is responsive to at least one time - derivative of the phase of at least one of the plurality of input signals . in an example implementation the controller function is responsive to at least one extremal value of the amplitude of at least one of the plurality of input signals . in another implementation the controller function is responsive to at least an integration of the amplitude of at least one of the plurality of input signals . in another implementation the controller function is responsive to at least one time - derivative of the amplitude of at least one of the plurality of input signals . in an example implementation the controller function is responsive to at least one extremal value of a quantity responsive to the signal spectrum of at least one of the plurality of input signals . in another implementation the controller function is responsive to at least an integration of a quantity responsive to the signal spectrum of at least one of the plurality of input signals . in another implementation the controller function is responsive to at least one time - derivative of of a quantity responsive to the signal spectrum of at least one of the plurality of input signals . a wide range of possiblities are possible for implementations and embodiments of the controller function as testified by the discussion made thus far , and the examples provided above are in no way limiting . an argument can be made that hysteretic properties of materials depends on so many factors that any representation of hysteresis processes should be provided in terms of vector quantities ([ b ], p . 11 ). there are also spatial aspects of materials , mechanical systems , chemical systems , electrical systems , etc . that can merit consideration of additional input variables and / or additional output variables . the broader environment of other types of hysteretic processes ( for example those occurring in financial and economics models , chemical systems , biological systems , optical systems , etc .) also can merit consideration of additional input variables and / or additional output variables . multiple - input and / or multiple - output hysteresis processes can also be of value in new types of electronic music sound synthesis and electric guitar signal processing . there are a number of ways in which hysteresis can be imposed on multiple input variables or vector - valued quantities . these include but are not limited to : arrangements wherein the hysteresis is variable - separable ; arrangements wherein the hysteresis is hierarchical in the variables ; arrangements wherein the hysteresis is cross - coupled in the variables ; arrangements wherein the hysteresis comprises covariant nonlinearity . fig3 depicts a multi - variable hysteresis synthesis arrangement wherein the hysteresis is variable - separable . here a separate hysteresis synthesis element , such as the one depicted in fig2 , can be used for each of the input variables . in some situations and applications , the resulting output quantities can be further combined in some manner , for example subjected to a linear transformation , a non - linear vector - domain function , vector input dynamical system , etc . there are many possible ways to obtain multi - variable hysteresis synthesis arrangements wherein the hysteresis is hierarchical in some fashion . fig4 depicts a multi - variable hysteresis synthesis arrangement wherein the hysteresis is hierarchical in the variables . in this particular example , the output of the hysteresis synthesis 1 element is used to control , entirely or in part , the hysteresis control parameter ( s ) c 2 of hysteresis synthesis 2 element via the function f (*). in some embodiments , the function f (*) can be provided with additional external control parameter ( s ) d . if there are a plurality of such parameters structured as an external control input , d is a vector . if there is only a single such parameter structured as an external control input , d is a scalar . many other hysteresis synthesis arrangements wherein the hysteresis is hierarchical are possible and are provided for by the invention . there are many possible ways to obtain multi - variable hysteresis synthesis arrangements wherein the hysteresis is cross - coupled in some fashion . to begin it is noted that the scalar or vector parameter input c in the parameterized hysteresis synthesis arrangement depicted in fig2 can serve as one or more additional input variables . depending on what the scalar or vector parameter input c affects in the parameterized hysteresis synthesis , it could itself experience hysteretic effects and / or vary the hysteretic effects responsive to the input signal g ( x ). fig5 depicts another example multi - variable hysteresis synthesis arrangement wherein the hysteresis is cross - coupled in the variables . in this particular example , the output of the hysteresis synthesis 1 element is used to control , entirely or in part , the hysteresis control parameter ( s ) c 2 of hysteresis synthesis 2 element via the function f 2 (*). additionally , the output of the hysteresis synthesis 2 element is used to control , entirely or in part , the hysteresis control parameter ( s ) c 1 of hysteresis synthesis 1 element via the function f 1 (*). in some embodiments the function f 1 (*) can be provided with additional external control parameter ( s ) d 1 . if there are a plurality of such parameters structured as an external control input , d 1 is a vector . if there is only a single such parameter structured as an external control input , d is a scalar . in some embodiments , the function f 1 (*) can be provided with additional external control parameter ( s ) d 1 . if there are a plurality of such parameters structured as an external control input , d 1 is a vector . if there is only a single such parameter structured as an external control input , d 1 is a scalar . similarly , in some embodiments the function f 2 (*) can be provided with additional external control parameter ( s ) d 2 . if there are a plurality of such parameters structured as an external control input , d 2 is a vector . if there is only a single such parameter structured as an external control input , d is a scalar . in some embodiments , the function f 2 (*) can be provided with additional external control parameter ( s ) d 2 . if there are a plurality of such parameters structured as an external control input , d 2 is a vector . if there is only a single such parameter structured as an external control input , d 2 is a scalar . many other hysteresis synthesis arrangements wherein the hysteresis is hierarchical are possible and are provided for by the invention . more generally , multiple - input hysteresis processes comprises a multi - variable covariant nonlinearity . fig6 a and 6b depict two viewpoints of an exemplary two - input one - output multi - variable hollow - volume hysteresis surface comprised of joined but distinct hysteron surfaces each comprising covariant nonlinearity and inducing covariant hysteretic effects for each of the two input variables . here the single - variable traditional hysteresis curve ( such as that of fig1 a ) is replaced with a multiple - variable hysteresis surface . many other multi - variable covariant hysteron surfaces , volumes , and hysteresis synthesis arrangements are possible and are provided for by the invention . fig7 depicts a multiple - input multiple - output hysteresis synthesis arrangement wherein the hysteresis comprises multi - variable covariant nonlinearity . here there can be n - input variables and m - output variables . in some embodiments m = n , while in other embodiments m and n differ . traditionally hysteresis is an operation made on the amplitude history of an input signal . the invention provides for the synthesis of a hysteresis operation made on the phase history of an input signal . fig8 a depicts an example arrangement for phase hysteresis synthesis . in an example implementation , signal phase is modulated by a selectable all - pass filter . in another example implementation , signal phase is modulated by a parameterized all - pass filter responsive to at least one parameter value , and the selection or parameter value is in turn controlled by a controller function responsive to the outputs of selectors , signal time - derivative sign detectors , integrators , fractional dynamical processors , control systems , system measurement sensors , etc . in an example implementation the parameterized filter serves as a parameterized hysteron . in an example implementation the phase modulation if further responsive to spectral content of the at least one input signal . the phenomenon driving the phase hysteresis can include input signal phase , but also or alternatively can include input signal amplitude , input signal spectrum , etc . in an example implementation the controller function is responsive to at least one extremal value of the phase of at least one of the plurality of input signals . in another implementation the controller function is responsive to at least an integration of the phase of at least one of the plurality of input signals . in another implementation the controller function is responsive to at least one time - derivative of the phase of at least one of the plurality of input signals . in an example implementation the controller function is responsive to at least one extremal value of the amplitude of at least one of the plurality of input signals . in another implementation the controller function is responsive to at least an integration of the amplitude of at least one of the plurality of input signals . in another implementation the controller function is responsive to at least one time - derivative of the amplitude of at least one of the plurality of input signals . in an example implementation the controller function is responsive to at least one extremal value of a quantity responsive to the signal spectrum of at least one of the plurality of input signals . in another implementation the controller function is responsive to at least an integration of a quantity responsive to the signal spectrum of at least one of the plurality of input signals . in another implementation the controller function is responsive to at least one time - derivative of of a quantity responsive to the signal spectrum of at least one of the plurality of input signals . many other hysteresis synthesis arrangements for phase hysteresis synthesis are possible and are provided for by the invention . combine signal - phase and signal - amplitude hysteresis synthesis ( hysteretic filter , hysteretic pid controller ) fig8 b depicts an example arrangement for combined amplitude and phase hysteresis synthesis . in an example implementation , both signal phase and signal amplitude are modulated by a selectable or parameterized filter affecting both signal amplitude and phase , and the selection or parameter value is in turn controlled by a controller function responsive to the outputs of selectors , signal time - derivative sign detectors , integrators , fractional dynamical processors , control systems , system measurement sensors , etc . the result can be used as a hysteretic filter , hysteretic p . i . d ( proportional , time - integral , time - derivative ) controllers , higher order controllers , etc . in an example implementation the parameterized filter serves as a parameterized hysteron . in an example implementation the comprises a parameterized filter imposing at least amplitude modulation on at least one input signal , the amplitude modulation if further responsive to spectral content of the at least one input signal . in an example implementation the phase modulation if further responsive to spectral content of the at least one input signal . the phenomenon driving the amplitude and phase hysteresis can include input signal phase , but also or alternatively can include input signal amplitude , input signal spectrum , etc . in an example implementation the controller function is responsive to at least one extremal value of the amplitude of at least one of the plurality of input signals . in another implementation the controller function is responsive to at least an integration of the amplitude of at least one of the plurality of input signals . in another implementation the controller function is responsive to at least one time - derivative of the amplitude of at least one of the plurality of input signals . in an example implementation the controller function is responsive to at least one extremal value of the phase of at least one of the plurality of input signals . in another implementation the controller function is responsive to at least an integration of the phase of at least one of the plurality of input signals . in another implementation the controller function is responsive to at least one time - derivative of the phase of at least one of the plurality of input signals . in an example implementation the controller function is responsive to at least one extremal value of a quantity responsive to the signal spectrum of at least one of the plurality of input signals . in another implementation the controller function is responsive to at least an integration of a quantity responsive to the signal spectrum of at least one of the plurality of input signals . in another implementation the controller function is responsive to at least one time - derivative of of a quantity responsive to the signal spectrum of at least one of the plurality of input signals . many other hysteresis synthesis arrangements comprising combined amplitude and phase hysteresis synthesis are possible and are provided for by the invention . the invention provides for the synthesis of a hysteresis operation that is frequency dependent . fig8 c depicts an arrangement for hysteresis synthesis that is frequency dependent . in another implementation , a hysteresis synthesis element can internally comprise rate - dependent and / or frequency dependent elements or attributes which in tern invoke rate - dependent and / or frequency dependent hysteresis processes . many other rate - dependent and frequency - dependent hysteresis synthesis arrangements wherein the hysteresis is hierarchical are possible and are provided for by the invention . the invention provides for the synthesis of a hysteresis operation that comprises dynamics . fig9 depicts an arrangement for hysteresis synthesis that varies according to dynamics as defined by a dynamical system . many other hysteresis synthesis arrangements wherein the hysteresis is hierarchical are possible and are provided for by the invention . in one embodiment , the control input d is a function of , or in other ways responsive to , the input signal g ( t ). many other hysteresis synthesis arrangements wherein the hysteresis is hierarchical are possible and are provided for by the invention . the invention provides for the use of synthesized hysteresis as a linearizing pre - emphasis element in conjunction with a natural hysteretic element or process . fig1 a depicts an example arrangement wherein a hysteresis synthesis element is used to create a compensated input signal to apply to a hysteretic system or process . in an embodiment , the hysteresis synthesis element is designed so as to approximately compensate for the hysteresis effects of the hysteretic system or process so that the output response is adequately approximate to a linear function of the input . the invention provides for the use of synthesized hysteresis as a linearizing post - deemphasis element in conjunction with a natural hysteretic element or process . fig1 b depicts an example arrangement wherein a hysteresis synthesis element is used to create a compensated output signal from the output of a hysteretic system or process . in an embodiment , the hysteresis synthesis element is designed so as to approximately compensate for the hysteresis effects of the hysteretic system or process so that the output response is adequately approximate to a linear function of the input . the invention provides for the use of synthesized hysteresis in conjunction with or as an element within a control system . fig1 a through 11d depict various topological arrangements employing hysteresis synthesis in feedback control systems . fig1 a through 12e depict arrangements employing hysteresis synthesis in both pre - emphasis / post - deemphasis and feed - back control systems . the invention provides for hysteresis synthesis in a computer simulation or computer model . such a computer simulation or computer model can be used in physics , engineering , economics , etc . fig1 depicts arrangements employing hysteresis synthesis in a computer simulation . fig1 depicts arrangements employing hysteresis synthesis in a computer model . the aforementioned , as well as other variations , can be implemented as an algorithm on a digital computer , embedded processor , signal processor , or combination of two or more of these . the terms “ certain embodiments ”, “ an embodiment ”, “ embodiment ”, “ embodiments ”, “ the embodiment ”, “ the embodiments ”, “ one or more embodiments ”, “ some embodiments ”, and “ one embodiment ” mean one or more ( but not all ) embodiments unless expressly specified otherwise . the terms “ including ”, “ comprising ”, “ having ” and variations thereof mean “ including but not limited to ”, unless expressly specified otherwise . the enumerated listing of items does not imply that any or all of the items are mutually exclusive , unless expressly specified otherwise . the terms “ a ”, “ an ” and “ the ” mean “ one or more ”, unless expressly specified otherwise . while the invention has been described in detail with reference to disclosed embodiments , various modifications within the scope of the invention will be apparent to those of ordinary skill in this technological field . it is to be appreciated that features described with respect to one embodiment typically can be applied to other embodiments . the invention can be embodied in other specific forms without departing from the spirit or essential characteristics thereof . the present embodiments are therefore to be considered in all respects as illustrative and not restrictive , the scope of the invention being indicated by the appended claims rather than by the foregoing description , and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein . although exemplary embodiments have been provided in detail , various changes , substitutions and alternations could be made thereto without departing from spirit and scope of the disclosed subject matter as defined by the appended claims . variations described for the embodiments may be realized in any combination desirable for each particular application . thus particular limitations and embodiment enhancements described herein , which may have particular advantages to a particular application , need not be used for all applications . also , not all limitations need be implemented in methods , systems , and apparatuses including one or more concepts described with relation to the provided embodiments . therefore , the invention properly is to be construed with reference to the claims . 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