Generalized lag control

Abstract

A hysteresis compensation system and method are disclosed. For each of a plurality of different state conditions, hysteresis compensation is provided using a known response curve. In response to determining that a state transition has occurred (i.e., from one response curve to another), the system generates a transition response curve extending from an origin on a first response curve to an endpoint on a second response curve based, at least in part, on a known or determined difference between an input value at the origin and an input value at the endpoint. In some embodiments, this difference is determined experimentally, and in other cases, the difference is estimated based on measured feedback. Hysteresis compensation is then provided by identifying an input value on the transition response curve that corresponds to a target system output value (e.g., as defined by a reference curve) for the received indicated input value.

Description

Technical Field

[0001] The present invention relates to a method and a system for controlling an actuator. Background Art

[0002] For example, the methods and systems described herein may be adapted for use in controlling a hydraulic valve actuator. Summary of the Invention

[0003] The systems and methods described herein adjust control commands (e.g., current signals) to actuators that exhibit hysteresis and operate in a repeatable manner. This results in more reliable, predictable, and repeatable component control. In some embodiments, hysteresis compensation drives an electrohydraulic servo valve (EH valve). Hysteresis can be caused by physical phenomena such as (but not limited to): flow forces in the hydraulic portion of the valve, magnetic properties of a solenoid, and / or friction effects due to relative motion of components in the assembly.

[0004] In one embodiment, the present invention provides a system comprising a controller and at least one actuator. A system output is controlled by applying a control input to the actuator. However, the value of the system output can vary depending on the value of the control input and the state condition of the system (e.g., whether the received input sequence is ascending or descending). A plurality of response curves (each corresponding to a different state condition of the system) each define a desired system output for each of a plurality of different input values. In response to determining that a state transition has occurred (i.e., from one response curve to another), the system generates a transition response curve extending from an origin on a first response curve to an endpoint on a second response curve based, at least in part, on a known or determined difference between an input value at an origin and an input value at an endpoint. In some embodiments, this difference is determined experimentally, and in other instances, the difference is estimated based on measured feedback. Hysteresis compensation is provided by identifying an input value on an applicable response curve or transition response curve that corresponds to a target system output value defined for the received indicated input value.

[0005] In some embodiments, the state transition comprises receiving a decrementing input value after a sequence of incrementing input values, or receiving an incrementing input value after a sequence of decrementing input values.

[0006] In some embodiments, a transition response curve is modeled by applying a first input value as a control value to an actuator and measuring an actual system output response. Based on the known applied first input value relative to the input value at the origin of the transition response curve and the measured actual system output response relative to a target system output value defined by a reference curve for the applied first input value, the controller can estimate a difference between the input value at the origin and the input value at the endpoint of the transition response curve.

[0007] Other aspects of the invention will become apparent by consideration of the detailed description and accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] Figure 1 is a block diagram of a first example of a control system for hysteresis compensation.

[0009] Figure 2 is a block diagram of a second example of a control system for hysteresis compensation.

[0010] Figure 3A Graphs showing rising and falling response curves of the hysteresis gap.

[0011] Figure 3B The rising response curve is used as a reference curve, and the Figure 3A A graph of an example of hysteresis compensation for consistent response performance in a system of a rising response curve and a falling response curve.

[0012] Figure 3C is a diagram showing the control input sequence changing from a rising control input sequence to a falling control input sequence. Figure 3A A graph of an example of a transition response curve of a hysteresis gap transition.

[0013] Figure 3D is shown when the control input is fully across Figure 3C A graph showing an example of response performance when the control input sequence is changed from a falling control input sequence to a rising control input sequence again before the hysteresis gap in the example.

[0014] Figure 3E It shows that Figure 3C A graph of a detailed example of hysteresis gap transition in an example of simultaneous application of multiple sequential hysteresis input compensation.

[0015] Figure 3F is a graph illustrating a mechanism for determining various variables in the process of modeling a transition response curve.

[0016] Figure 3G is shown for use by Figure 3F The variables identified in the example are plotted on the transition response curve to represent points to create a graph of the mechanism that models the transition response curve.

[0017] Figure 4 is a flow chart of a method for modeling a transition response curve based on a known origin of the transition response curve and a known difference between an input at the origin of the transition response curve and an input at an end point of the transition response curve.

[0018] Figure 5is a flow chart of a method for modeling a transition response curve based on a measured output of an actuator as feedback.

[0019] Figure 6 is a flow chart of a method for applying hysteresis compensation to account for hysteresis gap transitions. DETAILED DESCRIPTION

[0020] Before explaining any embodiments of the present invention in detail, it should be understood that the present invention is not limited in its application to the details of construction and the arrangement of parts set forth in the following description or shown in the following drawings. The present invention is capable of other embodiments and of being practiced or carried out in various ways.

[0021] Figure 1 A control system for an actuator in a system exhibiting hysteresis is shown. Controller 101 includes an electronic processor 103 and a computer-readable non-transitory memory 105. Memory 105 stores data and instructions executed by electronic processor 103 to provide the functionality of controller 101 as described below. Controller 101 receives input from user controls 107 (e.g., in the form of a voltage or current indicating the relative position of a user-manipulable control) and provides an output to actuator 109 to control the operation of the actuator. However, because the system exhibits a degree of hysteresis, an output provided to the actuator while the input rises will result in different behavior than when the same output is provided to the actuator while the input falls. Therefore, controller 101 is configured to provide hysteresis compensation to help ensure that the actuator / system operates similarly for the same input by the user on controls 107, regardless of whether the input is rising or falling at any given moment.

[0022] Although Figure 1 The example of FIG100 shows a control input received from a user control 107, but in some embodiments, the control input can be received by the electronic processor 103 as an electronic command from another controller or component that indicates a desired end state of a component output (e.g., pressure, velocity, etc.). Additionally, in some embodiments, instead of adjusting an actuator in response to a command input received from an external source, the controller can be configured to adjust the actuator in response to a signal received from a sensor that indicates a measured condition as a feedback response. Figure 2One such example of a feedback based controller 201 is shown, which includes an electronic processor 203 and a computer readable non-transitory memory 205. Again, the memory 205 stores data and instructions that, when executed by the electronic processor, provide the functionality of the controller 201. The controller 201 provides an output to a hydraulic valve 207 that controls the operation of the valve 207 (e.g., the degree to which the valve 207 is opened or closed). A pressure sensor 209 monitors the hydraulic fluid pressure 209 and provides a feedback signal to the controller 201, which in turn is used by the controller to determine the appropriate "input" signal for controlling the hydraulic valve 207. However, as Figure 1 Same system, Figure 2 The system also exhibits a certain degree of hysteresis. Therefore, the controller 201 is configured to provide hysteresis compensation to help ensure that the hydraulic valves behave similarly for the same input determined by the feedback loop, regardless of whether the input is rising or falling at any given moment.

[0023] Many types of hysteresis are characterized by a nonlinear function bounded by two response curves, each indicating the system response to a particular input under various conditions. While the examples below describe hysteresis characterized by two response curves, these methods and systems can be adapted and applied to situations where the hysteresis is characterized by a family of nonlinear functions and / or is characterized by a multidimensional function where the output response of an actuator or system to a particular input is based not only on whether the input sequence is increasing or decreasing, but also on other variables (e.g., temperature).

[0024] Figure 3A An example of a pair of response curves in a system exhibiting hysteresis is shown. An ascending curve 301 defines the actuator performance (e.g., system "output") in response to a sequence of increasing command inputs. Conversely, a descending curve 303 defines the actuator performance (e.g., system "output") in response to a sequence of decreasing command inputs. For example, in the case of a variable position hydraulic valve actuator, the "output" may indicate the position of the valve (e.g., the relative degree of valve closure) in response to a given voltage or current input signal provided to the valve actuator.

[0025] The gap between the rising curve 301 and the falling curve 303 demonstrates the difference in system performance in response to a given input, depending on whether the actuator is responding to an increasing sequence of input commands or a decreasing sequence of input commands. This difference is referred to herein as the hysteresis gap. Despite having two different response curves, the output is generally piecewise continuous and a true "function" in that, for each unique input value, the output is single-valued, depending on the input's previous state(s). Due to the physical phenomena present in the system (which manifest as hysteresis), the rising curve 301 and the falling curve 303 are independent of each other.

[0026] Despite this hysteresis, control systems (e.g. Figure 1 or Figure 2 A system (e.g., a controller) can be configured to compensate for the indicated control input to achieve a consistent actuator response. For example, a "reference curve" can be defined that identifies the expected system output for each possible "indicated input" value (e.g., a command input indicated by a user control, a feedback calculation, or by a command signal from another controller / system). Using the reference curve, the system is able to compensate for hysteresis by adjusting the value of the indicated input to a particular reference curve based on the current operating state of the system to achieve the performance output indicated by the reference curve. Thus, the indicated input (e.g., from a user control or as an electronic command from another system) can be determined and provided to the controller as if there were no hysteresis effects in the system operation.

[0027] Figure 3B An example of hysteresis compensation using an increasing response curve 301 and a decreasing response curve 303 is shown. In this example, the increasing response curve 301 is defined as the "reference curve." As discussed above, due to the hysteresis gap between the increasing response curve 301 and the decreasing response curve 303, the same input provided to the actuator may result in different performance outputs (ΔO) depending on whether the current input sequence is increasing or decreasing. For example, the same indicated input may result in lower output performance (ΔO) when the input is part of an increasing sequence of inputs. Figure 3B Point A R ” indication), and can lead to higher output performance when the input is part of a decreasing sequence of inputs (indicated by Figure 3B Point A F ” indication). To provide the same actuator performance output for a given indicated input value, the controller is configured to adjust the indicated input value by a value equal to the hysteresis gap distance between the reference curve and the applicable response curve at the desired performance output.

[0028] exist Figure 3B In the specific example of FIG, because the rising response curve 301 is defined as a “reference curve”, when the controller receives a “point A” that corresponds to an input value that is part of an indication of an increasing sequence, R When the input level corresponds to the indicated input, the controller provides the same input value of the controller without compensation, and the output performance of the actuator matches the "point A" indicated on the rising response curve 301 (i.e., the reference curve). R However, when the controller receives an input value that is part of the indication of a decrementing sequence, R”, the controller determines a compensation input value on the descent response curve 303 (i.e., an input value corresponding to the same output value on the descent response curve as the output value of the indicated input value defined by the reference curve), and provides the compensation input value (defined by Figure 3B Point B in the figure) is used as the input of the actuator to achieve the same R ” corresponds to the same performance output.

[0029] In other words, when the applicable response curve for the state of the system does not match the reference curve, hysteresis compensation is achieved by (1) identifying a specific output value corresponding to an indicated input on the reference curve, and (2) offsetting the indicated input by a certain value that indicates the hysteresis gap between the applicable response curve and the reference curve at the identified output value.

[0030] and Figure 3A Shown are separate rising response curves 301 and falling response curves 303 of the system, with the system responding differently when the increasing / decreasing direction of the input sequence changes from increasing to decreasing (or vice versa). Figure 3C An example of a system response to a changing input direction is shown in Figure 1. In this example, the input value provided to the actuator begins at "Point C," followed by an increasing sequence of input values ​​until the input value at "Point D." The sequence of input values ​​then decreases back to the original input value at "Point C."

[0031] As the input value increases from "Point C" to "Point D," the system's output response follows the rising response curve 301. However, when the direction of the input changes from rising to falling, the system's performance transitions across the hysteresis gap defined by the transition response curve 305. At "Point E," the hysteresis gap has been completely traversed, and the transition response curve 305 ends at a point on the falling response curve 303. Therefore, as the input value decreases from the input value at "Point D" to the input value at "Point E," the system's output response follows the transition response curve 305, and as the input value continues to decrease from the input value at "Point E" to the input value at "Point C," the system's output response follows the falling response curve 303.

[0032] In some systems (and / or under certain conditions), when the decreasing sequence of input values ​​(following the falling response curve 303) changes to an increasing sequence of input values ​​before the system performance completely crosses the hysteresis gap, the system performance will follow the same transition response curve to cross the hysteresis gap. For example, in Figure 3D, the input provided to the actuator starts at an input value at "point C", followed by a sequence of increasing input values ​​until the input value at "point D". The input value then decreases sequentially from the input value at "point D" to the input value at "point F" before changing direction again and gradually increasing to the input value at "point G". Similar to Figure 3C , as the input value increases from "point C" to "point D," the output performance of the system follows the rising response curve 301, and then follows the transition response curve 305 as the input value decreases from "point D" to "point F." However, when the input direction changes again at "point F," the transition response curve 305 has not yet completely crossed the hysteresis gap. As the input value increases from "point F" back to "point D" (where the transition response curve 305 rejoins the rising response curve 301), the system performance again follows the transition response curve 305, and as the sequence of input values ​​continues to increase from the input at "point D" to the input at "point G," the system performance follows the rising response curve 301.

[0033] When the transition response curve 305 is known (or modeled), the indicated input can be adjusted to compensate for hysteresis, similar to the above reference. Figure 3B As indicated. Figure 3E A specific example is provided where the sequence of input values ​​indicated increments to an input value corresponding to "point D" followed by an input value corresponding to point X. A1 、X A2 、X A3 、X A4 and X A5 The first three indicated input values ​​after the change in direction indicated by the reference curve 301 (ie, X A1 、X A2 and X A3 ) corresponds to an output level on the transition response curve 305 (i.e., before the transition response curve 305 completely crosses the hysteresis gap and ends at the falling response curve 303). Therefore, in response to receiving each of these first three indicated input values, the controller determines the compensation input value by identifying the input value on the transition response curve 305 that corresponds to the same output value as the output value of the indicated input defined by the reference curve 301. The last two indicated input values ​​(i.e., X) indicated by the reference curve 301 A4 and X A5) corresponds to an output level on falling response curve 303 after transition response curve 305 has rejoined falling response curve 303. Thus, in response to receiving each of these last two indicated input values, the controller determines a compensation input value by identifying an input value on falling response curve 303 that corresponds to the same output value as the output value for the indicated input as defined by reference curve 301.

[0034] In some embodiments, the transition response curve 305 can be modeled based on the proportion of the hysteresis gap that the output of a given input crosses relative to the proportion of the hysteresis gap that the input crosses. An example of modeling the transition response curve 305 based on this relationship can be illustrated with reference to the following equation:

[0035]

[0036] Wherein, ΔI is the difference between the input value at the origin of the transition response curve 305 and the input value at the end point of the transition response curve; wherein ΔI p is the difference between a specific input value I and the input value at the origin of the transition response curve 305; wherein ΔO is the difference between the output for a specific input value I defined by the rising response curve 301 and the output for a specific input value I defined by the falling response curve 303; and wherein ΔO p It is the difference between the output for a specific input value I on the transition response curve and the output for the specific input value I defined by the rising response curve 301 .

[0037] Figure 3F and Figure 3G A specific example of modeling a transition response curve 305 based on the relationship defined by equation (1) above is provided, wherein both the input value at the origin of the transition response curve 305 (i.e., "point D") and ΔI (i.e., the difference between the input value at the origin of the transition response curve ("point D") and the input value at the end point of the transition response curve ("point E") are known. In this example, I0 is the input value at which the sequence of inputs changes from an increasing sequence to a decreasing sequence. Because I0 is known (from the actual received input), the output value corresponding to that input (i.e., "point D") can be determined based on the known rising response curve 301. Similarly, because ΔI for a given origin of the transition response curve 305 (i.e., "point D") is known, the input value I0 at the end point of the transition curve 305 is known. n can also be determined, and conversely, the output value corresponding to the determined input at the end point of the transition response curve (ie, “point E”) can also be determined based on the known falling response curve 303 .

[0038] Given this known and determinable information, we can n The transition response curve 305 is modeled using the relationship defined by equation (1) for one or more input points between . Figure 3F and Figure 3G This process is shown for two such input values ​​I1 and I2. Figure 3F As shown, the difference ΔI between the first modeled input value I1 and the original input I0 of the transition response curve 305 is calculated. p1 , and the width of the hysteresis gap ΔO1 of the first modeled input value I1 can be calculated as the difference between the outputs of the first modeled input I1 defined by the known falling response curve 303 and the known rising response curve 301. The estimated output on the transition response curve 305 of the first modeled input I1 can then be determined relative to the output on the rising response curve 301 by the following equation, as Figure 3G is shown as "Point 1":

[0039]

[0040] The same process can be used to determine the estimated output for the second modeled input I2 on the transition response curve using similar equations, such as Figure 3G is shown as "point 2":

[0041]

[0042] The rest of the transition response curve 305 can be calculated by comparing the starting input I0 and the ending input I n Alternatively or additionally, the transition response curve 305 may be modeled by determining a “best fit” curve based on the determined outputs of known and modeled points on the transition response curve 305 .

[0043] Figure 4 Shown according to Figure 3F and Figure 3G For a particular point of the input sequence with a change in direction (step 401) (i.e., the origin I0 of the transition response curve), a lookup table is used to identify the ΔI of the transition response curve 305 (step 403). Figure 4 A lookup table is used in the example of , but in other embodiments, alternative mechanisms for determining ΔI may be utilized, including, for example, calculating ΔI as a function of one or more system variables. For example, by nA defined number of evenly spaced input points are selected between the input points 301 and 303 to define a representative set of input points along the transition response curve 305 (step 405). For the first representative input point in the representative input value set (step 407), the controller calculates ΔI based on the known rising response curve 301 and the known falling response curve 303. p (Step 409) and determines the ΔO of the first representative input point (Step 411). Based on this known and determined information, the controller then calculates the ΔO of the first representative input point. p (Step 413). The next representative input point in the set of representative input values ​​is selected (Step 417), and the process for calculating ΔO is repeated for the second representative input value and for each other representative input value in the set of representative input values. p process.

[0044] When the output value on the transition response curve 305 has been calculated for each representative input value in the set of representative input values ​​(step 415), the estimated output for each representative input in the set of representative inputs (based on the calculated ΔO for each representative input) is calculated by defining p ) to draw an initial model of the transition response curve (step 419). The final transition response curve 305 is then modeled by using a "best fit" algorithm to determine the best fit curve corresponding to the modeled points of the transition response curve based on the representative input set (step 421).

[0045] In some embodiments, Figure 4 The method can be applied in real time to determine a transition response curve in response to detecting a change in direction of an input sequence. In other embodiments, Figure 4 The method can be applied during manufacturer testing and calibration to define / model multiple transition response curves for each of multiple possible transition response curve origins. These pre-modeled transition response curves are then stored in memory and accessed in response to detecting a change in direction of an input sequence.

[0046] Despite the above Figure 3F and Figure 3G The described example uses a known ΔI for a particular origin input I0 of the transition response curve 305, but other mechanisms for modeling the transition response curve 305 are possible based on the relationship of equation (1). For example, a feedback method can be implemented by the electronic controller to model the transition response curve in real time for hysteresis compensation. Figure 5 An example of such a feedback-based system is shown for modeling a transition response curve based on the relationship defined by equation (1).

[0047] Figure 5The example begins with the controller receiving an increasing sequence of input values ​​(step 501) and using the rising response curve 301 as a reference curve for hysteresis compensation. As the received values ​​continue to increase (step 503), the controller applies the input to the actuator without compensation (step 505). In response to receiving a first input value indicating a change in direction in the sequence of input values ​​(i.e., an input value that is lower than the previously received input value), the controller again applies the input without compensation (step 507) and then measures the output generated by the actuator in response to the applied decreasing input value (step 509). Based on the measured output value, the controller then calculates ΔO for the applied input value based on the difference between the measured output and the output for the applied input value indicated by the rising response curve 301. p (Step 511). The controller can also determine ΔO for the applied input value based on the difference between the output defined by the known falling response curve for the applied input value and the output defined by the known rising response curve for the applied input value. Based on these known and determined values, the controller then calculates an estimate of ΔI (i.e., the difference between the input value at the origin of the transition response curve and the input value at the end of the transition response curve) using the following equation (Step 513):

[0048]

[0049] Using the estimated value of ΔI, the controller then proceeds to model the estimated transition response curve, for example using Figure 4 When the next input value is received that is still within the range corresponding to the transition response curve (step 517), the controller determines and applies appropriate hysteresis compensation to the received input based on the modeled transition response curve (step 519).

[0050] In some embodiments, the controller is configured to further refine and adjust the estimated transition response curve as additional compensation inputs are applied to the actuator. When each subsequent input on the same transition response curve is applied to the actuator, the controller measures the corresponding output (step 509) and calculates the ΔO for the subsequently applied input value. p (Step 511). In some such embodiments, ΔI is recalculated for each subsequently applied input value (Step 513), and the ΔI used to adjust / model the transition response curve is updated to the average of the ΔI values ​​determined for each applied input. Additionally or alternatively, the transition response curve is remodeled (at Step 515) using, for example, a "best fit" curve based on the data points for all applied input values ​​on the transition curve and their corresponding measured outputs.

[0051] To summarize the examples presented above, Figure 6 An example of a method for controlling an actuator exhibiting hysteresis using a hysteresis compensation mechanism as described above is shown. In response to receiving an indicated input value (step 601), a controller determines whether the compensation mechanism has operated according to a defined transition curve (step 603). If so, the controller determines the output corresponding to the indicated input value on a reference curve (step 605) and determines a compensation input value corresponding to the same output on the transition response curve (step 607). The compensated input value is then applied as input to the actuator (step 609).

[0052] If the hysteresis compensation is not already operating according to the defined transition curve when the new indicated input value is received (step 603), the controller determines whether the newly received indicated input value indicates a change in the increasing / decreasing direction of the sequence of inputs (step 611). If a change in direction is detected, a new transition response curve is determined or modeled (e.g., as described above with reference to Figure 4 and Figure 5 The controller 100 further comprises a controller 100 for executing the control step 100 of FIG100 . ...

[0053] If hysteresis compensation has not yet been run according to the defined transition curve (step 603) and no change in the increasing / decreasing direction of the sequence of inputs is detected (step 611), the controller determines whether the newly received input value indicates a continuation of an increasing sequence of inputs or a continuation of a decreasing sequence of inputs (step 615). If the new indicated input value is part of a decreasing sequence of inputs, the controller determines the output corresponding to the indicated input value on the reference curve (step 617) and then identifies the input value corresponding to the same output value on the descending response curve (step 619). This identified input value from the descending response curve is then applied to the actuator as a compensation input (step 609). However, if the newly received indicated input value is part of an increasing sequence of inputs and the controller is configured to use the ascending response curve as a reference curve or hysteresis control compensation, the indicated input value is provided as input to the actuator without any compensation or adjustment (step 621).

[0054] While the above examples primarily focus on the case where the transition response curve 305 is derived from the rising response curve 301 in response to a decreasing input value received after a sequence of increasing input values, the same methods and systems described above, however, can be adapted and applied to estimate (and then used for hysteresis compensation) the transition response curve 305 derived from the falling response curve 303 in response to an increasing input value received after a sequence of decreasing input values.

[0055] Similarly, while the above examples discuss hysteresis compensation in the context of an ascending response curve 301 being used as a reference curve for hysteresis compensation, in some embodiments, the above methods and systems can be adapted to utilize a descending response curve as a reference curve for hysteresis compensation. In other embodiments, the reference curve used for hysteresis compensation is neither an ascending response curve nor a descending response curve. In such embodiments, hysteresis compensation is applied to both an ascending sequence of input values ​​and a descending sequence of input values ​​to generate an output value for each received input that corresponds to a defined reference curve. In some such embodiments, the reference curve can be defined as a linear curve (e.g., a straight line) or can be defined as an average of an ascending response curve and a descending response curve.

[0056] Finally, in the above examples, the output generated for a given input on a transition response curve generally follows the transition response curve, regardless of whether subsequently received values ​​follow the same increasing / decreasing direction along the transition response curve as previously received values. However, this is not always the case. For example, in some systems, a reverse path along the same transition response curve is only applicable under constant temperature conditions. Therefore, in some embodiments, in response to a change in the increasing / decreasing direction of an input value received while crossing a hysteresis gap on the transition response curve, the controller can be configured to model a new transition response curve that extends from the previous transition response curve back to the rising response curve or the falling response curve.

[0057] Thus, the present invention provides, among other things, a system for controlling one or more actuators in a system by compensating for command input to account for hysteresis and by enhancing a compensating mechanism to account for changes in input command direction as the input command crosses a hysteresis gap. Various features and advantages of the present invention are illustrated in the accompanying drawings.

Claims

1. A system comprising: at least one actuator; as well as A controller configured to: defining a plurality of response curves, each response curve indicating a system output value expected to be generated for the system in response to providing each of a plurality of input values ​​to the at least one actuator under a different state condition among a plurality of state conditions, defining a reference curve indicating a target system output value corresponding to each of the plurality of input values ​​regardless of the state condition, Receive the indicated input value, identifying a target system output value on the reference curve corresponding to the indicated input value, When the indicated input value is received, determining whether a state transition has occurred, In response to determining that no state transition has occurred, a compensation input value is determined by: identifying an input value on a first response curve corresponding to a system output value equal to the identified target system output value, wherein the first response curve is a response curve among the plurality of response curves corresponding to the current state condition, and defining the compensation input value based on a difference between the indicated input value and the identified input value on the first response curve, In response to determining that a state transition has occurred, generating a transition response curve, The transition response curve extends from an origin on the first response curve to an end point on the second response curve. wherein the first response curve corresponds to a state condition before the detected state transition, and the second response curve corresponds to a state condition after the detected state transition, and wherein the controller is configured to generate a transition response curve based on a transition response curve length, wherein the transition response curve length indicates a difference between an input value at an origin of the transition response curve and an input value at an end point of the transition response curve, In response to determining that the state transition has occurred, determining the compensation input value by: identifying an input value on the transition response curve corresponding to a system output value equal to the identified target system output value, and defining the compensation input value based on a difference between the indicated input value and an identified input value on the transition response curve, and controlling the operation of the at least one actuator by transmitting the determined compensation input value as a control input to the at least one actuator, The controller is configured to generate the transition response curve by generating a transition response curve defined by the following equation: For each of the plurality of input values ​​between the input value at the origin of the transition response curve and the input value at the end point of the transition response curve, indicating a difference between an output value on the transition response curve and an output value on the first response curve for an input value on the transition response curve, indicating a difference between an output value on the second response curve and an output value on the first response curve for an input value on the transition response curve, indicating a difference between an input value on the transition response curve and an input value at the origin of the transition response curve, and Indicates the difference between the input value at the origin of the transition response curve and the input value at the end point of the transition response curve.

2. The system according to claim 1, wherein: The controller is configured to generate the transition response curve by: accessing a lookup table that defines, for each of a plurality of input values, a value corresponding to a length of the transition response curve, and The transition response curve is modeled for a previously indicated input value received prior to the state transition based on the transition response curve length accessed from a lookup table.

3. The system according to claim 1, wherein: The controller is configured to generate the transition response curve by: applying a first input value as an input to the at least one actuator, measuring an actual system output value generated in response to applying the first input value as an input to the at least one actuator, Calculating the difference between the measured actual system output value and the output value on the first response curve for the applied first input value , Calculating the difference between the output value on the second response curve for the applied first input value and the output value on the first response curve for the applied first input value , Calculate the difference between the first input value applied and the input value at the origin of the transition response curve , Based on the calculated difference between the applied first input value and the measured actual system output value , the calculated difference and the calculated difference to estimate the transition response curve length, and The transition response curve is modeled based on the estimated transition response curve length.

4. The system according to claim 1, wherein: the first response curve is a rising response curve, and the state condition corresponding to the rising response curve is the system receiving an increasing sequence of indicated input values, wherein the second response curve is a decreasing response curve, and the state condition corresponding to the decreasing response curve is that the system receives a decreasing sequence of indicated input values, and Wherein, the controller is configured to determine whether the state transition has occurred when the indicated input value is received by determining that when receiving a sequence of indicated inputs each having a continuously increasing value, the indicated input value is less than the previously indicated input value in the sequence of indicated input values.

5. The system according to claim 1, wherein the first response curve is a decreasing response curve, and the state condition corresponding to the decreasing response curve is the system receiving a decreasing sequence of indicated input values, wherein the second response curve is an ascending response curve, and the state condition corresponding to the ascending response curve is that the system receives an increasing sequence of indicated input values, and Wherein, the controller is configured to determine whether the state transition has occurred when the indicated input value is received by determining that when receiving a sequence of indicated inputs each having a successively decreasing value, the indicated input value is greater than a previously indicated input value in the sequence of indicated input values.

6. The system according to claim 1, wherein: The controller is further configured to: determining whether a previously generated transition response curve was used to determine said compensated input value for a most recent previously indicated input value, and In response to determining that the previously generated transition response curve is used to determine the compensation input value for the most recent previous indicated input value, the compensation input value is determined by: determining the compensation input value using the transition response curve when the indicated input value is within a range of input values ​​between an origin and an end point of the transition response curve, and The second response curve is used to determine the compensation input value when the indicated input value exceeds an end point of the transition response curve.

7. The system according to claim 6, wherein: The controller is configured, in response to determining that the previously generated transition response curve was used to determine the compensation input value for the most recent previously indicated input value, to further determine the compensation input value by: determining the compensation input value using the transition response curve when the indicated input value is within the input value range between an origin and an end point of the transition response curve, regardless of whether the state transition is detected when using the transition response curve, and The compensating input value is determined using the first response curve when the indicated input value exceeds the origin of the transition response curve.

8. The system according to claim 1, wherein: The controller is configured to define the reference curve by defining the first response curve or the second response curve as the reference curve.

9. A method for hysteresis compensation of a system, the system comprising at least one actuator configured to receive a control input, the method comprising: defining a plurality of response curves, each response curve indicating a system output value expected to be generated for the system in response to providing each of a plurality of input values ​​to the at least one actuator under a different state condition among a plurality of state conditions, defining a reference curve indicating a target system output value corresponding to each of the plurality of input values ​​regardless of the state condition, Receive the indicated input value, identifying a target system output value on the reference curve corresponding to the indicated input value, When the indicated input value is received, determining whether a state transition has occurred, In response to determining that no state transition has occurred, a compensation input value is determined by: identifying an input value on a first response curve corresponding to a system output value equal to the identified target system output value, wherein the first response curve is a response curve among the plurality of response curves corresponding to the current state condition, and defining the compensation input value based on a difference between the indicated input value and the identified input value on the first response curve, In response to determining that a state transition has occurred, generating a transition response curve, The transition response curve extends from an origin on the first response curve to an end point on the second response curve. wherein the first response curve corresponds to a state condition before the detected state transition, and the second response curve corresponds to a state condition after the detected state transition, and wherein the transition response curve is generated based on a transition response curve length, the transition response curve length indicating a difference between an input value at an origin of the transition response curve and an input value at an end point of the transition response curve, In response to determining that the state transition has occurred, determining the compensation input value by: identifying an input value on the transition response curve corresponding to a system output value equal to the identified target system output value, and defining the compensation input value based on a difference between the indicated input value and an identified input value on the transition response curve, controlling the operation of the at least one actuator by transmitting the determined compensation input value as a control input to the at least one actuator, Wherein, generating the transition response curve includes generating the transition response curve based on a relationship defined by the following formula: For each of the plurality of input values ​​between the input value at the origin of the transition response curve and the input value at the end point of the transition response curve, indicating a difference between an output value on the transition response curve and an output value on the first response curve for an input value on the transition response curve, indicating a difference between an output value on the second response curve and an output value on the first response curve for an input value on the transition response curve, indicating a difference between an input value on the transition response curve and an input value at the origin of the transition response curve, and Indicates the difference between the input value at the origin of the transition response curve and the input value at the end point of the transition response curve.

10. The method according to claim 9, wherein: Generating the transition response curve includes: accessing a lookup table that defines, for each of a plurality of input values, a value corresponding to a length of the transition response curve, and The transition response curve is modeled for a previously indicated input value received prior to the state transition based on the transition response curve length accessed from a lookup table.

11. The method according to claim 9, wherein Generating the transition response curve further includes applying a first input value as an input to the at least one actuator, measuring an actual system output value generated in response to applying the first input value as an input to the at least one actuator, Calculating the difference between the measured actual system output value and the output value on the first response curve for the applied first input value , Calculating the difference between the output value on the second response curve for the applied first input value and the output value on the first response curve for the applied first input value , Calculate the difference between the first input value applied and the input value at the origin of the transition response curve , Based on the calculated difference between the applied first input value and the measured actual system output value , the calculated difference and the calculated difference to estimate the transition response curve length, and The transition response curve is modeled based on the estimated transition response curve length.

12. The method according to claim 9, wherein the first response curve is a rising response curve, and the state condition corresponding to the rising response curve is the system receiving an increasing sequence of indicated input values, wherein the second response curve is a decreasing response curve, and the state condition corresponding to the decreasing response curve is that the system receives a decreasing sequence of indicated input values, and Wherein, determining whether the state transition has occurred when the indicated input value is received comprises determining that when receiving a sequence of indicated inputs each having successively increasing values, the indicated input value is less than a previously indicated input value in the sequence of indicated input values.

13. The method according to claim 9, wherein: the first response curve is a decreasing response curve, and the state condition corresponding to the decreasing response curve is an input value at which the system receives an indication of a decreasing sequence, wherein the second response curve is an ascending response curve, and the state condition corresponding to the ascending response curve is that the system receives an increasing sequence of indicated input values, and Wherein, determining whether the state transition has occurred when the indicated input value is received includes: determining that when receiving a sequence of indicated inputs each having a successively decreasing value, the indicated input value is greater than a previously indicated input value in the sequence of indicated input values.

14. The method according to claim 9, wherein determining whether a previously generated transition response curve was used to determine said compensated input value for a most recent previously indicated input value, and In response to determining that the previously generated transition response curve is used to determine the compensation input value for the most recent previous indicated input value, the compensation input value is determined by: determining the compensation input value using the transition response curve when the indicated input value is within a range of input values ​​between an origin and an end point of the transition response curve, and The second response curve is used to determine the compensation input value when the indicated input value exceeds an end point of the transition response curve.

15. The method according to claim 14, wherein In response to determining that the previously generated transition response curve is used to determine the compensation input value for the most recent previously indicated input value, determining the compensation input value further comprises: determining the compensation input value using the transition response curve when the indicated input value is within the input value range between an origin and an end point of the transition response curve, regardless of whether the state transition is detected when using the transition response curve, and The compensating input value is determined using the first response curve when the indicated input value exceeds the origin of the transition response curve.

16. The method according to claim 9, wherein The defining the reference curve includes defining the first response curve or the second response curve as the reference curve.

17. A hysteresis compensation system comprising a controller, the controller being configured to: defining an ascending response curve indicating an expected system output value for each of a plurality of different input values ​​as part of an increasing sequence of input values ​​when applied as input to at least one actuator of the system; defining a descending response curve indicating an expected system output value for each of a plurality of different input values ​​as part of a decreasingly increasing sequence of input values ​​when applied as input to at least one actuator of the system; Receives new indicated input values, In response to determining that the new indicated input value is a decreasing input value received after a series of increasing input values ​​received, modeling a transition response curve, wherein the transition response curve extends from an origin of the ascending response curve to an endpoint of the descending response curve, wherein the origin corresponds to a last indicated input value in the sequence of received increasing input values, wherein modeling the transition response curve comprises: applying a first input value as a control input to at least one actuator of the system, wherein the first input value is less than a most recently previously indicated input value applied to the at least one actuator, measuring an actual system output value produced by the system in response to applying the first input value as input to at least one actuator, Calculate the difference between the measured actual system output value and the output value on the rising response curve for the applied first input value , Calculate the difference between the output value on the falling response curve for the applied first input value and the output value on the rising response curve for the applied first input value , Calculates the difference between the first input value applied and the input value at the origin of the transition response curve , For the applied first input value and the measured actual system output value, based on the proportional relationship defined below, the calculated difference , calculated difference The difference between the calculated , estimates the difference between the input value at the end point and the input value at the origin , By defining additional points on the transition response curve as input values ​​between the origin and the end points, the estimated difference , Determination of additional points , Determination of additional points and defined proportional relationships to model the transition response curve; receiving a subsequent new indicated input value, and determining a compensation input value based on the subsequent new indicated input value using the modeled transition response curve when the subsequent new indicated input value is between the input value at the origin and the input value at the endpoint of the transition response curve; and The operation of one or more actuators of the system is controlled by inputting the determined compensated input value as a command to the one or more actuators.

18. The hysteresis compensation system according to claim 17, wherein: The controller is configured to determine a compensation input value based on a subsequent new indicated input value using the simulated transition response curve by: Identify the system output value corresponding to the subsequent new indicated input value on the rising response curve, identifying a system output value on the transition response curve that matches the system output value identified on the ramp response curve, and The compensation input value is defined as the input value corresponding to the system output value identified on the transition response curve.

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