Motor control device

Abstract

To provide a motor control device in which the accuracy of restraining torque ripples can be maintained in a wide rotational speed region while interference between FF and FB is avoided.SOLUTION: A processor determines a harmonic control command value (φ*dqh) from a torque command value 10 (τ*) (harmonic control command output unit 8). The processor determines a response characteristic compensation value (Δφ*dqh) from the harmonic control command value and an electric angular velocity (ωe) (response characteristic compensation unit 92). The processor determines a feed-forward voltage command value from the harmonic control command value and the electric angular velocity (feed-forward voltage computation unit 91). The processor determines a voltage command value (v*dq) on the basis of a control command value (φ*dq) corresponding to the torque command value 10 and the harmonic control command value (voltage command computation unit 3). The processor performs switching between first control to superimpose the feed-forward voltage command value (v*dqh) on the voltage command value and second control to compensate for the harmonic control command value with the response characteristic compensation value in accordance with a switching condition (switching unit 93).SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to a motor control device. [Background technology]

[0002] Motors are becoming more powerful in order to be used in applications where loading space is limited, such as in automobiles. This has led to motors being used more in the region where magnetic saturation occurs. In the magnetic saturation region, torque ripple increases, inducing vibration and noise, so torque ripple suppression control is particularly required.

[0003] In torque ripple suppression control, current harmonics that generate torque in the opposite phase to the generated torque ripple are passed. To achieve this, the required output voltage of the inverter is calculated from the harmonic current command value by feedforward (FF). At this time, an inverse model of the motor is required to calculate the required voltage command from the harmonic current command value, and the realization accuracy of the harmonic current is determined by the accuracy of the inverse model of the motor. For example, the inverse model used in Patent Document 1 considers the effects of the motor's inductance, resistance, and induced voltage, and calculates the voltage command value from the harmonic current command value.

[0004] When using an inverse model to achieve harmonic currents, some of the parameters used in the motor inverse model may be omitted because it takes time to adjust the parameters of the inverse model. Even in this case, there is almost no error as long as the harmonic frequency is above a certain level. Therefore, the required current harmonics are achieved by FF in the high-speed range, and by current FB (feedback) in the low-speed range by superimposing the harmonic current command value on the current command value. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] Patent No. 5574790 Summary of the Invention [Problem to be solved by the invention]

[0006] When the FB control band is lower than the threshold frequency where the error in the feedforward voltage calculated from the parameter-free inverse motor model becomes sufficiently small, there will be a region where neither FF nor FB can provide sufficient accuracy. To prevent this, the FB control band can be transparently expanded up to the threshold frequency by superimposing a harmonic command value whose phase and amplitude are corrected to correspond to the response characteristics of the FB control. However, if you try to suppress torque ripple by superimposing these FF and FB at the same time, the two will interfere with each other and it will not be possible to suppress the torque ripple.

[0007] An object of the present invention is to provide a motor control device that can maintain torque ripple suppression accuracy over a wide range of rotation speeds while avoiding interference between feedforward and feedback. [Means for solving the problem]

[0008] In order to achieve the above-mentioned object, the present invention provides a motor control device that drives a motor using an inverter, and includes a processor that determines a harmonic control command value from a torque command value, determines a response characteristic compensation value from the harmonic control command value and an electrical angular velocity, determines a feedforward voltage command value from the harmonic control command value and the electrical angular velocity, determines a voltage command value based on a control command value corresponding to the torque command value and the harmonic control command value, and switches between a first control that superimposes the feedforward voltage command value on the voltage command value and a second control that compensates for the harmonic control command value with the response characteristic compensation value according to a switching condition. Effect of the Invention

[0009] According to the present invention, it is possible to maintain the accuracy of torque ripple suppression over a wide range of rotation speeds while avoiding interference between feedforward and feedback. Problems, configurations, and effects other than those described above will become apparent from the following description of the embodiments. [Brief description of the drawings]

[0010] [Figure 1] 1 is a schematic block diagram of a motor control device according to a first embodiment of the present invention. [Diagram 2] 1 is a schematic block diagram of a switching unit according to a first embodiment of the present invention. [Diagram 3] FIG. 11 is a schematic block diagram of a motor control device according to a second embodiment of the present invention. [Figure 4] FIG. 11 is a schematic block diagram of a switching unit according to a second embodiment of the present invention. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0011] Example 1 1 is a functional block diagram showing the configuration of a motor control device according to a first embodiment of the present invention. The motor control device suppresses torque ripples generated from a motor during motor control.

[0012] In the following description, the term "dq-axis" refers to the "d-axis and q-axis." In addition, for the subscripted parameters X (such as "i" and "v") described below, unless otherwise specified, "Xdq" refers to "vector quantity (Xd, Xq)" and "Xuvw" refers to "vector quantity (Xu, Xv, Xw)." Here, "uvw" refers to the three phases of AC, that is, "U phase, V phase, and W phase."

[0013] The motor control device 1 controls the speed and torque of the motor 5 by controlling the switching of an inverter 4 that supplies AC power to the motor 5.

[0014] In this embodiment, the motor control device 1 is configured with an arithmetic processing device such as a microcomputer, a gate driver, etc. The arithmetic processing device includes a processor, a memory, an input / output circuit, etc., and functions as each unit by executing a predetermined program.

[0015] In this embodiment, the inverter 4 is a three-phase inverter having a three-phase full-bridge circuit, which is configured from semiconductor switching elements such as IGBTs and MOSFETs, as its main circuit.

[0016] In this embodiment, the motor 5 is a three-phase AC synchronous motor, which is a rotating machine, such as a permanent magnet synchronous motor.

[0017] The motor 5 is not limited to a synchronous machine, and may be an induction machine. The motor 5 is not limited to a rotating machine, and may be a linear motor. The motor 5 may have a power generation function.

[0018] As shown in FIG. 1, the motor control device 1 includes a torque command value 10 (τ*), a control command output unit 2, a voltage command calculation unit 3, an electrical angle detection unit 6, an electrical angular velocity calculation unit 7, a harmonic control command output unit 8, a judgment unit 9, a voltage command value dq / three-phase axis converter 11, a measurement current three-phase / dq axis converter 12, and a current flux converter 13.

[0019] The torque command value 10 is given from a higher-level controller or operation system.

[0020] The control command output unit 2 outputs the dq-axis magnetic flux command value (φ* dq ) is output. Generally, it is determined as a magnetic flux value equivalent to a current value that maximizes the torque output per current (MTPA), but the present invention is effective for any magnetic flux command value that realizes a torque command. Also, the magnetic flux command value may be calculated from the torque command, or may be found by referring to a previously set table.

[0021] The voltage command calculation unit 3 calculates the dq-axis magnetic flux detection value φ dq and the dq-axis magnetic flux command value φ** after harmonic superposition dq Depending on the difference with dq is φ* dq The voltage command value v* is set to match dq Calculate.

[0022] The electrical angle detection unit 6 detects an electrical angle θ based on a rotation position signal from a rotation sensor (not shown) provided in the motor 5. e The rotation sensor calculates and outputs the mechanical angle (θm ), the electrical angle detector 6 detects the number of pole pairs (p) of the motor 5 and θ e and θ m and p(θ e =p θ m ) and use θ e Calculate.

[0023] The rotation sensor may be a mechanical angle resolver, a hall sensor, a rotary encoder, etc. Alternatively, a configuration may be used in which the electrical angle is estimated from the current or voltage using a general position sensorless control method.

[0024] The electrical angle velocity calculation unit 7 calculates the electrical angle velocity ω based on a rotation position signal from a rotation sensor (not shown) provided in the motor 5, similarly to the electrical angle detection unit 6 (electrical angle calculation unit). e The electrical angular velocity calculation unit 7 calculates and outputs the number of pole pairs (p) of the motor 5 and the electrical angle θ e and mechanical angle θ m and p(θ e =p θ m ) and θ e and ω e The relationship (ω e = dθ e / dt) and ω e The electrical angle velocity calculation unit 7 calculates θ e Differentiate and get ω e It may also be comprised of a differentiator that calculates:

[0025] The harmonic control command output unit 8 outputs a harmonic control command value φ* in response to τ*. dqh Output is φ* dqh may be calculated from the torque command, or may be obtained by referring to a preset table.

[0026] The determination unit 9 includes a feedforward voltage calculation unit 91 , a response characteristic compensation unit 92 , and a switching unit 93 .

[0027] The feedforward voltage calculation unit 91 calculates φ* dqh and electrical angular velocity ω eThe FF voltage v*dqh is calculated and output based on equation (1). Note that s in equation (1) is the Laplace operator.

[0028]

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[0029] Here, we will explain how to derive equation (1). The inverse model of a general motor on the dq axes is given by equation (2).

[0030]

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[0031] However, in equation (2), Ldq and Lqd represent the interference inductance between the d and q axes, while Kedh and Keqh represent the d-axis and q-axis harmonic components of the magnetic flux of the magnet. A variable with a t at the end of the L subscript, which represents inductance, represents dynamic inductance, while a variable without a t represents static inductance. Static inductance is a value determined by the ratio of the dq-axis current to the dq-axis magnetic flux, while dynamic inductance refers to the rate of change in magnetic flux near the reference current. Here, the relationship between the magnetic flux defined in equation (3) and the dynamic inductance shown in equation (4) is used.

[0032]

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[0033]

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[0034] By transforming equation (2) using equations (3) and (4) and extracting only the harmonic components, we obtain equation (5).

[0035]

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[0036] Here, the second and third terms on the right-hand side of equation (5) grow in proportion to the frequency of the harmonic control command value, so above a certain threshold frequency the effect of the first term on the right-hand side becomes small enough that it can be ignored, yielding equation (1). Conversely, in the low-speed region, the effect of the first term on the right-hand side is large, making it impossible to calculate the correct FF voltage, so FB control must be effective up to the threshold frequency.

[0037] The response characteristic compensation unit 92 includes a response characteristic compensation table or a response characteristic compensation function, and calculates the electrical angular velocity ω e The harmonic control command value φ* is calculated by the amount of correction of the phase θmod and amplitude Imod calculated from the table or function based on the order of the harmonic. dqh The harmonic control command difference Δφ* when the equation (6) is corrected dqh where n is the order of the harmonic, such as 6 or 12, which is the order of the target for torque ripple suppression, and φ* dqnh indicates the n-th harmonic control command value component.

[0038]

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[0039] As mentioned above, since the threshold frequency is determined by the motor constant, if the FB band is equal to or lower than this frequency, the torque ripple suppression control will not operate sufficiently in the region from the upper limit frequency of the FB band to the threshold frequency. Here, the response characteristic compensation unit 92 corresponds to an inverse function of the transfer characteristic of the FB control, and by applying response characteristic compensation to the harmonic control command value, the FB control band can be expanded only for harmonics.

[0040] The switching unit 93 is composed of a voltage command value calculation 931, a harmonic component calculation 932, and a difference comparison 933 as shown in FIG. dq and φ* dq and φ* dqh and Δφ* dqh Based on v*dqh, Δφ* dqh At least one of the outputs v*dqh is set to 0.

[0041] The operation and function of the switching unit 93 will be described below.

[0042] First, the operation when the speed increases from low to high is shown. At low speed, v*dqh is set to 0 by the difference comparison 933. The voltage command value calculation 931 calculates Δφ* dqh The same calculation as that of the voltage command calculation unit 3 is performed on the result of adding the above. The harmonic component calculation 932 extracts and outputs the harmonic component of the nth electrical angle from the output components of 931. The difference comparison 933 compares Δφ* with the output value of 932 when the frequency of the harmonic increases and the output value of the feedforward calculation unit matches within a certain error. dqh The output of the feedforward calculation part is set to 0, and the value of the feedforward calculation part is output as v*dqh.

[0043] Next, we will show the operation when the speed decreases from high speed to low speed. At high speed, Δφ* dqh is set to 0 by the difference comparison 933. The harmonic component calculation 932 extracts and outputs the harmonic component of the nth electrical angle from 930. The difference comparison 933 calculates Δφ* when the frequency of the harmonic falls and the output value of 932 becomes equal to or greater than a certain value. dqh and output 0 as v*dqh.

[0044] When the switching unit 93 is not present, Δφ* dqh and v*dqh are superimposed at the same time. At this time, Δφ* dqh The transfer characteristics of the FB control used to calculate v*dqh change from the designed value due to the superposition of v*dqh, causing the two controls to interfere with each other and preventing the torque ripple suppression control from operating properly.

[0045] The voltage command value dq / three-phase axis converter 11 converts the voltage command value v* output from the voltage command calculation unit 3 into dq θ e The inverter 4 is then switched on and off by converting the input voltage to a three-phase voltage in accordance with the input voltage. e Instead of θ, the delay until the voltage command value is actually reflected in the inverter is compensated. ec may also be used.

[0046] The measurement current three-phase / dq axis converter 12 converts the three-phase current detected by the current sensor into θ e Depending on the dq axis current i dq In this case, θ e Instead of θ, which takes into account the current detection delay ed may also be used.

[0047] The main features of the first embodiment can be summarized as follows.

[0048] The motor control device 1 drives a motor 5 by an inverter 4. The processor of the motor control device 1 derives a harmonic control command value (φ*) from a torque command value 10 (τ*). dqh ) (harmonic control command output unit 8). The processor determines the harmonic control command value (φ* dqh ) and electrical angular velocity (ω e ) to the response characteristic compensation value (Δφ* dqh ) (response characteristic compensation unit 92). The processor determines the harmonic control command value (φ* dqh ) and electrical angular velocity (ω e The processor determines a feedforward voltage command value (v*dqh) from the torque command value 10 (τ*) (feedforward voltage calculation unit 91). dq ) and harmonic control command value (φ* dqh ) and the voltage command value (v* dq ) is determined (voltage command calculation unit 3). The processor determines the voltage command value (v* dq ) and the first control superimposes the feedforward voltage command value (v*dqh) on the response characteristic compensation value (Δφ* dqh ) for the harmonic control command value (φ* dqh ) is compensated for (switching unit 93).

[0049] By switching exclusively between the first control and the second control, the first control and the second control do not interfere with each other. The feedforward voltage of the first control causes a harmonic current to flow, generating a torque in the motor that suppresses the torque ripple. In addition, the feedforward voltage does not become a disturbance when compensating for the response characteristics of the second control, so the accuracy of suppressing the torque ripple does not decrease. This makes it possible to maintain the accuracy of suppressing the torque ripple over a wide range of rotation speeds while avoiding interference between the feedforward and feedback. As a result, it is possible to suppress motor noise and vibration. The value is determined, for example, by calculating the value using a formula or deriving the value from a table.

[0050] The processor, for example, calculates the voltage command value (v* dq The first control (FF voltage superposition) and the second control (response characteristic compensation) are switched depending on the difference between the harmonic components of the harmonic component (output of the harmonic component calculation 932) of the output of the harmonic component calculation 932 and the feedforward voltage command value (v*dqh).

[0051] In the first embodiment, the frequency of the harmonics increases, and the voltage command value (v* dq When the harmonic components of the input voltage Vdqh and the feedforward voltage command value (v*dqh) match within a certain error, the control is switched from the second control (response characteristic compensation) to the first control (FF voltage superposition).

[0052] This makes it possible to execute the more accurate control out of the first control (FF voltage superposition) and the second control (response characteristic compensation), with the frequency at which the harmonic component of the voltage command value and the feedforward voltage command value become equal as the boundary. Note that in the first embodiment, the first control (FF voltage superposition) is executed in the region where the harmonic frequency is high, and the second control (response characteristic compensation) is executed in the region where the harmonic frequency is low.

[0053] The processor calculates the harmonic control command value (φ* dqh ) is the same physical quantity as the measurement and control quantity (φ dq ) and harmonic control command value (φ* dqh ) the first control (FF voltage superposition) and the second control (response characteristic compensation) may be switched between.

[0054] This makes it possible to execute, for example, the more accurate control of the first control (FF voltage superposition) and the second control (response characteristic compensation), with the frequency at which the difference between the measured control amount and the harmonic control command value becomes a predetermined value as the boundary.

[0055] The processor calculates the harmonic control command value (φ* dqh ) contains multiple frequency components, the harmonic control command value (φ* dqh The first control (FF voltage superposition) and the second control (response characteristic compensation) are switched for each frequency component (n-th electrical angle harmonic component) included in the frequency component. This makes it possible to maintain the accuracy of torque ripple suppression for each frequency component.

[0056] The processor calculates a response characteristic compensation value (Δφ* dqh ) for the harmonic control command value (φ* dqh ) is subjected to gain compensation and phase compensation. This results in, for example, good transient response to harmonic currents.

[0057] In the first embodiment, the control command value (φ* dq ) and harmonic control command value (φ* dqh The physical quantity of is a magnetic flux, but may be a current. When the physical quantity is a magnetic flux, the number of motor constants used in the calculation of the feedforward voltage command value can be reduced compared to when the physical quantity is a current.

[0058] Control command value (φ* dq ) is, for example, a magnetic flux command value that causes the motor 5 to output a torque corresponding to the torque command value 10 (τ*). dqh ) is, for example, a magnetic flux command value that causes the motor 5 to generate a torque in the opposite phase to the torque ripple. dqh ) superimposed on the control command value (φ* dq ) and the measured magnetic flux value (φ dq ) and the response characteristic compensation value (Δφ* dqh The voltage command value (v* dqThe first control (FF voltage superposition) and the second control (response characteristic compensation) are switched depending on the difference between the harmonic components of the input voltage Vdqh and the feedforward voltage command value (v*dqh).

[0059] This makes it possible to execute the more accurate control between the first control (FF voltage superposition) and the second control (response characteristic compensation), for example, with the frequency at which the accuracy of the harmonic components of the voltage command value due to response characteristic compensation and the accuracy of the feedforward voltage command value becoming equal as the boundary.

[0060] The processor calculates the control command value (φ* dq ) and the measurement and control quantity (φ dq ) so that the voltage command value (v* dq ) is determined. This provides feedback control of the harmonic current.

[0061] Example 2 The difference from the first embodiment will be described with reference to the block diagram of the present embodiment shown in Fig. 3. In this embodiment, the configuration of the determination unit 9 is different, and a switching unit 93 as shown in Fig. 4 is provided.

[0062] The switching unit 93 is made up of a threshold frequency setting unit 934 , a comparator 935 , and a harmonic control command switching unit 936 .

[0063] The threshold frequency setting 934 is set as a value that allows for an error between equation (1) and equation (5). This value may be a fixed value, or it may be a function or table having a variable that affects the first term of equation (5), such as a torque command value or a current value, thereby making it possible to specify the frequency at which switching should be performed more accurately.

[0064] A comparator 935 compares the electrical angle frequency for each order with the threshold frequency, and when the threshold frequency is higher, a harmonic control command switch 936 outputs φ* to the response characteristic compensation unit for each order. dqnh and output 0 to the feedforward voltage calculation unit, otherwise, output 0 to the response characteristic compensation unit and output φ* to the feedforward voltage calculation unit. dqnh Determines the state in which to output.

[0065] Moreover, by providing hysteresis characteristics to the harmonic control command switch 936, the effects of chattering can be suppressed.

[0066] The main features of the second embodiment can be summarized as follows.

[0067] The processor calculates the electrical angular velocity (ω e In the second embodiment, the processor switches between the first control (FF voltage superposition) and the second control (response characteristic compensation) depending on the electrical angular velocity (ω e When the electrical angular velocity (ω e ) is smaller than the threshold value, the second control (response characteristic compensation) is performed. As a result, for example, in a region where the electrical angular velocity is high, the first control (FF voltage superposition) is performed, and in a region where the electrical angular velocity is low, the second control (response characteristic compensation) is performed.

[0068] In the second embodiment, the switching condition has a hysteresis characteristic, which makes it possible to suppress chattering.

[0069] The present invention is not limited to the above-mentioned embodiment, but includes various modified examples. For example, the above-mentioned embodiment has been described in detail to clearly explain the present invention, and is not necessarily limited to those including all of the configurations described. It is also possible to replace a part of the configuration of one embodiment with the configuration of another embodiment, and it is also possible to add the configuration of another embodiment to the configuration of one embodiment. It is also possible to add, delete, or replace a part of the configuration of each embodiment with another configuration.

[0070] In addition, the above configurations, functions, etc. may be realized in hardware, partly or in whole, by designing them as integrated circuits, etc. In addition, the above configurations, functions, etc. may be realized in software by a processor interpreting and executing a program that realizes each function. Information such as the program, table, file, etc. that realizes each function can be stored in a memory, a recording device such as a hard disk or SSD (Solid State Drive), or a recording medium such as an IC card, SD card, or DVD.

[0071] The embodiment of the present invention may have the following aspects.

[0072] (A1). A motor control device that drives a motor using an inverter, comprising: a harmonic control command calculation unit that calculates a harmonic control command value from a torque command; a response characteristic compensation unit that calculates a response characteristic compensation value from the harmonic control command value and its frequency; a feedforward voltage calculation unit that calculates a feedforward voltage command value from the harmonic control command value; a voltage command calculation unit that calculates a voltage command value based on a control command corresponding to the torque command; and a switching unit that switches between superimposing the feedforward voltage command value on the voltage command value or calculating the voltage command value based on an output value of the response characteristic compensation unit, depending on the harmonic control command value.

[0073] (A2). A motor control device according to (A1), wherein the switching unit switches based on the difference between the harmonic components of the voltage command value and the feedforward voltage command value.

[0074] (A3). A motor control device according to (A1), wherein the switching unit switches based on the difference between a measured control quantity having the same physical quantity as the harmonic control command value and the harmonic control command value.

[0075] (A4). A motor control device according to (A1), wherein the switching unit switches depending on the frequency of the harmonic control command value.

[0076] (A5) A motor control device according to any one of (A2) to (A4), wherein the switching unit has a hysteresis characteristic with respect to the switching condition.

[0077] (A6) A motor control device according to any one of (A2) to (A5), wherein the switching unit switches for each frequency when the harmonic control command value includes a plurality of frequency components.

[0078] According to (A1)-(A6), the torque ripple suppression effect can be ensured over a wide range of rotation speeds without significantly extending the adaptation time. [Explanation of symbols]

[0079] 1...Motor control device 2...Control command output section 3…Voltage command calculation section 4…Inverter 5. Motor 6…Electrical angle detector 7...Electrical angular velocity calculation section 8...Harmonic control command output section 9…Judgment section 91...Feedforward voltage calculation section 92...Response characteristic compensation section 93…Switching section 10...Torque command value

Claims

1. A motor control device that drives a motor by an inverter, A harmonic control command value is determined from the torque command value. determining a response characteristic compensation value from the harmonic control command value and the electrical angular velocity; determining a feedforward voltage command value from the harmonic control command value and the electrical angular velocity; determining a voltage command value based on a control command value corresponding to the torque command value and the harmonic control command value; A motor control device comprising: a processor that switches between a first control in which the feedforward voltage command value is superimposed on the voltage command value and a second control in which the harmonic control command value is compensated for with the response characteristic compensation value, depending on a switching condition.

2. 2. The motor control device according to claim 1, The processor, The first control and the second control are switched depending on a difference between a harmonic component of the voltage command value and the feedforward voltage command value. A motor control device comprising:

3. 2. The motor control device according to claim 1, The processor, The first control and the second control are switched depending on a difference between a measured control amount of the same physical quantity as the harmonic control command value and the harmonic control command value. A motor control device comprising:

4. 2. The motor control device according to claim 1, The processor, The first control and the second control are switched depending on the electrical angular velocity. A motor control device comprising:

5. 2. The motor control device according to claim 1, The switching condition has a hysteresis characteristic. A motor control device comprising:

6. 2. The motor control device according to claim 1, The processor, When the harmonic control command value includes a plurality of frequency components, the first control and the second control are switched for each frequency component included in the harmonic control command value. A motor control device comprising:

7. 2. The motor control device according to claim 1, The processor, In the second control, gain compensation and phase compensation are performed on the harmonic control command value using the response characteristic compensation value. A motor control device comprising:

8. 2. The motor control device according to claim 1, The physical quantity of the control command value and the harmonic control command value is a magnetic flux or a current. A motor control device comprising:

9. 2. The motor control device according to claim 1, the control command value is a magnetic flux command value that causes the motor to output a torque corresponding to a torque command value, the harmonic control command value is a magnetic flux command value that causes the motor to generate a torque having an opposite phase to a torque ripple, The processor, The first control and the second control are switched depending on a difference between a harmonic component of the voltage command value, which is determined by adding the response characteristic compensation value to a difference between the control command value superimposed with the harmonic control command value and a measured magnetic flux value, and the feedforward voltage command value. A motor control device comprising:

10. 2. The motor control device according to claim 1, The processor, The voltage command value is determined so that the control command value and the measured control amount coincide with each other. A motor control device comprising:

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