Rail vehicle constant speed stability control method and corresponding rail vehicle

Abstract

The present invention provides a method for controlling the constant speed stability of a rail vehicle and a corresponding rail vehicle. The control method adopts a speed PI regulator and an acceleration regulator to jointly control the output of the torque. The specific steps are as follows: Step 1: Set a speed difference threshold △V a , acceleration upper limit a a and acceleration lower limit a b ; Step 2, speed difference △V and speed difference threshold △V a Compare and compare the acceleration a with the upper limit value a a And the lower limit of acceleration a b Compare and judge the working condition, speed difference △V = Vset-Spdact, Vset is the set speed, Spdact is the actual speed; step 3, according to the different working conditions, choose to use the output value of the speed PI regulator or the acceleration regulator to control the output torque Fout, and the output torque Fout is used to reset the reference value of the speed PI regulator or the acceleration regulator in various working conditions. This method improves the rapid responsiveness of the control system to the working conditions of undulating slopes and acceleration mutations, and avoids the frequent torque oscillations caused by acceleration mutations.

Description

Technical Field

[0001] The present disclosure relates to the technical field of rail locomotives, and in particular to a method for controlling constant speed stability of a rail locomotive and a corresponding rail locomotive. Background Art

[0002] The operation of rail locomotives is controlled according to the speed mode. When the driver sets the speed target value, the control system automatically calculates the traction electric brake output value to control the acceleration or deceleration of the entire train set, and finally approaches the set target speed. During the adjustment process, the entire train set should run smoothly without impulse. However, in actual line operation, due to differences in operating environment, marshaling type, passenger capacity, line ramp and other factors, special road conditions such as long uphill slopes and undulating roads will cause actual speed overshoot or frequent oscillation of traction electric brakes, affecting the riding comfort of passengers. Therefore, an effective impulse suppression method is needed to perform dynamic adjustment to improve speed calibration accuracy and operational stability.

[0003] Prior art 1 is a locomotive and a cruise control method thereof (CN 110723173 A), which performs PI regulation through speed difference, and the control parameter is the difference between the set speed and the actual speed. When an impulse occurs on a large slope section, the direct acting parameter is the coupler force, which is related to traction, resistance and vehicle load, and directly affects the acceleration change. The change in speed difference lags behind the change in acceleration. If only the speed difference is used for control, when the slope of the large slope is converted, the PI regulator integral value is too large to quickly switch to the electric brake force, and the speed overshoot occurs. Therefore, this method has a certain lag in response to the impulse.

[0004] Prior art 2 is a method, device and equipment for controlling constant speed of electric locomotive (CN 112083649 A). This control method improves the response performance and reduces the amount of calculation compared with prior art 1 by adjusting the acceleration in real time. However, it is necessary to pre-calculate the acceleration limit curve, and the setting error of the acceleration limit curve will directly affect the accuracy of the control model. At the same time, when the set speed is close to the actual speed, the threshold of the acceleration limit curve will be set smaller to ensure stability. If the line slope changes, the PI regulator based on acceleration is more predictive and responsive in real time than the PI regulator based on speed difference. The output force will be adjusted quickly following the acceleration fluctuation, and it is very easy to touch the acceleration limit curve, causing the traction force to increase or decrease suddenly. Although this rapid responsiveness improves the speed control accuracy, it will cause unnecessary impulse problems due to the repeated oscillation of the traction force.

[0005] Prior art 3: Stability control method for electric locomotives under constant speed operation conditions (CN 107487228A). The control essence of this method is still to use the speed difference for PI adjustment, and to limit the output of the calculated torque according to the size of the speed difference. Compared with the prior art solution 1, it does not filter the sudden increase or decrease of the set speed, only limits the extreme value of the output torque, and cannot respond to changes in acceleration in real time. In the application scenarios of undulating slopes or sudden changes in acceleration, rapid response cannot be achieved due to the limitation of the extreme value of the torque. At the same time, since this method dynamically adjusts the proportion and integral coefficient of the PI controller according to the speed difference, the stability of the original PI controller will be destroyed during switching, causing the output torque to oscillate, which is not conducive to operational stability.

[0006] Based on this, the existing technology still needs to be improved. Summary of the invention

[0007] In order to solve the above technical problems, the embodiments of the present invention provide a method for controlling the constant speed stability of a railway locomotive and a corresponding railway locomotive.

[0008] A method for controlling the constant speed stability of a railway locomotive provided by an embodiment of the present disclosure adopts a speed PI regulator and an acceleration regulator to jointly control the output of torque, including:

[0009] Step 1: Set the speed difference threshold △V a , acceleration upper limit a a and acceleration lower limit a b ;

[0010] Step 2: Speed ​​difference △V and speed difference threshold △V a Compare and compare the acceleration a with the upper limit value a a And the lower limit of acceleration a b Compare and judge the working condition: speed difference △V = Vset-Spdact, where Vset is the set speed and Spdact is the actual speed;

[0011] Step 3: According to the different working conditions, the output value of the speed PI regulator or the acceleration regulator is selected to control the output torque Fout.

[0012] Among them, the output torque Fout is used to reset the reference value of the speed PI regulator or the acceleration regulator in various working conditions.

[0013] Furthermore, the speed difference threshold △V a >0, acceleration upper limit a a >0, acceleration lower limit a b >0.

[0014] Furthermore, the working conditions in step 2 include:

[0015] Operating condition 1: The speed difference △V is greater than the speed difference threshold value △V a , and the acceleration a is greater than the acceleration upper limit value a a , or the speed difference △V is less than the negative speed difference △V a and the acceleration a is less than 0 and greater than the negative acceleration lower limit value a b ;

[0016] Operating condition 2: The speed difference △V is greater than the speed difference threshold value △V a , and the acceleration a is greater than 0 and less than the acceleration lower limit value a b , or the speed difference △V is less than the negative speed difference threshold value △V a , and the acceleration a is less than the negative acceleration upper limit value a a ;

[0017] Operating condition 3: The absolute value of the speed difference △V is less than the speed difference threshold value △V a .

[0018] Furthermore, the output torque Fout is controlled according to the intermediate variable Fchange_temp of the acceleration regulator output value, and the intermediate variable Fchange_temp is -1, 0, and 1 respectively.

[0019] Furthermore, the output torque Fout is controlled according to the first-order inertial filtering output value Fchange of the intermediate variable Fchange_temp, and -1 < Fchange < 1.

[0020] Furthermore, in step 3:

[0021] Operating condition 1: Fchange_temp = -1, and the smaller value of the outputs of the speed PI regulator and the acceleration regulator is used to control the output torque Fout;

[0022] Operating condition 2: Fchange_temp = 1, and the larger value of the outputs of the speed PI regulator and the acceleration regulator is used to control the output torque Fout;

[0023] Operating condition 3: Fchange_temp = 0, and the output value of the speed PI regulator is used to control the output torque Fout.

[0024] Furthermore, in step 3:

[0025] Operating condition 1: -1 < Fchange < 0, and the smaller value of the outputs of the speed PI regulator and the acceleration regulator is used to control the output torque Fout;

[0026] Operating condition 2: 0 < Fchange < 1, and the larger value of the outputs of the speed PI regulator and the acceleration regulator is used to control the output torque Fout;

[0027] Working condition 3: Fchange = 0, the output torque Fout is controlled by the output value of the speed PI regulator.

[0028] Furthermore, the reference value is reset according to the intermediate variable Fchange_temp:

[0029] Working condition 1: The output torque value is assigned to the larger value of the output value of the speed PI regulator and the acceleration regulator, and the reference value of the corresponding regulator is reset;

[0030] Working condition 2: The output torque value is assigned to the smaller value of the output value of the speed PI regulator and the acceleration regulator, and the reference value of the corresponding regulator is reset;

[0031] Working condition 3: The output values ​​of the PI regulator and the acceleration regulator remain unchanged.

[0032] Furthermore, the reference value is reset according to the first-order inertial filter output value Fchange:

[0033] Working condition 1: assign the output torque calculated in the previous cycle to the larger value of the output value of the PI regulator and the acceleration regulator, and reset the reference value of the corresponding regulator;

[0034] Working condition 2: assign the output torque calculated in the previous cycle to the smaller value of the output value of the PI regulator and the acceleration regulator, and reset the reference value of the corresponding regulator;

[0035] Working condition 3: The output values ​​of the PI regulator and the acceleration regulator remain unchanged.

[0036] In addition, the present invention also discloses a rail locomotive, which uses the above-mentioned rail locomotive constant speed stability control method to perform constant speed stability control.

[0037] By adopting the above technical solution, the present invention has at least the following beneficial effects:

[0038] The rail vehicle constant speed stability control method disclosed in the present invention avoids the disadvantage of using speed difference alone for PI regulation by introducing the joint action of an acceleration regulator and a speed PI regulator, and improves the rapid response of the control system to undulating slopes and acceleration mutation conditions; by comprehensively selecting the output values ​​of the speed PI regulator and the acceleration regulator, performing comparison processing and resetting the base value of the regulator, the steady-state responsiveness advantage of the speed PI regulator and the dynamic responsiveness advantage of the acceleration regulator are taken into account, and the frequent torque oscillation caused by the acceleration mutation is avoided; by performing hysteresis processing and first-order inertia filtering on the acceleration limit value, and using only one set of PI regulator setting parameters during continuous acceleration or continuous deceleration, the influence of repeated parameter changes on the continuity of the controller is avoided. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the embodiments of the present disclosure or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present disclosure. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0040] Figure 1 is a structural diagram of a method for controlling constant speed stability of a railway locomotive according to an embodiment of the present disclosure;

[0041] Figure 2 is a conditional block diagram of an intermediate variable Fchange_temp of an acceleration regulator output value of an embodiment of the present disclosure;

[0042] Figure 3 It is a block diagram of resetting the reference value based on the first-order inertial filter output value Fchange disclosed in an embodiment of the present disclosure. DETAILED DESCRIPTION

[0043] The following is a further detailed description of the embodiments of the present disclosure in conjunction with the accompanying drawings and examples. The detailed description of the following embodiments and the accompanying drawings are used to exemplarily illustrate the principles of the present disclosure, but cannot be used to limit the scope of the present disclosure. The present disclosure can be implemented in many different forms and is not limited to the specific embodiments disclosed herein, but includes all technical solutions that fall within the scope of the claims.

[0044] The present disclosure provides these embodiments to make the present disclosure thorough and complete, and to fully express the scope of the present disclosure to those skilled in the art. It should be noted that unless otherwise specifically stated, the relative arrangement of the parts and steps, the composition of the materials, the numerical expressions and the numerical values ​​set forth in these embodiments should be interpreted as being merely exemplary, and not as limiting.

[0045] It should be noted that, in the description of the present disclosure, unless otherwise specified, the meaning of "multiple" is greater than or equal to two; the terms "upper", "lower", "left", "right", "inner", "outer", etc., indicating the orientation or positional relationship, are only for the convenience of describing the present disclosure and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation of the present disclosure. When the absolute position of the object being described changes, the relative positional relationship may also change accordingly.

[0046] In addition, the words "first", "second" and similar words used in the present disclosure do not indicate any order, quantity or importance, but are only used to distinguish different parts. "Vertical" does not mean vertical in the strict sense, but is within the tolerance range. "Parallel" does not mean parallel in the strict sense, but is within the tolerance range. "Include" or "comprising" and similar words mean that the elements before the word include the elements listed after the word, and do not exclude the possibility of including other elements.

[0047] It should also be noted that in the description of the present disclosure, unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be directly connected or indirectly connected through an intermediate medium. For ordinary technicians in this field, the specific meanings of the above terms in the present disclosure can be understood according to the specific circumstances. When a specific device is described as being located between a first device and a second device, there may or may not be an intermediate device between the specific device and the first device or the second device.

[0048] All terms used in the present disclosure have the same meanings as those understood by those of ordinary skill in the art to which the present disclosure belongs, unless otherwise specifically defined. It should also be understood that terms defined in general dictionaries, for example, should be interpreted as having meanings consistent with their meanings in the context of the relevant technology, and should not be interpreted in an idealized or extremely formal sense, unless explicitly defined as such herein.

[0049] Technologies, methods, and equipment known to ordinary technicians in the relevant art may not be discussed in detail, but where appropriate, the technologies, methods, and equipment should be considered part of the specification.

[0050] like Figure 1 As shown, the present disclosure proposes a new control strategy to address the shortcomings of the stability control algorithm of a rail locomotive, solves the shortcomings of the prior art one by one, and greatly improves the running stability of the rail locomotive. Specifically, some embodiments of the present disclosure provide a constant speed stability control method for a rail locomotive, which uses a speed PI regulator and an acceleration regulator to jointly control the output of the torque, including:

[0051] Step 1: Set the speed difference threshold △V a , acceleration upper limit a a and acceleration lower limit a b ;

[0052] Step 2: Speed ​​difference △V and speed difference threshold △V a Compare and compare the acceleration a with the upper limit value a a And the lower limit of acceleration a bCompare and judge the working condition: speed difference △V = Vset-Spdact, where Vset is the set speed and Spdact is the actual speed;

[0053] Step 3: According to the different working conditions, the output value of the speed PI regulator or the acceleration regulator is selected to control the output torque Fout.

[0054] Among them, the output torque Fout is used to reset the reference value of the speed PI regulator or the acceleration regulator in various working conditions.

[0055] The control algorithm disclosed in the present invention performs segmented processing based on the threshold of the speed difference. When the speed difference is greater than the set threshold, it indicates that the current process is speeding up or speeding down. Usually, this process needs to ensure continuous and stable traction output so that the coupler is always in a stretched state. It cannot blindly respond to the acceleration changes caused by the ups and downs of the line and cause frequent adjustments to the traction. Therefore, the present invention adopts a strategy of co-adjusting the PI regulator based on the speed difference and the acceleration regulator.

[0056] In some embodiments, a speed difference threshold ΔV is set a >0 to limit the use conditions of PI regulator and acceleration regulator; set the acceleration upper limit value a a >0, acceleration lower limit a b >0 to limit the hysteresis range of the acceleration regulator during acceleration or deceleration, avoiding the frequent oscillation problem caused by the limitation of a single acceleration curve.

[0057] Specifically, the working conditions in step 2 include:

[0058] Condition 1: Speed ​​difference △V is greater than speed difference threshold △V a , acceleration a is greater than the upper limit value a a , or the speed difference △V is less than the negative speed difference △V a And the acceleration a is less than 0 and greater than the negative acceleration lower limit a b ;

[0059] Condition 2: Speed ​​difference △V is greater than speed difference threshold △V a , acceleration a is greater than 0 and less than the lower limit value a b , or the speed difference △V is less than the negative speed difference threshold △V a , acceleration a is less than the negative acceleration upper limit a a ;

[0060] Condition 3: The absolute value of the speed difference △V is less than the speed difference threshold △V a .

[0061] Furthermore, the present invention adopts an incremental PI regulator based on speed difference and an acceleration regulator to jointly control the output of torque, ensuring the stability of the torque during continuous acceleration or deceleration, and being able to smoothly transition when the actual speed approaches the set target speed, avoiding speed overshoot or traction oscillation problems.

[0062] Specifically, the speed PI regulator output value calculation formula is:

[0063] Fpi=Fpi'+K1×(Vset-Spdact) curterror -K2×(Vset-Spdact) preverror ,

[0064] Among them, Fpi is the output value of the speed PI regulator, K1=Kp+Ki, K2=Kp, Fpi' is the value of the previous calculation cycle of Fpi, Kp is the proportional coefficient of PI regulation, ki is the integral coefficient of PI regulation, (Vset-Spdact) curterror is the speed difference of the current cycle, (Vset-Spdact) preverror is the speed difference of the previous cycle.

[0065] The calculation formula of the acceleration regulator output value is:

[0066] Fa=Fa'+Fchange×a F

[0067] Among them, Fa is the output value of the acceleration regulator, Fa' is the value of Fa in the previous calculation cycle, Fchange is the first-order inertial filter output value of Fchange_temp, and a F is the acceleration adjustment coefficient.

[0068] Specifically, Fchange_temp is an intermediate variable of the output value of the acceleration regulator. Preferably, the output torque Fout is controlled by Fchange_temp, and the intermediate variable Fchange_temp is -1, 0 and 1 respectively.

[0069] Furthermore, in some embodiments,

[0070] Working condition 1: Fchange_temp = -1, the smaller value of the speed PI regulator and the acceleration regulator output is used to control the output torque Fout;

[0071] Working condition 2: Fchange_temp = 1, the larger value of the speed PI regulator and the acceleration regulator is used to control the output torque Fout;

[0072] Working condition 3: Fchange_temp = 0, the output torque Fout is controlled by the output value of the speed PI regulator.

[0073] To further enhance the smoothness of the acceleration regulator, a first-order inertial filter is applied to Fchange_temp to obtain the conditional value Fchange. Preferably, in some embodiments, the output torque Fout is controlled according to Fchange. Specifically, -1 < Fchange < 1.

[0074] In some embodiments,

[0075] Condition 1: -1 < Fchange < 0, the smaller value of the speed PI regulator and the acceleration regulator output is used to control the output torque Fout;

[0076] Condition 2: 0 < Fchange < 1, the larger value of the speed PI regulator and the acceleration regulator output is used to control the output torque Fout;

[0077] Condition 3: Fchange = 0, the output value of the speed PI regulator is used to control the output torque Fout.

[0078] Since the essence of the impulse of the multiple unit train is that when the coupler force changes unevenly with the change of the vehicle's acceleration, the coupler changes between the tensile and compressive states, it is necessary to avoid frequent adjustment of the traction force during continuous acceleration or deceleration and maintain a relatively stable state output. The PI regulation algorithm based on the speed difference takes the speed difference as the regulation input, and the proportional regulation has a low responsiveness to the short-term transient of acceleration. It can better maintain the stability of the output torque during continuous acceleration or deceleration, thereby effectively maintaining the state of the coupler force. However, during continuous acceleration, due to the continuous existence of the speed difference, the integral regulation will generate cumulative errors. When the set speed target value is reached, the traction force is still large. If the traction force is quickly unloaded, it will cause impulse phenomena. Therefore, to prevent impulse phenomena from occurring in the present disclosure, the reference value of the speed PI regulator or the acceleration regulator is reset through the output torque Fout.

[0079] In some embodiments, the reference value is reset according to the intermediate variable Fchange_temp. Specifically:

[0080] Condition 1: Fchange_temp = -1, the output torque value is assigned to the larger value of the output values of the speed PI regulator and the acceleration regulator, and the reference value of the corresponding regulator is reset;

[0081] Condition 2: Fchange_temp = 1, the output torque value is assigned to the smaller value of the output values of the speed PI regulator and the acceleration regulator, and the reference value of the corresponding regulator is reset;

[0082] Condition 3: Fchange_temp = 0, the output values of the PI regulator and the acceleration regulator remain unchanged at the current values.

[0083] Preferably, in some embodiments, the reference value is reset according to the first-order inertial filtering output value Fchange_temp of Fchange, specifically:

[0084] When -1 < Fchange < 0, the output torque Fout is equal to the smaller value of Fpi and Fa, and when Fpi > Fa, the output torque value Fout' calculated in the previous cycle is assigned to Fpi, otherwise Fout' is assigned to Fa. When 0 < Fchange < 1, the output torque Fout is equal to the larger value of Fpi and Fa, and when Fpi < Fa, the output torque value Fout' calculated in the previous cycle is assigned to Fpi, otherwise Fout' is assigned to Fa. When Fchange = 0, the output torque value is equal to Fpi, and Fpi and Fa remain unchanged at their current values.

[0085] In addition, the present invention also discloses a rail locomotive, which uses the above-mentioned constant-speed stability control method for rail locomotives to perform constant-speed stability control.

[0086] So far, the embodiments of the present disclosure have been described in detail. In order to avoid obscuring the concept of the present disclosure, some details known in the art have not been described. Those skilled in the art can fully understand how to implement the technical solutions disclosed here based on the above description.

[0087] Although some specific embodiments of the present disclosure have been described in detail by way of examples, those skilled in the art should understand that the above examples are only for illustration purposes and not for limiting the scope of the present disclosure. Those skilled in the art should understand that the above embodiments can be modified or some technical features can be equivalently replaced without departing from the scope and spirit of the present disclosure. In particular, as long as there is no structural conflict, the technical features mentioned in each of the embodiments can be combined in any way.

Claims

1. A method for controlling the constant speed stability of a railway locomotive, characterized in that: The speed PI regulator and acceleration regulator are used to jointly control the output of torque, including: Step 1: Set the speed difference threshold △V a 、Acceleration upper limit value a a and acceleration lower limit a b ; Step 2: speed difference △V and speed difference threshold △V a Compare and compare the acceleration a with the acceleration upper limit a a And the lower limit value of acceleration a b Compare and judge the working condition. The speed difference △V = - ,in, To set the speed, is the actual speed; Step 3, according to the different working conditions determined, select the output value of the speed PI regulator or the acceleration regulator to control the output torque , Among them, the output torque is used for each of the working conditions Resetting the reference value of the speed PI regulator or the acceleration regulator; The speed difference threshold ΔV a >0 and the acceleration upper limit a a >0 and the lower limit value of acceleration a b >0; The working conditions described in step 2 include: Condition 1: The speed difference △V is greater than the speed difference threshold △V a And the acceleration a is greater than the acceleration upper limit a a , or the speed difference △V is less than the negative speed difference △V a And the acceleration a is less than 0 and greater than the negative acceleration lower limit a b ; Condition 2: The speed difference △V is greater than the speed difference threshold △V a And the acceleration a is greater than 0 and less than the acceleration lower limit a b , or the speed difference △V is less than the negative speed difference threshold △V a And the acceleration a is less than the negative acceleration upper limit value a a ; Condition 3: The absolute value of the speed difference △V is less than the speed difference threshold △V a ; According to the intermediate variable of the acceleration regulator output value Fchange_temp Control the output torque Fout, The intermediate variable Fchange_temp They are -1, 0 and 1 respectively.

2. The method for controlling the constant speed stability of a railway locomotive according to claim 1, characterized in that: According to the intermediate variable The first-order inertial filter output value Control the output torque , -1< <1; the first-order inertial filter output value is the intermediate variable Conditional value obtained by first-order inertial filtering.

3. The method for controlling the constant speed stability of a railway locomotive according to claim 1, characterized in that: In step 3: Working condition 1: =-1, the output torque is controlled by using the smaller value output by the speed PI regulator and the acceleration regulator ; Working condition 2: =1, the larger value of the speed PI regulator and the acceleration regulator output is used to control the output torque ; Condition 3: =0, the output value of the speed PI regulator is used to control the output torque .

4. The method for controlling the constant speed stability of a railway locomotive according to claim 2, characterized in that: In step 3: Condition 1: -1< <0, the output torque is controlled by using the smaller value output by the speed PI regulator and the acceleration regulator ; Working condition 2: 0< <1, the output torque is controlled by using the larger value output by the speed PI regulator and the acceleration regulator ; Condition 3: =0, the output value of the speed PI regulator is used to control the output torque .

5. The method for controlling the constant speed stability of a railway locomotive according to claim 3, characterized in that: According to the intermediate variable To reset the reference value: Working condition 1: =-1, the output torque value is assigned to the larger value of the output value of the speed PI regulator and the acceleration regulator, and the reference value of the corresponding regulator is reset; Working condition 2: =1, the output torque value is assigned to the smaller value of the output value of the speed PI regulator and the acceleration regulator, and the reference value of the corresponding regulator is reset; Condition 3: =0, the output values ​​of the PI regulator and the acceleration regulator remain unchanged at the current values.

6. The method for controlling the constant speed stability of a railway locomotive according to claim 4, characterized in that: According to the first-order inertial filtering output value To reset the reference value: Condition 1: -1< <0, assign the output torque value calculated in the previous cycle to the larger value of the output value of the PI regulator and the acceleration regulator, and reset the reference value of the corresponding regulator; Working condition 2: 0< <1, assign the output torque value calculated in the previous cycle to the smaller value of the output value of the PI regulator and the acceleration regulator, and reset the reference value of the corresponding regulator; Condition 3: =0, the output values ​​of the PI regulator and the acceleration regulator remain unchanged at the current values.

7. A rail locomotive, characterized in that: The constant speed stability control of a railway locomotive is performed by adopting the constant speed stability control method of any one of claims 1 to 6.

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