Motion control method based on tower type pumping unit

Abstract

The invention provides a motion control method based on a tower type pumping unit, which relates to the technical field of oil field oil production engineering, and comprises the following steps of: establishing a dynamic relationship among components of the tower type pumping unit according to energy consumption through a novel tower type pumping unit dynamic model established based on a Lagrange equation; according to the method, the relation between the variable suspension point load and the displacement and the speed at the suspension point is visually given, so that the built model can more accurately describe the motion relation at the suspension point of the tower type pumping unit, a theoretical basis is provided for designing a more accurate and more energy-saving control method, the tower type pumping unit is accurately controlled, and the operation efficiency of the tower type pumping unit is improved. A physical model of the tower type pumping unit is simplified, and controller design and fault diagnosis of the tower type pumping unit are facilitated.

Description

Technical Field

[0001] The present invention relates to the technical field of oil production engineering in oil fields, and specifically to a motion control method based on a tower-type pumping unit. Background Art

[0002] Most oil fields nowadays use beam pumping units as the main oil production equipment. However, traditional beam pumping units not only have disadvantages such as complex mechanical structures, many transmission links, and high manufacturing costs, but also have very low working efficiency. Generally, the working efficiency of domestic beam pumping units is only 12 - 23%, and the average in foreign countries is only about 30%. Tower-type pumping units have many advantages such as compact structure, convenient installation, wide application range, strong applicability, high efficiency, and energy saving. However, tower-type pumping units require a relatively complex control system, which adds difficulties to the wide use of tower-type pumping units and energy conservation and production increase in oil fields. Therefore, it is very necessary to study the dynamic model of a tower-type pumping unit and its motion control system to achieve fault diagnosis and fault tolerance control.

[0003] In view of the above problems, a motion control method based on a tower-type pumping unit is proposed to solve the above problems. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to overcome the defects existing in the prior art, and a motion control method based on a tower-type pumping unit is proposed. By using this device for work, the problems of inaccurate control of the tower-type pumping unit and relatively complex establishment of the motion model are solved.

[0005] To solve the above problems, the technical solution adopted by the present invention is: a motion control method based on a tower-type pumping unit, including: S1. Conduct dynamic modeling on the tower-type pumping unit, establish the dynamic relationship of each component of the tower-type pumping unit according to the energy consumption, and intuitively give the relationship between the changing polished rod load and the displacement and velocity at the polished rod.

[0006] S2. Identify and correct the model parameters in real time: Collect vibration signals, torque signals, and displacement signals by arranging sensors, and use the particle swarm optimization algorithm to perform online identification and correction of the parameters in the dynamic model.

[0007] S3. Design a hierarchical control strategy: Set the polished rod motion trajectory according to the oil field working conditions, solve the motor driving torque compensation amount based on the dynamic model, generate a reference trajectory including velocity and acceleration constraints, design a sliding mode variable structure controller, and perform real-time control on the motor drive system based on the dynamic model corrected in step S2 to suppress tower vibration and load fluctuation interference.

[0008] S4. Improve fault diagnosis and fault tolerance control: Use model residual analysis or neural network algorithms to identify drive system faults and structural faults, and switch to a standby control strategy according to the fault type.

[0009] Furthermore, S1 includes the following steps:

[0010] S11. Simplify the physical model of the pumping unit and establish a physical model with the motor, reduction gearbox, drum, counterweight, head pulley, and rod pump as the main components;

[0011] S12. Establish generalized coordinates based on the motion relationships of the components;

[0012] S13. Establish equations for the kinetic energy, potential energy, and damping energy consumption of each component;

[0013] S14. Based on the changes in kinetic energy, potential energy, and damping consumption, establish Lagrangian dynamics equations to clarify the mathematical relationships between the components.

[0014] Furthermore, in S11, the physical entity of the tower-type pumping unit consists of a derrick, counterweight, motor, reduction gearbox, drum, head pulley, and rod pump. Feedback signals are obtained through a load sensor at the rod pump and an optical encoder of the motor and act on the controller to control the motor to make the tower-type pumping unit operate according to a specific speed curve. The motor provides the driving torque T of the system e , the reduction gearbox is responsible for increasing the driving torque, and its transmission ratio and transmission efficiency are i and η respectively. The increased driving torque of the reduction gearbox acts on the drum, and the moment of inertia of the drum is J d , the moment of inertia of the head pulley is J s , the rotational damping of the drum is D d , the rotational damping of the head pulley is D s , the rotational angle is θ d , the mass of the counterweight is m c , the rotational angle of the head pulley is θ s , ignoring the transmission damping and elastic deformation of the belt connection between the drum and the head pulley, the suspension point load at the sucker rod is P s , the distance the sucker rod moves is d s .

[0015] Furthermore, in S12, since the motor is connected to the drum by gears, the driving torque at the drum is calculated from the transmission ratio and efficiency of the gearbox and the electromagnetic torque of the motor. The generalized coordinates for the dynamic modeling are selected as the rotational angle θ of the drum d , the rotational angle θ of the head pulley s , the displacement d at the suspension point of the rod pump s .

[0016] Furthermore, in S13, according to the Lagrangian dynamics equation, Equation 1 can be obtained: where the kinetic energy, potential energy, and damping energy consumption of the system are T, U, and D respectively, q is the generalized coordinate, Let \(\dot{q}\) be the generalized velocity and \(F\) be the driving force of the system. When constructing the Lagrangian dynamics equation, first, taking the generalized coordinates as the reference system, obtain the generalized velocities of each component, and calculate the kinetic energy, potential energy, and damping dissipation energy of the entire system.

[0017] Furthermore, in S13, the kinetic energy of the system consists of the rotation of the drum, the rotation of the head pulley, the lifting and lowering of the counterweight, and the lifting and lowering of the sucker rod. Since the present invention simplifies the relationship between the speeds of the counterweight and the sucker rod, that is, assuming their speeds are equal, the kinetic energy equation 2 is obtained as follows:

[0018] Furthermore, in S13, considering the potential energy of the system and neglecting the elastic potential energy brought by the elastic deformation at the belt connecting the drum and the head pulley and the steel wire rope between the head pulley and the sucker rod, the main change in the potential energy of the system comes from the change in gravitational potential energy brought by the lifting and lowering of the counterweight and the sucker rod. Therefore, the potential energy equation 3 of the system is: \(U=(P - m g)d\). Considering the consumption of the system energy by damping and neglecting the damping at the connections between the drum and the belt, the head pulley and the belt, the head pulley and the steel wire rope, and the sucker rod and the steel wire rope, the main damping of the system is the rotational damping of the drum and the head pulley. The damping equation 4 of the system is: s -m b g)d s

[0019] Furthermore, in S14, substituting the kinetic energy equation 2, potential energy equation 3, and damping equation 4 calculated in S13 into the Lagrangian dynamics equation 1, we get:

[0020] where \(T d =\eta_iT e represents the torque transmitted to the drum through the speed reducer. The motion description equation of the suspension point of the tower-type pumping unit is established by modeling design, providing a theoretical basis and foundation for the intelligent control and fault diagnosis of the tower-type pumping unit.

[0021] Furthermore, in S2, acceleration sensors are arranged at the key nodes of the tower, torque sensors are installed at the motor, and displacement sensors are set at the suspension point to synchronously collect the tower vibration, motor torque, and suspension point displacement signals at a frequency not lower than 200 Hz. After anti-aliasing filtering, the signals are input into the identification module. Using the particle swarm optimization algorithm, the key parameters of the corresponding dynamic model are set as the objects to be identified. Through algorithm iteration optimization, the error between the model output torque and displacement is minimized. The population size of the algorithm is set to 30 - 50, and the inertia weight dynamically decreases from 0.9 to 0.4 with iteration. Each time a pumping stroke cycle is completed, a parameter identification is triggered, and the latest parameters are corrected to the dynamic model in real-time to realize the dynamic update of the system mass and damping matrix.

[0022] Further, in S4, when the fault feature disappears and the dynamic model residual is < 3% for three consecutive stroke cycles, the system automatically switches back from the standby control strategy to the main control strategy. During the switching process, a ramp function is used to smoothly transition the control quantity to avoid sudden changes in the polished rod load caused by the switching of the control mode. The transition time is 1 - 2 stroke cycles.

[0023] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0024] The motion control method for the tower - type pumping unit proposed by the present invention, a new dynamic model of the tower - type pumping unit established based on the Lagrange equation, establishes the dynamic relationship of each component of the tower - type pumping unit according to the energy consumption, and more intuitively gives the relationship between the changing polished rod load and the displacement and velocity at the polished rod. Therefore, the established model can more accurately describe the motion relationship at the polished rod of the tower - type pumping unit, providing a theoretical basis for designing a more accurate and energy - saving control method. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The disclosure of the present invention will be described with reference to the accompanying drawings. It should be understood that the drawings are only for illustrative purposes and are not intended to limit the scope of protection of the present invention. In the drawings, the same reference numerals are used to refer to the same components. Among them:

[0026] Figure 1 Schematically shows a flowchart of the motion control method for the tower - type pumping unit proposed according to an embodiment of the present invention;

[0027] Figure 2 Schematically shows a schematic diagram of the modeling structure of the tower - type pumping unit proposed according to an embodiment of the present invention;

[0028] Figure 3 Schematically shows a schematic diagram of the overall structure of the tower - type pumping unit proposed according to an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0029] It is easy to understand that according to the technical solution of the present invention, without changing the essence of the present invention, those of ordinary skill in the art can propose various interchangeable structural ways and implementation manners. Therefore, the following detailed description and the accompanying drawings are only exemplary descriptions of the technical solution of the present invention and should not be regarded as the whole of the present invention or as a limitation or restriction on the technical solution of the present invention.

[0030] According to an embodiment of the present invention, combined with Figures 1 - 3 , the motion control method for the tower - type pumping unit includes: S1. Perform dynamic modeling on the tower - type pumping unit, establish the dynamic relationship of each component of the tower - type pumping unit according to the energy consumption, and intuitively give the relationship between the changing polished rod load and the displacement and velocity at the polished rod;

[0031] S2. Identify and correct the model parameters in real time: By arranging sensors to collect vibration signals, torque signals, and displacement signals, the particle swarm optimization algorithm is used to identify and correct the parameters in the dynamic model online. Specifically, acceleration sensors are arranged at the key nodes of the tower, torque sensors are installed at the motor, and displacement sensors are set at the polished rod position. The vibration of the tower, the torque of the motor, and the displacement of the polished rod are synchronously collected at a frequency not lower than 200 Hz. After anti-aliasing filtering, they are input into the identification module. Using the particle swarm optimization algorithm, the key parameters of the corresponding dynamic model are set as the objects to be identified. Through algorithm iteration and optimization, the torque and displacement errors of the model output are minimized. The population size of the algorithm is set to 30 - 50, and the inertia weight decreases dynamically from 0.9 to 0.4 with iteration. Each time a pumping stroke cycle is completed, parameter identification is triggered, and the latest parameters are corrected in real time to the dynamic model to realize the dynamic update of the system mass and damping matrix;

[0032] S3. Design the strategy of hierarchical control: Set the motion trajectory of the polished rod according to the oilfield working conditions, solve the motor driving torque compensation amount based on the dynamic model, generate a reference trajectory including velocity and acceleration constraints, and design a sliding mode variable structure controller. Based on the dynamic model corrected in step S2, the motor drive system is controlled in real time to suppress the tower vibration and load fluctuation interference;

[0033] S4. Improve fault diagnosis and fault tolerance control: Use model residual analysis or neural network algorithms to identify drive system faults and structural faults, and switch to the standby control strategy according to the fault type. Specifically, when it is detected that the fault characteristics disappear and the dynamic model residual is < 3% for three consecutive stroke cycles, the system automatically switches back to the main control strategy from the standby control strategy. During the switching process, a ramp function is used to smoothly transition the control quantity to avoid sudden changes in the polished rod load caused by the control mode switching, and the transition time is 1 - 2 stroke cycles.

[0034] Among them, S1 includes the following steps:

[0035] S11. Simplify the physical model of the pumping unit and establish a physical model with the motor, reduction gearbox, drum, counterweight, crown block, and rod pump as the main components;

[0036] S12. Establish the generalized coordinates according to the motion relationships of each component;

[0037] S13. Establish the equations of kinetic energy, potential energy, and damping energy consumption of each component;

[0038] S14. Based on the changes in kinetic energy, potential energy, and damping consumption, establish the Lagrangian dynamics equation to clarify the mathematical relationships between each component.

[0039] In S11, the physical entity of the tower-type pumping unit consists of a derrick, a counterweight, a motor, a reduction gearbox, a drum, a head pulley, and a rod pump. Feedback signals are obtained through a load sensor at the rod pump and an optical encoder of the motor and act on the controller to control the motor to make the tower-type pumping unit operate according to a specific speed curve. Among them, the motor provides the driving torque T of the system. e , the reduction gearbox is responsible for increasing the driving torque. Its transmission ratio and transmission efficiency are i and η respectively. The increased driving torque of the reduction gearbox acts on the drum, and the moment of inertia of the drum is J. d , the moment of inertia of the head pulley is J. s , the rotational damping of the drum is D. d , the rotational damping of the head pulley is D. s , the rotational angle is θ. d , the mass of the counterweight is m. c , the rotational angle of the head pulley is θ. s , ignoring the transmission damping and elastic deformation of the belt connection between the drum and the head pulley, the hook load at the rod pump is P. s , the distance moved by the rod pump is d. s .

[0040] In S12, since the motor is connected to the drum by gears, the driving torque at the drum is calculated from the transmission ratio and efficiency of the gearbox and the electromagnetic torque of the motor. The generalized coordinates for kinetic modeling are selected as the rotational angle θ of the drum d , the rotational angle θ of the head pulley s , the displacement d at the hook of the rod pump s .

[0041] In S13, according to the Lagrange's equations of motion, Equation 1 can be obtained: where the kinetic energy, potential energy, and damping dissipation energy of the system are T, U, and D respectively, q is the generalized coordinate, is the generalized velocity, F is the driving force of the system. When constructing the Lagrange's equations of motion, first, the generalized velocities of each component are obtained with the generalized coordinate as the reference system, and the kinetic energy, potential energy, and damping dissipation energy of the entire system are calculated.

[0042] In S13, the kinetic energy of the system consists of the rotation of the drum, the rotation of the head pulley, the lifting and lowering of the counterweight, and the lifting and lowering of the rod pump. Since the present invention simplifies the relationship between the speeds of the counterweight and the rod pump, that is, assuming their speeds are equal, the kinetic energy equation 2 is obtained:

[0043] In S13, considering the potential energy of the system and ignoring the elastic potential energy brought by the elastic deformation at the belt connecting the drum and the head pulley and the wire rope connecting the head pulley and the rod pump, the main change in the potential energy of the system comes from the change in gravitational potential energy brought by the lifting and lowering of the counterweight and the rod pump. Therefore, the potential energy equation 3 of the system: U = (Ps -m b g)d s , considering the energy consumption of the damping on the system, ignoring the damping at the connections of the roller and the belt, the head pulley and the belt, the head pulley and the steel wire rope, and the sucker rod and the steel wire rope, the main damping of the system is the rotational damping of the roller and the head pulley. The damping equation of the system is Equation 4:

[0044] Substitute the kinetic energy Equation 2, potential energy Equation 3, and damping Equation 4 obtained in S13 into the Lagrangian dynamics Equation 1 to get: where T d = ηiT e , representing the torque transmitted to the roller through the speed reducer. The motion description equation of the suspension point of the tower-type pumping unit is established in the modeling design, providing a theoretical basis and foundation for the intelligent control and fault diagnosis of the tower-type pumping unit.

[0045] Use MATLAB and Simulink to construct a simulation platform for the tower-type pumping unit system to verify the accuracy of the new tower-type machine dynamics model. Based on the Lagrangian equation, the model is established, and the sub-modules include:

[0046] Drive module: The rated power of the motor P n = 55 kw, the rated speed n n = 1480 rpm, the transmission ratio of the reduction gearbox i = 30, the transmission efficiency η = 0.92, and the driving torque of the roller τ drive = ηiτ elec , τ elec is the electromagnetic torque of the motor;

[0047] Motion conversion module: The moment of inertia of the roller J1 = 20 kg·m 2 , the moment of inertia of the head pulley J2 = 5 kg·m 2 , the rotational damping D1 = 0.8 N·m·s, the radius of the head pulley r = 0.3 m, and the suspension point displacement s = rθ;

[0048] Load module: The mass of the counterweight m = 1500 kg, the suspension point load F = F 静载 + F 动载 , the static load F 静载 = 80 kN, the dynamic load where k f = 2000 N·s / m;

[0049] The control and sensor module integrates the design of the trajectory planning module. Input the stroke length L = 6 m and the stroke frequency n = 6 spm to generate the suspension point displacement trajectory, and configure the virtual sensors. The accuracy of the roller shaft torque sensor is ±0.5% FS, and the accuracy of the suspension point displacement sensor is ±0.1 mm.

[0050] During the operating condition test, the no-load start-up was performed with the suspension point acceleration constraint ≤1.5g and the tower vibration amplitude constraint ≤5mm. The maximum acceleration of the suspension point during startup was 1.2g, and the vibration amplitude of the tower top was 3.8mm. For steady-state operation with rated load, the input F = 80kN, the displacement root mean square error was 1.2mm, the motor torque was 3.5N·m, and the error rate was less than 2%. The variable load impact condition simulated a partial break in the sucker rod, causing a sudden drop in load of 30%. After the model parameters were corrected, the suspension point displacement fluctuations converged within two stroke cycles.

[0051] Field data validation involved data acquisition and preprocessing: Three tower-type pumping units were selected. High-precision torque sensors were installed on the motor shafts, and laser displacement sensors were installed at the suspension points. Data was collected at 500Hz for 30 days. Signal filtering, detrending, and outliers were removed. Model matching and result comparison: Measured data was input into the platform, and the particle swarm algorithm was used to identify parameters. After iteration, the parameter identification accuracy was as follows: the drum moment of inertia J1 had an error of 2.5%, and the head pulley damping B2 had an error of 6.25%. After correction, the suspension point displacement decreased from 4.8mm to 1.5mm, and the motor torque decreased from 12N·m to 4.2N·m. The model-predicted suspension point load fluctuations matched the measured values by 92%.

[0052] The technical scope of the present invention is not limited to the contents of the above description. Those skilled in the art can make various deformations and modifications to the above embodiments without departing from the technical concept of the present invention, and these deformations and modifications should all fall within the protection scope of the present invention.

Claims

1. A motion control method for a tower-mounted pumping unit, characterized in that, Including: S1. Conduct dynamic modeling of the tower-type pumping unit, establish the dynamic relationships of each component of the tower-type pumping unit based on energy consumption, and intuitively present the relationship between the changing polished rod load and the displacement and velocity at the polished rod. S2. Identify and real-time correct the model parameters: Collect vibration signals, torque signals, and displacement signals by arranging sensors, and use the particle swarm optimization algorithm to online identify and correct the parameters in the dynamic model. S3. Design a hierarchical control strategy: Set the polished rod motion trajectory according to the oilfield working conditions, solve the motor driving torque compensation amount based on the dynamic model, generate a reference trajectory including speed and acceleration constraints, design a sliding mode variable structure controller, and based on the dynamic model corrected in step S2, conduct real-time control of the motor drive system to suppress tower vibration and load fluctuation interference. S4. Improve fault diagnosis and fault tolerance control: Use model residual analysis or neural network algorithms to identify drive system faults and structural faults, and switch to backup control strategies according to the fault types.

2. The motion control method based on the tower-type pumping unit according to claim 1, wherein: The S1 includes the following steps: S11. Simplify the physical model of the pumping unit and establish a physical model with the motor, reduction gearbox, drum, counterweight, crown block, and rod pump as the main components. S12. Establish generalized coordinates according to the motion relationships of each component. S13. Establish equations for the kinetic energy, potential energy, and damping energy consumption of each component. S14. Based on the changes in kinetic energy, potential energy, and damping consumption, establish Lagrangian dynamic equations to clarify the mathematical relationships between each component.

3. The motion control method for a tower-mounted pumping unit according to claim 2, characterized in that, In S11, the physical entity of the tower-type pumping unit consists of a derrick, a counterweight, a motor, a reduction gearbox, a drum, a head pulley, and a rod pump. Feedback signals are obtained through a load sensor at the rod pump and an optical encoder of the motor and act on the controller to control the motor so that the tower-type pumping unit operates according to a specific speed curve. The motor provides the power torque T of the system. e , the reduction gearbox is responsible for increasing the power torque. Its transmission ratio and transmission efficiency are i and η respectively. The increased power torque of the reduction gearbox acts on the drum, and the moment of inertia of the drum is J. d , the moment of inertia of the head pulley is J. s , the rotational damping of the drum is D. d , the rotational damping of the head pulley is D. s , the rotational angle is θ. d , the mass of the counterweight is m. c , the rotational angle of the head pulley is θ. s , ignoring the transmission damping and elastic deformation of the belt connection between the drum and the head pulley, the hook load at the sucker rod is P. s , the moving distance of the sucker rod is d. s .

4. The motion control method for a tower-type pumping unit according to claim 3, characterized in that: In S12, since the motor is connected to the roller gear, the driving torque at the roller is calculated from the transmission ratio and transmission efficiency of the gearbox and the electromagnetic torque of the motor. The generalized coordinates for dynamic modeling are selected as the rotation angle θ of the roll d , the rotation angle θ of the head pulley s , the displacement d at the polished rod hanger s .

5. The motion control method for a tower-mounted pumping unit according to claim 4, characterized in that: In S13, Equation 1 can be obtained according to Lagrange's dynamical equation: where the kinetic energy, potential energy, and damping dissipation energy of the system are T, U, and D respectively, q is the generalized coordinate, is the generalized velocity, F is the driving force of the system. When constructing Lagrange's dynamical equation, the generalized velocities of each component are first obtained with the generalized coordinate as the reference frame, and the kinetic energy, potential energy, and damping dissipation energy of the entire system are calculated.

6. The motion control method based on a tower-type pumping unit according to claim 4, characterized in that: In the S13, the kinetic energy of the system consists of the rotation of the drum, the rotation of the crown block, the lifting and lowering of the counterweight, and the lifting and lowering of the sucker rod. Since the present invention simplifies the relationship between the speeds of the counterweight and the sucker rod, that is, assumes that their speeds are equal, the kinetic energy equation 2 is obtained:

7. The motion control method based on the tower-mounted pumping unit according to claim 6, characterized in that: In S13, considering the potential energy of the system and neglecting the elastic potential energy brought about by the elastic deformation at the belt connecting the drum and the head pulley and the wire rope between the head pulley and the sucker rod, the main change in the potential energy of the system comes from the change in gravitational potential energy caused by the lifting and lowering of the counterweight and the sucker rod. Therefore, the potential energy equation of the system is Equation 3: U = (P s -m b g)d s . Considering the consumption of the system energy by damping and neglecting the damping at the connections between the drum and the belt, the head pulley and the belt, the head pulley and the wire rope, and the sucker rod and the wire rope, the main damping of the system is the rotational damping of the drum and the head pulley. The damping equation of the system is Equation 4:

8. The motion control method based on the tower-type pumping unit according to claim 7, characterized in that: In S14, substituting the kinetic energy equation 2, potential energy equation 3, and damping equation 4 calculated in S13 into the Lagrangian dynamics equation 1 gives: where T d = ηiT e , representing the torque transmitted to the drum through the speed reducer.

9. The motion control method based on the tower-type pumping unit according to claim 1, characterized in that: In the S2, arrange acceleration sensors at the key nodes of the tower, install torque sensors at the motor, and set displacement sensors at the polished rod position to synchronously collect tower vibration, motor torque, and polished rod displacement signals at a frequency not lower than 200 Hz. After anti-aliasing filtering, input them into the identification module. Use the particle swarm optimization algorithm to set the key parameters of the corresponding dynamic model as the objects to be identified. Through algorithm iteration optimization, minimize the error between the model output torque and displacement. Set the algorithm population size to 30 - 50, and the inertia weight dynamically decreases from 0.9 to 0.4 with iteration. Trigger parameter identification once for each pumping stroke cycle, and real-time correct the latest parameters to the dynamic model to realize the dynamic update of the system mass and damping matrix.

10. The motion control method for a tower-mounted pumping unit according to claim 1, characterized in that: In the S4, when it is detected that the fault characteristics disappear and the dynamic model residual < 3% for 3 consecutive stroke cycles, the system automatically switches back from the backup control strategy to the main control strategy. During the switching process, use a ramp function to smoothly transition the control quantity to avoid sudden changes in the polished rod load caused by the control mode switching. The transition time is 1 - 2 stroke cycles.

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