Control device

Abstract

To provide a control device capable of reducing power consumption of an ignition system, without using expensive in-cylinder pressure sensor.SOLUTION: Respective one or more ignition coils include primary coils and secondary coils which are magnetically-coupled to each other. Respective one or more switches switch supply and interruption of primary electric current to the one more primary coils from an electric source. The one or more secondary coils generate secondary electric current according to interruption of the primary electric current. An ignition plug generates sparks by means of the secondary electric current generated according to interruption of the primary electric current. A control device controls movement of the one or more switches so as to generate a plurality of times of secondary electric currents at one cycle of an interval combustion engine onto one more of secondary coils. The control device controls an ignition system so that an inclination with respect to times of a plurality of times of secondary electric currents at the N+1 cycles decreases when inclination with respect to times of a plurality of times of secondary electric currents at the N'th cycle is positive.SELECTED DRAWING: Figure 1

Description

Technical Field

[0001] The present invention relates to a control device for an ignition system.

Background Art

[0002] As an invention related to a control device for a conventional ignition system, for example, an ignition control device described in Patent Document 1 is known. This ignition control device determines the magnitude of the energy input to the primary coil of the ignition coil based on the in-cylinder pressure detected by the in-cylinder pressure sensor. Thereby, in the ignition control device described in Patent Document 1, the occurrence of multiple discharges is suppressed and the wear of the spark plug is reduced.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0004] By the way, in the field of control devices for ignition systems, there is a desire to reduce the power consumption of the ignition system.

[0005] Therefore, an object of the present invention is to provide a control device capable of reducing the power consumption of an ignition system.

Means for Solving the Problems

[0006] A first aspect of the present invention is a control device for an ignition system of an internal combustion engine including a power source, one or more switches, one or more ignition coils, and a spark plug, each of the one or more ignition coils includes a primary coil and a secondary coil that are magnetically coupled to each other, Each of the one or more switches switches the supply and cutoff of the primary current from the power source to the one or more primary coils. The one or more secondary coils generate a secondary current in response to the cutoff of the primary current. The spark plug generates a spark by the secondary current generated in response to the cutoff of the primary current. The control device controls the operation of the one or more switches so that the one or more secondary coils generate the secondary current a plurality of times in one cycle of the internal combustion engine. The control device A calculation step of calculating a calculated slope with respect to the time of the secondary current based on the plurality of secondary currents in one or more cycles before the Nth cycle; A control step of controlling the ignition system so that the slope with respect to the time of the plurality of secondary currents in the (N + 1)th cycle approaches a target slope more than the calculated slope; Execute N is a natural number. The target slope is negative. It is a control device.

[0007] A second aspect of the present invention is In the calculation step, the control device calculates the calculated slope after removing noise from the plurality of secondary currents in one or more cycles before the Nth cycle. The control device according to the first aspect.

[0008] A third aspect of the present invention is In the calculation step, the control device calculates the calculated slope based on a value obtained by dividing a value obtained by adding the plurality of secondary currents in the (N - M)th cycle to the Nth cycle by (M + 1). M is a natural number smaller than N. The control device according to the first aspect or the second aspect.

[0009] A fourth aspect of the present invention is In the control step, the control device controls the amount of energy input to the one or more primary coils. The control device according to any one of the first aspect to the third aspect.

[0010] A fifth aspect of the present invention is In the control step, the control device controls the amount of energy input to the one or more primary coils by controlling the operation of the one or more switches. The control device according to the fourth aspect.

[0011] A sixth aspect of the present invention is The ignition system further includes a DC-DC converter, The DC-DC converter converts the voltage of the power supply, In the control step, the control device controls the amount of energy input to the one or more primary coils by controlling the operation of the DC-DC converter. The control device according to the fourth aspect.

[0012] A seventh aspect of the present invention is A control device for an ignition system of an internal combustion engine including a power supply, one or more switches, one or more ignition coils, and an ignition plug, Each of the one or more ignition coils includes a primary coil and a secondary coil that are magnetically coupled to each other, Each of the one or more switches switches the supply and interruption of the primary current from the power supply to the one or more primary coils, The one or more secondary coils generate a secondary current in response to the interruption of the primary current, The ignition plug generates a spark by the secondary current generated in response to the interruption of the primary current, The control device controls the operation of the one or more switches so as to generate a plurality of secondary currents in the one or more secondary coils in one cycle of the internal combustion engine. When the slope of the plurality of secondary currents with respect to time in the Nth cycle is positive, the control device controls the ignition system so that the slope of the plurality of secondary currents with respect to time in the (N + 1)th cycle decreases. N is a natural number. It is a control device.

Advantages of the Invention

[0013] According to the present invention, the power consumption of the ignition system can be reduced.

Brief Description of the Drawings

[0014]

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Embodiments for Carrying Out the Invention

[0015] (Embodiment) [Structure of the Ignition System 1] Hereinafter, an ignition system 1 including a control device 10 according to an embodiment of the present invention will be described with reference to the drawings. FIG. 1 is a circuit diagram of the ignition system 1. FIG. 2 is a graph showing the relationship between the secondary current and time in the Nth cycle. FIG. 3 is a graph showing the relationship between the secondary current and time in the (N + 1)th cycle. The vertical axis represents the magnitude of the secondary current. The horizontal axis represents time. T0 is the time when the piston of the internal combustion engine is at the top dead center. N is a natural number.

[0016] The ignition system 1 is used in the internal combustion engine of a vehicle. The internal combustion engine is a four-stroke engine. Therefore, the crankshaft of the internal combustion engine rotates twice in one cycle. The ignition system 1 generates a spark for burning the air-fuel mixture in the combustion chamber of the internal combustion engine. The ignition system 1 includes a control device 10, a power source 12, a DC-DC converter 14, ignition coils 16, 18, switches 20, 22, a current sensor 24, and an ignition plug 26.

[0017] The power source 12 is a DC power source. The power source 12 is a lead-acid battery used in an automobile. Therefore, the voltage of the power source 12 is 12V. The negative terminal of the power source 12 is grounded.

[0018] The DC-DC converter 14 converts the voltage of the power source 12. The DC-DC converter 14 steps up or steps down the voltage of the power source 12. The DC-DC converter 14 is connected to the positive terminal of the power source 12.

[0019] The ignition coil 16 functions as a step-up transformer. The ignition coil 16 includes a primary coil 16a and a secondary coil 16b that are magnetically coupled to each other. The primary coil 16a has a first end t1 and a second end t2. The first end t1 is electrically connected to the DC-DC converter 14. The second end t2 is electrically connected to the switch 20 described later. The secondary coil 16b has a third end t3 and a fourth end t4. The third end t3 is electrically connected to the ignition plug 26. The fourth end t4 is grounded.

[0020] The ignition coil 18 functions as a step-up transformer. The ignition coil 18 includes a primary coil 18a and a secondary coil 18b that are magnetically coupled to each other. The primary coil 18a has a fifth end t5 and a sixth end t6. The fifth end t5 is electrically connected to the DC-DC converter 14. The sixth end t6 is electrically connected to the switch 22 described later. The secondary coil 18b has a seventh end t7 and an eighth end t8. The seventh end t7 is electrically connected to the ignition plug 26. The eighth end t8 is grounded.

[0021] Switch 20 switches the supply and cut-off of the primary current from the power supply 12 to the primary coil 16a. The switch 20 is, for example, an IGBT (Insulated Gate Bipolar Transistor). The collector of the switch 20 is connected to the second end t2 of the primary coil 16a. The emitter of the switch 20 is grounded. The gate of the switch 20 is connected to the control device 10.

[0022] Switch 22 switches the supply and cut-off of the primary current from the power supply 12 to the primary coil 18a. The switch 22 is, for example, an IGBT. The collector of the switch 22 is connected to the sixth end t6 of the primary coil 18a. The emitter of the switch 22 is grounded. The gate of the switch 22 is connected to the control device 10.

[0023] The secondary coil 16b generates a secondary current in response to the cut-off of the primary current. More specifically, when the switch 20 is controlled to be in the on state, the primary current is supplied from the power supply 12 to the primary coil 16a via the DC-DC converter 14. As a result, energy is stored in the primary coil 16a. Then, when the switch 20 is controlled to be in the off state, the primary current is cut off. Thereby, the secondary coil 16b generates a high voltage by electromagnetic induction. The secondary coil 16b supplies the secondary current to a spark plug 26 described later by this high voltage. Note that the secondary coil 18b also generates a secondary current in response to the cut-off of the primary current by the same principle as the secondary coil 16b.

[0024] The spark plug 26 has a pair of electrodes exposed to the combustion chamber of the internal combustion engine. The spark plug 26 generates a spark between the pair of electrodes by the secondary current generated in response to the cut-off of the primary current. Thereby, the spark plug 26 burns the air-fuel mixture in the combustion chamber of the internal combustion engine. The spark plug 26 is electrically connected to the third end t3 of the secondary coil 16b and the seventh end t7 of the secondary coil 18b.

[0025] The current sensor 24 generates a current signal Sig1 indicating the value of the secondary current supplied to the ignition plug 26. The current signal Sig1 is output to the control device 10 described later. The current sensor 24 is electrically connected to the third terminal t3 of the secondary coil 16b, the seventh terminal t7 of the secondary coil 18b, and the ignition plug 26.

[0026] The control device 10 is an ECU (Electric Control Unit). The control device 10 includes a CPU (Central Processing Unit), a RAM (Random Access Memory), and a ROM (Read Only Memory). The control device 10 controls the operations of the DC-DC converter 14 and the switches 20, 22 by executing the programs stored in the ROM.

[0027] Specifically, the control device 10 controls the operations of the switches 20, 22 so as to generate a plurality of secondary currents in the secondary coils 16b, 18b in one cycle of the internal combustion engine. In the present embodiment, as shown in FIG. 2, ten secondary currents are generated. Therefore, the control device 10 generates five secondary currents in the secondary coil 16b by switching the switch 20 on and off five times. The control device 10 generates five secondary currents in the secondary coil 18b by switching the switch 22 on and off five times. Note that the control device 10 generates secondary currents alternately in the secondary coil 16b and the secondary coil 18b.

[0028] As shown in FIG. 2, when the slope KN of the plurality of secondary currents with respect to time in the Nth cycle is positive, the control device 10 controls the ignition system 1 so that the slope KN+1 of the plurality of secondary currents with respect to time in the (N + 1)th cycle decreases as shown in FIG. 3. In this specification, the slope of the plurality of secondary currents with respect to time is calculated, for example, by the least squares method.

[0029] [Operation of the control device 10] Next, the operation of the control device 10 will be described with reference to the drawings. FIG. 4 is an explanatory diagram of noise removal. FIG. 5 is a flowchart executed by the control device 10. The control device 10 executes the flowchart of FIG. 5 by reading out the program recorded in the ROM.

[0030] This process is started when the driver starts the internal combustion engine. The control device 10 sets N to 1 (step S1).

[0031] Next, the control device 10 acquires the relationship between the multiple secondary currents and time in the Nth cycle shown in FIG. 2 based on the current signal Sig1 output from the current sensor 24 (step S2). Further, the control device 10 removes noise from the relationship between the multiple secondary currents and time in the Nth cycle (step S3). Specifically, as shown in FIG. 4, the RAM of the control device 10 stores the relationship between the multiple secondary currents and time in the (N - M)th cycle to the relationship between the multiple secondary currents and time in the (N - 1)th cycle. M is a natural number smaller than N. The control device 10 reads out from the RAM the relationship between the multiple secondary currents and time in the (N - M)th cycle to the relationship between the multiple secondary currents and time in the (N - 1)th cycle. Next, the control device 10 divides the value obtained by adding the multiple secondary currents in the (N - M)th cycle to the multiple secondary currents in the Nth cycle by M + 1. That is, as shown in FIG. 4, the control device 10 calculates the average value of the multiple secondary currents in the (N - M)th cycle to the multiple secondary currents in the Nth cycle. Thereby, noise is removed from the relationship between the multiple secondary currents and time. Such an operation is realized by a digital low-pass filter. Hereinafter, the value obtained by dividing the value obtained by adding the multiple secondary currents in the (N - M)th cycle to the multiple secondary currents in the Nth cycle by M + 1 is called the average secondary current.

[0032] Next, the control device 10 calculates a calculated slope KA of the secondary current with respect to time based on the average secondary current in FIG. 4 (step S4). More specifically, the control device 10 calculates the calculated slope KA of the secondary current with respect to time in the plurality of secondary currents in the average secondary current in FIG. 4 using the least squares method. Thus, in the calculation steps shown in steps S3 and S4, the control device 10 calculates the calculated slope KA of the secondary current with respect to time based on the plurality of secondary currents in one or more cycles before the Nth cycle.

[0033] Next, the control device 10 determines whether the calculated slope KA is greater than the target slope K0 (step S5). In step S5, the control device 10 determines whether the energy input to the primary coils 16a and 18a is appropriate. More specifically, when the energy input to the primary coils 16a and 18a is too large, the ignition plug 26 cannot sufficiently consume the secondary current. As a result, the secondary current increases with the passage of time, so the calculated slope KA becomes positive. On the other hand, when the magnitude of the energy input to the primary coils 16a and 18a is appropriate, the ignition plug 26 can sufficiently consume the secondary current. As a result, the secondary current decreases with the passage of time, so the calculated slope KA becomes negative. However, when the energy input to the primary coils 16a and 18a is too small, the secondary current is insufficient. In this case, the calculated slope KA becomes negative and the absolute value of the calculated slope KA increases.

[0034] Therefore, the slope when the energy input to the primary coils 16a and 18a is appropriate is set as the target slope K0. The target slope K0 is negative. The target slope K0 is a value obtained through experiments. When the calculated slope KA is greater than the target slope K0, the control device 10 determines that the energy input to the primary coils 16a and 18a is too large. In this case, this process proceeds to step S6. When the calculated slope KA is not greater than the target slope K0, the control device 10 determines that the energy input to the primary coils 16a and 18a is too small. In this case, this process proceeds to step S7.

[0035] When the calculated slope KA is greater than the target slope, the control device 10 reduces the energy input to the primary coils 16a and 18a (step S6). More specifically, the control device 10 reduces the energy input to the primary coils 16a and 18a by reducing the voltage output by the DC-DC converter 14. As a result, as shown in FIG. 3, the slope KN+1 of the multiple secondary currents with respect to time in the (N + 1)-th cycle approaches the target slope K0 from the calculated slope KA. Further, the slope KN+1 of the multiple secondary currents with respect to time in the (N + 1)-th cycle approaches the target slope K0 more closely than the slope KN of the multiple secondary currents with respect to time in the N-th cycle. After that, this process proceeds to step S8.

[0036] When the calculated slope KA is less than the target slope, the control device 10 increases the energy input to the primary coils 16a and 18a (step S7). More specifically, the control device 10 increases the energy input to the primary coils 16a and 18a by increasing the voltage output by the DC-DC converter 14. As a result, the slope KN+1 of the multiple secondary currents with respect to time in the (N + 1)-th cycle approaches the target slope K0 from the calculated slope KA. Further, the slope KN+1 of the multiple secondary currents with respect to time in the (N + 1)-th cycle approaches the target slope K0 more closely than the slope KN of the multiple secondary currents with respect to time in the N-th cycle. After that, this process proceeds to step S8.

[0037] As described above, in the control steps shown in steps S7 and S8, the control device 10 controls the ignition system 1 so that the slope KN+1 of the multiple secondary currents with respect to time in the (N + 1)-th cycle approaches the target slope K0 from the calculated slope KA. This control is achieved by feedback control. The feedback control is, for example, PID (Proportional Integral Differential) control.

[0038] In step S8, the control device 10 determines whether to end this process (step S8). In step S8, the control device 10 determines whether the driver has performed an operation to stop the internal combustion engine. If this process does not end, this process proceeds to step S9.

[0039] If this process does not end, the control device 10 increments N by 1 (step S9). After that, this process returns to step S2. Then, the processes of steps S2 to S9 are repeated for each cycle of the internal combustion engine.

[0040] [Effect] According to the control device 10, the power consumption of the ignition system 1 can be reduced. More specifically, decarbonization is required in the internal combustion engine. As technologies to meet such decarbonization requirements, for example, lean burn combustion technology and high EGR (exhaust gas recirculation) technology have been developed.

[0041] However, in an internal combustion engine to which lean burn combustion technology and high EGR technology are applied, the change in the combustion state is large. Therefore, in an internal combustion engine to which lean burn combustion technology and high EGR technology are applied, it is difficult to burn the air-fuel mixture. Therefore, in an internal combustion engine to which lean burn combustion technology and high EGR technology are applied, a large amount of energy is input to the spark plug, and a strong spark is generated at the spark plug (hereinafter referred to as strong ignition). Thereby, the air-fuel mixture is burned.

[0042] However, when strong ignition is performed, since the energy input to the spark plug increases, the power consumption of the ignition system increases. Furthermore, the combustion temperature of the air-fuel mixture rises, and the NOx concentration in the exhaust gas rises. Also, the spark plug and the ignition coil are likely to deteriorate.

[0043] Here, when the energy input to the primary coils 16a and 18a is too large, the ignition plug 26 cannot sufficiently consume the secondary current. As a result, since the second current increases with the passage of time, the slope KN becomes positive. Therefore, when the slope KN with respect to the time of the secondary current in multiple cycles in the Nth cycle is positive, the control device 10 controls the ignition system 1 so that the slope KN+1 with respect to the time of the secondary current in multiple cycles in the (N + 1)th cycle decreases. Thereby, according to the control device 10, the power consumption of the ignition system 1 can be reduced. Furthermore, an increase in the NOx concentration in the exhaust gas is suppressed, and deterioration of the ignition plug and the ignition coil is suppressed.

[0044] Also, when the energy input to the primary coils 16a and 18a is too large, the ignition plug 26 cannot sufficiently consume the secondary current. As a result, since the second current increases with the passage of time, the calculated slope KA becomes positive. On the other hand, when the magnitude of the energy input to the primary coils 16a and 18a is appropriate, the ignition plug 26 can sufficiently consume the secondary current. As a result, since the second current decreases with the passage of time, the calculated slope KA becomes negative. However, when the energy input to the primary coils 16a and 18a is too small, the second current is insufficient. Therefore, the calculated slope KA becomes negative and the absolute value of the calculated slope KA becomes large.

[0045] Therefore, the slope when the energy input to the primary coils 16a and 18a is appropriate is defined as the target slope K0. Then, the control device 10 calculates the calculated slope KA with respect to the time of the secondary current based on the secondary current in multiple cycles in one or more cycles before the Nth cycle. Furthermore, the control device 10 controls the ignition system 1 so that the slope with respect to the time of the secondary current in multiple cycles in the (N + 1)th cycle approaches the target slope K0 more than the calculated slope KA. Thereby, the energy input to the primary coils 16a and 18a becomes appropriate. From the above, according to the control device 10, the power consumption of the ignition system 1 can be reduced. Furthermore, an increase in the NOx concentration in the exhaust gas is suppressed, and deterioration of the ignition plug and the ignition coil is suppressed.

[0046] In addition, in the ignition system 1, for the control device 10 to perform the above control, it is sufficient to be able to acquire the secondary current. Therefore, the ignition system 1 may be provided with a current sensor 24. The current sensor 24 is an inexpensive resistor. Thus, the control device 10 does not require an expensive in-cylinder pressure sensor.

[0047] Also, in the calculation step, the control device 10 calculates the calculated slope KA after removing noise from the secondary currents in a plurality of cycles before the Nth cycle. As a result, the fine changes in the secondary currents in a plurality of cycles disappear. As a result, according to the control device 10, the calculation of the calculated slope KA becomes easy and accurate. Therefore, the control device 10 can input appropriate energy to the primary coils 16a and 18a.

[0048] (Other embodiments) The control device according to the present invention is not limited to the control device 10 and can be changed within the scope of the gist thereof.

[0049] Note that the internal combustion engine may have a plurality of combustion chambers. When there are a plurality of combustion chambers, a spark plug 26 is provided in each of the plurality of combustion chambers.

[0050] In the control step, the control device 10 controls the magnitude of the energy input to the primary coils 16a and 18a by controlling the operation of the DC-DC converter 14. However, the control device 10 only needs to control the magnitude of the energy input to the primary coils 16a and 18a, and the control method is not limited to this. The control device 10 may control the magnitude of the energy input to the primary coils 16a and 18a by controlling the operation of the switches 20 and 22.

[0051] Note that the number of ignition coils is not limited to 2. The number of ignition coils may be 1 or more. Similarly, the number of switches may be 1 or more.

[0052] Note that the vehicle may be a four-wheeled vehicle, a three-wheeled vehicle, or a two-wheeled vehicle. The two-wheeled vehicle is a lean vehicle in which the vehicle body tilts in the same direction as the traveling direction of the corner. The three-wheeled vehicle may be a lean vehicle or a vehicle that rolls in the direction opposite to the traveling direction of the corner.

[0053] Note that the internal combustion engine may be used as a power source for vehicles other than automobiles. Vehicles other than automobiles are, for example, ships, aircraft, etc. Also, the vehicle may or may not carry people. Further, the internal combustion engine may be used as a generator for generating the electric power of an EV (Electric Vehicle).

[0054] Note that the ignition system 1 does not include a cylinder pressure sensor. However, the ignition system 1 may include a cylinder pressure sensor for purposes other than the purpose of controlling the slope of the secondary current to reduce the power consumption in the ignition system.

[0055] Note that it is preferable that the control device 10 always performs the control shown in FIG. 4 during the period when the powerful ignition is being performed.

[0056] Note that in the ignition system 1, the DC-DC converter 14 is not an essential component. That is, the control device 10 is also applicable to the control device 10 in which the powerful ignition is not performed.

[0057] Note that the noise removal in step S3 is not an essential component. Therefore, in step S4 which is a calculation step, the control device 10 may calculate the slope KN of the secondary current with respect to time in a plurality of times in the Nth cycle as the calculated slope KA. Also, the control device 10 may calculate the slope of the secondary current with respect to time in a plurality of times in one cycle before the Nth cycle as the calculated slope KA. However, it is preferable that one cycle before the Nth cycle is close to the Nth cycle.

[0058] Note that the target inclination K0 may vary depending on the rotational speed of the crankshaft of the internal combustion engine. In this case, the correction coefficient calculated by experiment may be multiplied by the target inclination K0.

Explanation of Signs

[0059] 1: Ignition system 10: Control device 12: Power supply 14: DC-DC converter 16, 18: Ignition coil 16a, 18a: Primary coil 16b, 18b: Secondary coil 18b: Secondary coil 20, 22: Switch 24: Current sensor 26: Spark plug

Claims

1. A control device for an ignition system of an internal combustion engine, comprising a power source, one or more switches, one or more ignition coils, and an ignition plug, each of the one or more ignition coils includes a primary coil and a secondary coil that are magnetically coupled to each other, each of the one or more switches switches the supply and interruption of a primary current from the power source to the one or more primary coils, the one or more secondary coils generate a secondary current in response to the interruption of the primary current, the ignition plug generates a spark by the secondary current generated in response to the interruption of the primary current, the control device controls the operation of the one or more switches so as to generate the secondary current a plurality of times in one cycle of the internal combustion engine in the one or more secondary coils, the control device, a calculation step of calculating a calculated slope with respect to the time of the secondary current based on the plurality of secondary currents in one or more cycles before the Nth cycle; a control step of controlling the ignition system so that the slope with respect to the time of the plurality of secondary currents in the (N + 1)th cycle approaches a target slope closer than the calculated slope; executes, N is a natural number, the target slope is negative, Control device.

2. In the calculation step, the control device calculates the calculated slope after removing noise from the plurality of secondary currents in one or more cycles before the Nth cycle. The control device according to claim 1.

3. In the calculation step, the control device calculates the calculated slope based on a value obtained by dividing a value obtained by adding the plurality of secondary currents in the (N - M)th cycle to the plurality of secondary currents in the Nth cycle by M + 1, M is a natural number smaller than N, The control device according to claim 1 or claim 2.

4. A control device for an ignition system of an internal combustion engine, comprising a power source, one or more switches, one or more ignition coils, and an ignition plug, each of the one or more ignition coils includes a primary coil and a secondary coil that are magnetically coupled to each other, each of the one or more switches switches the supply and interruption of a primary current from the power source to the one or more primary coils, the one or more secondary coils generate a secondary current in response to the interruption of the primary current, the ignition plug generates a spark by the secondary current generated in response to the interruption of the primary current, The control device controls the operation of the one or more switches so as to generate a plurality of secondary currents in the one or more secondary coils in one cycle of the internal combustion engine. When the slope of the plurality of secondary currents with respect to time in the Nth cycle is positive, the control device controls the ignition system so that the slope of the plurality of secondary currents with respect to time in the (N + 1)th cycle decreases. N is a natural number. Control device.

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