20.

That is, Equation (c1) is derived by use of simultaneous equations of Equations (c2) and (c3) as follows.

tanθ2=cosα1·θh (c2)

tan(θp′)=cosα2·tan(θ2+ψ) (c3)

Note that “θ2” is the rotation angle of the intermediate shaft 18. Further, “θp” indicates a phase difference of the pinion angle θp from “θh.” More specifically, Equation (c4) is found from Equation (c2) and Equation (c3).

θp′=arctan(tan[arctan{tan(θh)·cos(α1)}+ψ]·cos(α2)) (c4)

Accordingly, the pinion angle θp is expressed by Equation (c5) as follows.

θp=θp′−arctan {tan(ψ)·cos(α2)} (c5)

By removing θp′ from Equation (c4) and Equation (c5), Equation (c1) is derived.

A compensating torque calculation process M20 is a process of calculating a steering torque Th by removing gravitational influence from a torque Trq. That is, the rotation center of the steering wheel 12 deviates from the gravitational center of the steering wheel 12. Accordingly, the torque Trq detected by the torque sensor 72 is a resultant force of a torque input in the steering wheel 12 by a driver and gravity. The compensating torque calculation process M20 is a process of calculating the steering torque Th by removing a gravitational component included in the torque Trq.

Here, the magnitude of the gravity that contributes to the torque Trq changes periodically depending on the steering angle θh. Accordingly, the compensating torque calculation process M20 is a process of calculating the steering torque Th with the use of the steering angle θh as an input.

In the meantime, the column shaft 14 can rotate around a tilt rotation center OT illustrated in FIG. 1. Hereby, the position of the steering wheel 12 is adjustable. Note that, in a case where a tilt angle θtl as a rotational amount around the tilt rotation center OT changes, even when the steering angle θh is the same, the magnitude of the gravity that contributes to the torque Trq changes. Accordingly, the compensating torque calculation process M20 is a process of calculating the steering torque Th with the use of the tilt angle θtl as an input.

An assist torque calculation process M22 is a process of calculating an assist torque Ta with the use of the steering torque Th as an input. That is, the assist torque calculation process M22 is a process of changing the magnitude of the assist torque Ta in accordance with the magnitude of the steering torque Th so as to achieve a suitable magnitude of the assist torque Ta for the steering intended by the driver. The assist torque calculation process M22 may be a process of causing the magnitude of the assist torque Ta at the time of the magnitude of the steering torque Th being large to be equal to or more than the magnitude of the assist torque Ta at the time of the magnitude of the steering torque Th being small. Further, the assist torque calculation process M22 may be a process of setting the assist torque Ta to different values for turning and for turning back even when the magnitude of the steering torque Th is the same.

An operation signal output process M24 is a process of generating and outputting an operation signal MS of the inverter 60 to control the torque of the assist motor 42 to the assist torque Ta, with the use of the assist torque Ta, the rotation angle θm, and the currents iu, iv, iw as inputs. Note that the operation signal MS is an operation signal to each switching element of the inverter 60 in practice.

Estimation of Tilt Angle

As described above, the tilt angle θtl changes. In a case where the tilt angle θtl changes, the first bending angle α1, the second bending angle α2, and the difference angle variable ψ also change. Accordingly, in the present embodiment, the first bending angle α1, the second bending angle α2, the difference angle variable ψ, and the tilt angle θtl are not values determined univocally by specifications but are variables that change when the driver changes the tilt angle θtl.

The following describes details of an estimation process of estimating these variables. FIGS. 4, 5 illustrate the procedure of the estimation process. The processes illustrated in FIGS. 4, 5 are implemented by the PU 52 executing the assist control program 54a stored in the storage device 54 repeatedly at a predetermined cycle, for example.

In a series of processes illustrated in FIG. 4, the PU 52 first determines whether or not an update flag F is “1” (S10). In a case where the update flag F is “1,” the update flag indicates execution of a process of updating the variables. In a case where the update flag F is “0,” the update flag indicates non-execution of the process of updating the variables.

In a case where the PU 52 determines that the update flag F is “0” (S10: NO), the PU 52 determines whether or not an activation switch is just switched from an OFF state to an ON state (S12). The activation switch is a switch for bringing the vehicle to a runnable state. For example, in a case where only an internal combustion engine is provided as a thrust generation device in the vehicle, the activation switch may be an ignition switch. Further, in a case where the thrust generation device in the vehicle includes a motor, the activation switch may be a switch configured to open and close an electrical path between the motor and a battery.

In a case where the PU 52 determines that the activation switch is switched to the ON state (S12: YES), the PU 52 substitutes “1” into the update flag F (S14). In a case where the PU 52 makes an affirmative determination in the process of S10, or in a case where the PU 52 ends the process of S14, the PU 52 acquires a pinion angle θp (S16). Further, the PU 52 acquires a steering angle θh by communication with the upper ECU 80 (S18). Then, the PU 52 stores a set of the pinion angle θp and the steering angle θh in the storage device 54 (S20). The pinion angle θp and the steering angle θh are synchronous data. This can be achieved by setting a period of the series of processes illustrated in FIG. 5 to a reception interval of the steering angle θh, for example.

Subsequently, the PU 52 determines whether or not the difference between a maximum value and a minimum value among absolute values of the steering angle θh, stored by the process of S20, is equal to or more than a predetermined value Δth (S22). When the PU 52 determines that the difference is a predetermined value Δth or more (S22: YES), the PU 52 finds a first bending angle α1, a second bending angle α2, and a difference angle variable ψ by the method of least squares (S24).

That is, for each set of the pinion angle θp and the steering angle θh stored in the process of S20, the PU 52 calculates the square of the difference between a value obtained by substituting the pinion angle θp into the right side of Equation (c1) and the steering angle θh. Then, the PU 52 searches for the first bending angle α1, the second bending angle α2, and the difference angle variable ψ that minimize the sum total of respective squares of the differences of the sets of the pinion angle θp and the steering angle θh stored in the process of S20.

Subsequently, the PU 52 updates the first bending angle α1, the second bending angle α2, and the difference angle variable ψ defined in the relationship definition data 54b (S26). Subsequently, the PU 52 calculates respective coordinates of a point A and a point B illustrated in FIG. 6 (S28 in FIG. 5).

In FIG. 6, an axial center on an end part side connected to the steering wheel 12 out of end parts of the column shaft 14 is taken as the point A. Further, the point B is the center of the joint cross 16c of the first Cardan joint 16. A point C is the center of a joint cross of the second Cardan joint 20. Further, a point D is one point on the rotational central axis of the pinion shaft 22. The point D is introduced to define a vector parallel to the pinion shaft 22 together with the point C.

As described above, since the intermediate shaft 18 expands and contracts, when the tilt angle θtl changes, the distance between the point B and the point C changes. In the meantime, since the point B rotates around the tilt rotation center OT, the distance between the tilt rotation center OT and the point B does not change depending on the change in the tilt angle θtl. Similarly, the distance between the tilt rotation center OT and the point A also does not change. In consideration of them, coordinates (xa, ya, za) of the point A and coordinates (xb, yb, zb) of the point B that are six unknowns are calculated by use of six simultaneous equations Eq1 to Eq6.

Here, Equation Eq1 is an equation about the square of the length between the tilt rotation center OT and the point A. The square of the length is a predetermined fixed value. Further, coordinates (xO, yO, zO) of the tilt rotation center OT are also fixed values. Mapping data 54c stored in the storage device 54 illustrated in FIG. 1 includes data about the coordinates of the tilt rotation center OT, and data about the square of the length.

Equation Eq2 is an equation obtained by substituting coordinate components of the point A into an equation expressing a plane on which the point A and the point B are present. The plane does not change depending on the change in the tilt angle θtl. The mapping data 54c includes data defining an equation expressing the plane.

Equation Eq3 is an equation expressing the inner product of a vector advancing from the point B to the point A and a vector advancing from the point B to the point C by use of the first bending angle α1. The mapping data 54c includes data defining coordinates of the point C.

Equation Eq4 is an equation about the square of the length between the tilt rotation center OT and the point B. The square of the length is a predetermined fixed value. The mapping data 54c includes data related to the square of the length.

Equation Eq5 is an equation obtained by substituting coordinate components of the point B into the equation expressing the plane on which the point A and the point B are present. Equation Eq6 is an equation expressing the inner product of a vector advancing from the point C to the point B and a vector advancing from the point C to the point D by use of the second bending angle α2.

Subsequently, the PU 52 calculates the vector advancing from the point B to the point A, by use of the coordinate components found by the process of S28 (S30). Then, the PU 52 calculates the tilt angle θtl (S32). The tilt angle θtl is quantified as an angle formed by a direction advancing from the point B to the point A relative to a direction advancing from a reference point B0 to a reference point A0 illustrated in FIG. 6, as an example. The reference point B0 is a reference point for the point B. The reference point A0 is a reference point for the point A. In a case where the steering wheel 12 is at a reference position, the point A is placed at the reference point A0. Further, in a case where the steering wheel 12 is at the reference position, the point B is placed at the reference point B0.

The PU 52 calculates the tilt angle θtl based on the inner product of a vector advancing from the reference point B0 to the reference point A0 and the vector advancing from the point B to the point A, the distance between the reference point B0 and the reference point A0, and the distance between the point B and the point A. The mapping data 54c includes data defining the vector advancing from the reference point B0 to the reference point A0.

Then, the PU 52 substitutes “0” into the update flag F (S34). Note that, in a case where the PU 52 ends the process of S34, or in a case where the PU 52 makes a negative determination in the process of S12 or S22, the PU 52 ends the series of processes illustrated in FIGS. 4, 5 once.

Operations and Effects of Present Embodiment

The PU 52 estimates the first bending angle α1, the second bending angle α2, and the difference angle variable ψ based on Relational Expression (c1) by use of sequential data of the steering angle θh and the pinion angle θp. Then, the PU 52 calculates coordinate components of the point A and the point B by use of the first bending angle α1, the second bending angle α2, and the difference angle variable ψ. Then, the PU 52 calculates the tilt angle θtl based on the coordinate components of the point A and the point B. With the use of the tilt angle θtl, the PU 52 can remove the influence of the gravitational component on the torque Trq with accuracy and grasp the steering torque Th.

Correspondence

The correspondence between what is described in the above embodiment and what is described in the field of “SUMMARY” is as follows. In the following description, the correspondence is described for each number of the means for solving the problem described in the field of SUMMARY.

[1] The steering computing device corresponds to the control device 50. The input shaft corresponds to the column shaft 14. The output shaft corresponds to the pinion shaft 22. The bending angle acquisition process corresponds to the processes of S20 to S24. The tilt angle calculation process corresponds to the processes of S28 to S32. The mapping data corresponds to the mapping data 54c. The mapping corresponds to a mapping achieved by the processes of S28 to S32.

[2] The “rotation center of the first Cardan joint” corresponds to the point B. The “rotation center of the second Cardan joint” corresponds to the point C. The “vector parallel to the reference direction” corresponds to the vector advancing from the reference point B