JP4775059B2 - Command pattern generation method - Google Patents

Description

  The present invention relates to a command pattern generation method for minimizing an effective acceleration value when a motor is driven under a certain condition.

  The temperature rise of the motor when the motor is driven is roughly proportional to the square of the drive current. This is because the copper loss component obtained by multiplying the resistance of the motor by the square of the current occupies a large part due to the temperature rise of the motor. Therefore, reducing the drive current effective value leads to lowering the temperature rise of the motor.

  Since the motor drive current is controlled to have a proportional relationship with the normal torque, it is proportional to the motor acceleration. Accordingly, if a command pattern that minimizes the effective value of acceleration is generated when performing position control, the effective value of drive current can be minimized, and the temperature rise of the motor can also be minimized.

As a conventional method for specifying such acceleration effective value, the command pattern represented by the normalization function is transformed by performing scaling operation or time axis expansion / contraction operation, and the specified acceleration effective value is limited under the limit performance limit. A method for obtaining a value has been proposed (see, for example, Patent Document 1).
JP-A-9-128031

  However, although the effective acceleration value can be specified by the above method, a pattern in which this is the minimum cannot be indicated. Further, the normalization function itself is also a design matter of the user, and does not indicate what normalization function minimizes the effective acceleration value for a certain movement amount and tact.

  Furthermore, in order to realize this method, a very high-speed calculation capability and a complicated algorithm are required.

  SUMMARY OF THE INVENTION The present invention solves the above-described conventional problems, and an object thereof is to provide a method that can generate a command pattern that truly minimizes an effective acceleration value with a small amount of calculation.

In order to solve the above-described problem, the present invention designates the movement amount θmax and the tact tact, and when the time 0 to the time tact are equally divided into n (n is an integer of 2 or more), the section i (i = 1 to n) ) Is constant, the difference from the acceleration α (i + 1) of the adjacent section i + 1 is constant, the speed at time 0 and time tact is 0, and from time 0 to time tact This is a command pattern generation method in which the movement amount is θmax and the acceleration α (i) is expressed by the following (formula 11).

In the above description, as the number of divisions n increases, the speed gradually approaches a parabolic pattern .

  The acceleration effective value can be minimized under the constraints of the movement amount, the tact, and the division number n.

  When the movement amount θmax and the tact tact are specified and the time 0 to the time tact are divided into n equal parts (n is an integer of 2 or more), the acceleration α (i) in the section i (i = 1 to n) is constant, A command pattern is generated in which the difference from the acceleration α (i + 1) in the adjacent section i + 1 is constant, the speed at time 0 and time tact is 0, and the movement amount from time 0 to time tact is θmax. To do.

  FIG. 1 shows the case of n = 7 (odd number) and n = 8 (even number).

  When the movement amount θmax and the tact tact are specified and the time 0 to the time tact are equally divided into n (n is an integer of 2 or more), the acceleration α (i) in the section i (i = 1 to n) is constant. From this, it is understood that this command pattern has n degrees of freedom.

  Equation 1 can be derived from the condition that the difference between the acceleration α (i) in a certain section i and the acceleration α (i + 1) in the adjacent section i + 1 is constant.

  Therefore, if the acceleration α (1) in section 1 is set as A in equation 1, the acceleration α (i) in section i can be expressed by equation 2.

  Further, since the acceleration α (i) in the section i (i = 1 to n) is constant, the speed ω (i) at the time i × tact / n is obtained by integrating the acceleration from time 0 to time tact. Thus, Equation 3 is obtained.

  Substituting equation 2 into equation 3, equation 4 is obtained.

  The condition that the speed at time tact is 0 can be expressed by Equation 5 from ω (n) = 0 where i = n in Equation 4.

  When Expression 5 is substituted into Expression 2, acceleration α (i) is expressed by Expression 6.

  Further, when Expression 5 is substituted into Expression 4, the speed ω (i) is expressed by Expression 7.

  Finally, the position θ (i) at the time i × tact / n is the sum of the areas of the speeds for each section, and as can be seen from FIG. 1, the upper side and the lower side are ω (i−1). And ω (i) and the sum of the trapezoidal areas whose height is tact / n. When this is expressed by an equation, it becomes an equation 8.

  Further, when Expression 7 is substituted into Expression 8, the position θ (i) becomes Expression 9.

  The condition that the position θ (n) at the time tact is equal to the movement amount θmax can be expressed by Expression 10 from θ (n) = θmax set as i = n in Expression 9.

  By substituting this into Equation 9, Equation 11 for obtaining the acceleration α (i) in the section i is obtained.

  The acceleration effective value at this time is expressed by Equation 12.

  FIG. 2 shows a graph in which the normalized acceleration effective value is normalized by multiplying the division number n by the horizontal axis and multiplying the acceleration effective value by the square of the tact tact and dividing by the movement amount θmax.

  As the division number n is increased, the coefficient part of the normalized acceleration effective value approaches 6 / √3 which is the true minimum value. However, practically, it can be said that even if n = 10 divisions, the effective value can be suppressed to about 0.5% increase with respect to the true minimum value.

  Here, the rotary motor is taken as an example, but it is obvious that the same method can be used for a linear system such as a linear motor. Further, when this method is applied particularly for the purpose of reciprocating the same moving distance, it is very suitable because acceleration commands can be made continuous and vibrations are hardly excited.

  Furthermore, by considering the response characteristics from the command pattern to the acceleration effective value and using the output through the command pattern for the inverse model, the acceleration effective value can be minimized more accurately.

  As described above, since the command pattern generation method of the present invention can minimize the effective acceleration value of the motor and minimize the temperature rise of the motor, it is useful for miniaturization and energy saving of the motor.

Explanatory drawing of the command pattern in Example 1 of this invention Graph of command pattern division number n and normalized acceleration effective value of the present invention

Claims (1)

When the movement amount θmax and the tact tact are specified and the time 0 to the time tact are divided into n equal parts (n is an integer of 2 or more), the acceleration α (i) in the section i (i = 1 to n) is constant, and the difference between the acceleration interval i + 1 of the next alpha (i + 1) is constant and at a rate at time 0 and time tact is 0 and the movement amount from time 0 to time tact is .theta.max, acceleration alpha (i ) Is represented by the following (formula 11) .