Image forming apparatus with speed control function

1. An image forming apparatus configured to form a toner image on a sheet, comprising:

a transfer belt configured to bear and transfer the toner image to the sheet conveyed at given conveying speed;

a drive roller configured to drive the transfer belt;

a motor configured to drive the drive roller;

a speed detection roller held in contact with the transfer belt and configured to output speed data about rotational speed of the speed detection roller when the speed detection roller rotates as the transfer belt runs, the speed data being obtained during at least one revolution of the motor;

a motor speed output portion configured to output motor information on rotational speed of the motor; and

a control element configured to control the rotational speed of the motor,

wherein the control element includes:

a reference speed generator configured to generate first reference speed as a reference for the rotational speed of the motor and second reference speed as a reference for the rotational speed of the speed detection roller based on the given conveying speed of the sheet;

a first controller configured to generate a first error signal for reducing a difference between the rotational speed of the motor obtained from the motor information and the first reference speed;

a second controller configured to generate a second error signal for reducing a difference between the rotational speed of the speed detection roller obtained from the speed data and the second reference speed; and

an adder configured to add the first and second error signals and output a drive signal for driving the motor,

the speed detection roller includes:

a roller held in contact with the transfer belt and configured to rotate as the transfer belt runs;

a rotary disk configured to coaxially rotate with the roller and formed with a radial pattern;

a first sensor configured to read the pattern; and

a second sensor configured to read the pattern at a position different from the first sensor,

the first and second sensors are aligned along a diameter of the rotary disk;

the control element includes an averaging portion configured to output, as the speed data, an averaged sensor signal between signals from the first sensor and the second sensor, a first filter and a second filter connected in series with the first filter,

the control element outputs the speed data to the second filter,

the second filter converts the speed data output from the averaging portion into moving average speed data to remove a periodic component of the motor and outputs the moving average speed data to the first filter,

the first filter removes a first frequency variation component varying at a rotational frequency of the speed detection roller and a second frequency variation component varying at a rotational frequency of the motor from the moving average speed data, and

the second controller receives the moving average speed data from the first filter after removal of the first and second frequency variation components to generate the second error signal.

2. The image forming apparatus according to claim 1 , wherein

the first filter includes a first dip in correspondence to the drive roller, a second dip in correspondence to the motor, and a third dip in correspondence to the speed detection roller.

3. The image forming apparatus according to claim 1 , wherein the speed detection roller is held in contact with the transfer belt at an upstream position of the drive roller.

4. The image forming apparatus according to claim 3 , wherein the speed detection roller is held in contact with the transfer belt near the drive roller.

5. The image forming apparatus according to claim 1 , wherein

the first controller compares the first reference speed to the first rotational speed of the speed detection roller obtained from the speed data.

6. The image forming apparatus according to claim 1 , wherein

the second controller compares the second reference speed to the rotational speed of the speed detection roller obtained from the speed data.

7. The image forming apparatus according to claim 1 , wherein

the first error signal causes a decrease in a speed variation of the motor.

8. The image forming apparatus according to claim 7 , wherein

the second error signal causes a decrease in a speed variation resulting from eccentricity of the motor and the drive roller.

9. The image forming apparatus according to claim 7 , wherein

the decrease caused by the second error signal is less responsive than the decrease caused by the first error signal.

10. The image forming apparatus according to claim 9 , wherein

the first controller includes (i) a first subtracter configured to output a first information signal about a difference between the first reference speed and the first rotational speed of the speed detection roller obtained from the speed data, (ii) a first delay device configured to output a first delay component of the first information signal and (iii) a second subtracter that subtracts the first delay component from the first information signal to output a differential signal, and

the differential signal is used for generating the first error signal.

11. The image forming apparatus according to claim 10 , wherein

the second controller includes (i) a third subtracter configured to output a second information signal about a difference between the second reference speed and the rotational speed of the speed detection roller obtained from the speed data, (ii) a first adder that adds a correction value to correct the second reference speed and outputs a corrected signal, (iii) a second delay device configured to output a second delay component from the second information signal and (iv) a second adder that adds the second delay component to the corrected signal to output an integral signal, and

the second controller exclusively uses the integral signal to cause the less responsive decrease than the decrease caused by the first error signal.