LOGO! Pulse-to-Analog Conversion for Paper Winder Speed Control

1. Winder Control Problem Statement

Paper, foil, film, and textile winders share a common motion control problem: as material accumulates on a take-up roll, the effective winding diameter grows from an empty core (D_min, typically 70-150 mm) to a full roll (D_max, often 600-1500 mm). Holding the linear (web) velocity constant at the material surface requires the rotational speed of the drive shaft to decrease in inverse proportion to the diameter. At the same time, a constant web tension must be maintained to prevent slack, telescoping, or web breaks.

The reference design in this article uses:

• A Siemens LOGO! 8 (6ED1052-1xx08-0BA1 series) logic module as the supervisory controller.
• An ultrasonic distance sensor with pulse-frequency output for roll diameter measurement.
• A 0-10 V potentiometer (AI1) for the operator setpoint of linear speed.
• The internal PI controller block of LOGO! Soft Comfort (V8.3 or later).
• An analog output 0-10 V (AQ1) to command the AC drive or DC motor controller.

2. Winder Kinematics

The fundamental relationship between surface (linear) velocity and shaft speed is:

v = π · D · n / 60

Where:

• v = linear web velocity, m/s
• D = current roll diameter, m
• n = motor shaft speed, rpm (post-gearbox if a reducer is fitted)

Rewriting for the required motor speed at a target linear velocity:

n = 60 · v / (π · D)

For an empty core of 100 mm and a full roll of 600 mm at a target linear velocity of 1 m/s, the motor must run at:

• 191 rpm empty (D = 0.1 m)
• 31.8 rpm full (D = 0.6 m)

A 6:1 speed range must be commanded from a single 0-10 V reference. The diameter signal becomes the divisor, so the diameter measurement quality dominates the closed-loop behavior. A 2 % error in diameter becomes a 2 % error in linear velocity at the material surface, which in turn maps to a 2 % error in web tension on a typical dancer-loaded winder.

2.1 Inertia and Friction Compensation

For high-speed winders (v > 5 m/s) or large roll-mass applications, the steady-state equation above is insufficient. The torque balance at the winder shaft is:

T_motor = T_tension · (D/2) + J · dω/dt + T_friction + T_wind_loss

Where:

• T_tension = web tension × radius
• J = combined roll and motor inertia (kg·m²). For a solid roll, J = 0.5 · m · r²; for a hollow core, integrate across the wall thickness
• dω/dt = angular acceleration, rad/s²
• T_friction = bearing and seal friction (typically 1-3 % of rated torque)
• T_wind_loss = hysteresis and eddy-current loss in the wound material (small for paper, significant for metallized film)

The acceleration term is non-negligible when the diameter doubles during a single unwind cycle. For a 1 m/s line accelerating at 0.5 m/s², the required torque correction is J · (2 · a / D) and changes by a factor of 6 across the roll build. In a LOGO!-based architecture this term is usually omitted; the drive's internal speed loop absorbs the disturbance within its bandwidth. For winding where diameter doubles faster than the drive's ramp rate, add a derivative term to the LOGO! output or use the VFD's built-in inertia compensation.

3. Ultrasonic Sensor with Pulse Output

Common industrial ultrasonic sensors (Banner Q4X series, SICK UC4, IFM UGT, Pepperl+Fuchs UB-series) typically emit an analog 0-10 V or 4-20 mA signal. A smaller subset offers a frequency or pulse-width modulated output, which is more robust against electrical noise on long cable runs (10-30 m typical between sensor and control cabinet) because each edge can be re-clocked at the receiver. When the sensor is specified to translate distance to pulse frequency:

f = f_min + (D_max - d) · (f_max - f_min) / (D_max - D_min)

Where:

• d = measured distance from sensor face to roll surface, m
• D_max, D_min = physical roll diameter extremes (or distance extremes, depending on sensor convention)
• f_min, f_max = sensor output frequency at the corresponding extremes

A typical full-scale bandwidth is 100 Hz to 2 kHz. The 2 kHz figure cited in the source is the worst-case input frequency, which sets the high-speed counter requirements. Where a non-frequency-output sensor is already installed, a distance-to-frequency converter module (Phoenix Contact MINI MCR-F-UI-UI, or a generic V/F converter) can be inserted between the sensor's analog output and the LOGO! HSC input.

4. LOGO! Hardware Selection

Confirm the LOGO! base module has high-speed inputs and an analog output. The following catalog numbers apply to the LOGO! 8 generation (Firmware FS04 and later):

Reference: see the Siemens Industry Online Support LOGO! 8 system manual (entry ID 109741041) for the high-speed input frequency ratings per firmware version and for the input circuit schematics. With firmware FS04 and later, the LOGO! 8 high-speed counter is rated up to 5 kHz on I3-I6 of the 12/24 V variants. The 230 V variant does not support high-speed counting - this is a common field mistake and is the first item on the troubleshooting matrix.

5. Frequency-to-Analog Conversion: Three Implementation Options

5.1 Option A - Time-Windowed Counting Inside LOGO!

The high-speed counter (HSC) block in LOGO! Soft Comfort supports up/down counting with configurable gate and reset inputs. The procedure below is the recommended path when only LOGO! hardware is available.

1. Wire the ultrasonic sensor output to terminal I3 (24 V sourcing, rising-edge count).
2. Insert a "High-Speed Counter" block. Set direction to "up", enable the "On" gate permanently via a digital marker.
3. Add a "Pulse Generator" (Blinker) block configured as asymmetric, with PT = 0.5 s and a marker output (M1) that pulses high for one cycle every 500 ms.
4. Use M1 to drive the "R" (reset) input of the HSC, so the count is cleared at the end of every window.
5. Capture the count value just before reset using an edge-triggered latch block: trigger on the falling edge of M1 into a marker word MW10. This is the engineering trick that recovers the count without losing the live count during the window.
6. Convert the linearized frequency to a 0-1000 scaled value (0-10 V after analog amplifier offset/gain) using the "Analog Amplifier" math block: f_avg_Hz = MW10 / 0.5 = 2 · MW10.
7. Apply scaling for diameter: D_m = 2 · (S - d), where d is the linearized distance in metres. S is a parameter entered in the arithmetic block.
8. Compute the speed setpoint: n_setpoint_rpm = 60 · v_setpoint / (π · D_m).

Pro: no external hardware. Con: at 2 kHz input the count over 0.5 s is 1000 pulses, so the quantization is 1 Hz per LSB. For a 100-2000 Hz sensor, the effective resolution is 9-10 bits, which is acceptable for winding but not for precision slitting or for very thin material where tension is critical.

5.2 Option B - External F/U or F/I Converter

The Phoenix Contact MINI MCR-F-UI-UI (Order No. 2902050) accepts a frequency or pulse input from 0.002 Hz to 200 kHz and outputs a configurable 0-10 V, 0-20 mA, or 4-20 mA signal. The 0-10 V output is wired directly to the LOGO! AI1 (or to the drive speed reference) and the LOGO! HSC input is no longer required for this signal - it can be replaced by a plain digital input for fault monitoring.

Pro: clean analog signal, 200 kHz bandwidth eliminates the LOGO! cycle-time bottleneck. Con: extra panel space, additional wiring, additional cost (~150 EUR per unit). The 35 ms response time still allows the LOGO! PI block to operate at 0.5 s without becoming the bottleneck.

5.3 Option C - LOGO! as Diameter Indicator, Drive Closes the Loop

For new installations, the recommended architecture is to place the PI loop inside the AC drive (VFD) and have LOGO! supply a corrected analog speed reference. ABB ACS580, Danfoss VLT Micro FC-051, Schneider ATV320, and Siemens V20 all support PID with external setpoint and feedback. LOGO! then only computes the diameter-compensated speed reference and transmits it via 0-10 V. See Danfoss drives for winding and unwinding for the application pattern and the ABB DCS800 Winder Physics manual (G563e) for the equations.

6. Scaling Math for the Diameter Path

Assume the ultrasonic sensor is mounted at a fixed standoff distance S from the roll axis. The roll diameter is:

D = 2 · (S - d)

Where d is the measured distance from sensor face to roll surface. The sensor's frequency output is:

f(d) = f_max - (f_max - f_min) · (d - d_min) / (d_max - d_min)

Combining and substituting into the speed equation:

n_setpoint = (60 · v_setpoint) / (π · 2 · (S - d))

For 0-10 V output to a drive scaled 0-50 Hz (or 0-1500 rpm):

V_AQ1 = 10 · n_setpoint / n_max

Worked example: S = 0.5 m, v_setpoint = 1.0 m/s, n_max = 1500 rpm, d_min = 0.05 m (full roll), d_max = 0.45 m (empty core).

• Empty core, d = 0.45 m: D = 0.10 m, n = 191 rpm, V_AQ1 = 1.27 V
• Full roll, d = 0.05 m: D = 0.90 m, n = 21.2 rpm, V_AQ1 = 0.14 V

The full 0-10 V range is never used if the drive is configured 0-max; instead, configure the drive's analog input for the actual speed range used (e.g., 0-200 rpm) to obtain 0-10 V across the operating speed. This is configured in the drive's parameter block (e.g., ABB parameter group 99, Schneider ATV320 conf menu, Danfoss FC-051 parameter 3-02/3-03). Rescaling the drive's analog input to a tight range is the single most common cause of resolution loss on retrofits where the application was originally implemented on a 0-10 V analog board with 8-bit DAC.

7. PI Controller Configuration in LOGO! Soft Comfort

Insert the "PI Controller" block from the regulators folder. Configuration values:

The PI block updates every LOGO! cycle (0.3-0.5 s typical for a small program). For tension-critical applications, supplement with a feed-forward term by adding the diameter-compensated speed reference directly to the AQ output via an analog adder; the PI block only trims the residual error. The feed-forward path also gives the system a non-zero output during PI saturation (drive at clamp), preventing the integrator from winding up and producing a large overshoot when the disturbance clears.

8. Program Structure

Block order in LOGO! Soft Comfort (V8.3+ recommended, project file .lsc):

1. I3 → High-Speed Counter (HSC), configured as up-counter with continuous count.
2. B001 → Pulse generator (PT = 0.5 s), output M1.
3. M1 → drives the reset input of the HSC.
4. B002 → "Edge-triggered latch" capturing the HSC count into a marker word MW10 on the falling edge of M1 (i.e., just before the counter is reset).
5. B003 → "Arithmetic" block: f_Hz = MW10 / 0.5. Output range scaled to 0-2000 corresponding to 0-10 V after the next amplifier.
6. B004 → "Analog amplifier" with gain = 0.005 to convert 0-2000 Hz → 0-10 V scaled value, stored in AQ1 if used as the diameter indicator only, or routed onward to the diameter calculation.
7. B005 → "Arithmetic" block computing D = 2 · (S - d_sensor), with S as a constant offset parameter entered in the block.
8. B006 → "Arithmetic" block computing n_setpoint = K1 / D, where K1 = 60 · v_setpoint / π.
9. B007 → PI Controller, SP from AI1, PV from the actual linear velocity feedback (use a separate speed sensor, e.g., a tachogenerator or second frequency channel on the take-up motor).
10. B008 → Analog adder: AQ1 = feedforward_n_setpoint + PI_output.

Constant K1 and S are entered in the arithmetic block's parameter table. Use the LOGO! display to view the live value of MW10 (raw count), MW12 (computed D in mm), and MW14 (computed n_setpoint in rpm) during commissioning. The display pages are configured under Tools → Parameter VM Mapping in LOGO! Soft Comfort.

9. Wiring Diagram

10. Commissioning Procedure

1. Sensor check. With the roll empty, measure the distance from sensor face to the empty core. Confirm the sensor output frequency at d_max and d_min against the datasheet. If the frequency is at the wrong end of the range, swap the sensor's rising/falling direction in its configuration menu or invert the HSC direction.
2. LOGO! wiring verification. Use the LOGO! display in online mode (LOGO! Soft Comfort → Tools → Online → Display) to read the live HSC value at I3 while the sensor is running. The count must increment in real time, not in 0.5 s steps.
3. Time-window alignment. Set the pulse generator to 500 ms, monitor MW10 after the latch. The value should equal 0.5 · f_Hz within ±1 count. Use a separate frequency counter on the sensor output as the ground truth.
4. Empty-core test. With the drive in manual mode (PI disabled, AQ1 forced to a fixed value), command 1.27 V and measure the resulting motor speed. Confirm it is 191 rpm ±5 %.
5. Full-roll test. Wind a known length of material, command 0.14 V, measure 21.2 rpm.
6. Close the loop. Enable the PI block. Set Kp = 0.5, Tn = disabled (pure P). Apply a step disturbance (operator turns the pot). Tune Kp upward until you see one or two oscillations, then back off 30 %.
7. Add integral action. Enable Tn at 5.0 s, halve it on each step until you see a small overshoot, then increase Tn by 50 %.
8. Tension verification. Measure the actual web tension with a load cell or tension roller. Tension variation should be < ±5 % of setpoint across the full roll build. For tension-critical applications such as film or foil, add a tension feedback signal into the PI block and switch the controller from velocity-mode to tension-mode.

11. Verification Tests

12. Troubleshooting Matrix

13. Common Engineering Pitfalls

• Forgetting that LOGO! HSC counts on the rising edge only; if the sensor is open-collector, add a pull-up to 24 V.
• Forgetting the LOGO! scan time. The HSC increments asynchronously, but the program only sees the value at the next cycle. A 0.5 s window must be measured with a hardware timer (the pulse generator block) and not by counting program cycles.
• Computing diameter from frequency with a linear equation and then dividing by it; a 1 % error in the linear approximation becomes a 5-10 % error in the speed reference near full roll. Use a look-up table (LOGO! Soft Comfort analog curve block) if the sensor's response is non-linear.
• Operating the ultrasonic sensor into its dead-band (the near range within which it cannot detect). Verify the maximum roll diameter does not push the sensor into this zone.
• Running the PI block without anti-windup. LOGO! PI block has built-in anti-windup, but if the output is being fed to a clamped drive (AQ1 max set lower than PI block max), the integrator will keep winding up. Use a separate marker for the enable signal and a min/max clamp before the output.
• Forgetting to set the analog output range on the AM2 AQ module. The default after a cold start is 0-10 V; the module also supports 4-20 mA via DIP switch, and connecting a current input device to a voltage-output module will produce wrong readings.
• Mapping the LOGO! output to a drive parameter range that does not match the winder's full operating range. Always re-scale the drive's min/max speed parameters to the actual winder speed range, not the motor nameplate.

14. Unwinding (Payoff) Operation

The same architecture applies in reverse for an unwinder. The differences are:

1. As the unwind roll depletes, the diameter shrinks, so the required speed increases (the inverse of winding). The diameter equation becomes D_unwind = 2 · (d - S_unwind) if the sensor is mounted on the opposite side, or the same equation with the sign of the diameter change reversed in the LOGO! math block.
2. Web tension is usually controlled by a brake (or a regenerative drive in torque mode), not by a motor speed reference. The LOGO! computes a tension setpoint or a diameter-compensated torque reference, output via AQ1 to a tension controller.
3. Inertia compensation is more critical on unwinds because the roll's rotational inertia is decreasing as it shrinks. The acceleration torque term J · dω/dt may dominate and require an additional feed-forward term proportional to the rate of change of diameter.
4. When the roll is almost empty, the brake torque can spike as the remaining material tries to drag the roll. Add a stall-detection input (low frequency on HSC, meaning very small diameter) to clamp the brake output.

15. Tension Taper for Winders

A constant-tension winding profile produces a roll with high internal pressure at the core (because the same tension is wound onto a small radius, generating high radial force P = T/r). For sensitive materials (film, foil, non-wovens), a tension taper is applied: tension is highest at the start (small diameter) and decreases as the roll builds. A common taper is:

T(d) = T_0 · (D_core / D_current)^x

Where x ranges from 0.3 (light taper) to 0.7 (heavy taper). In LOGO!, this is a second arithmetic block applied to the setpoint path:

SP_after_taper = SP_AI1 · (D_core / D_current)^x

The exponent is implemented as a power block or as an exponential curve block. For non-critical applications, the linear approximation T(d) = T_0 · (1 - x · (D_current - D_core) / (D_max - D_core)) is adequate.

16. Advanced: Tension Control Extension

The architecture in this article is speed-controlled, not tension-controlled. For constant-tension winding, replace the linear velocity feedback with a tension sensor (load cell on a dancer roller, or a web tension transducer such as the Montano BS-02 or Loadstar Sensors DI-100) and let the PI block regulate tension instead. The diameter compensation remains as a feed-forward to bias the speed reference, with the tension loop trimming out the residual error. The Danfoss winding application note describes the load-cell-to-drive wiring in detail. The ABB DCS800 winder physics manual provides the explicit transfer functions for the closed-loop analysis, including the natural frequency of the dancer system and the recommended PI bandwidth for stable operation.

17. Web Transport Delay and Stability

The web itself introduces a transport delay from the winder to any downstream sensor (or from the unwind to the winder). For a 1 m/s web and a 2 m distance to the tension sensor, the delay is 2 s. The PI loop must be tuned slower than 1 / (2 · τ_delay) ≈ 0.25 Hz for stability. This is one reason the LOGO!'s 0.5 s cycle and 3-5 s integral time are well-suited: they are conservatively below the stability limit. For a multi-section machine with several tension zones, each zone's loop must be tuned to the longest delay in the controlled path, which is often the take-up reel itself.

18. Summary of Key Parameters