Resolving S7-313C FB41 PI Instability on Cable Spooler Winder

Problem Statement: S7-313C FB41 Spooler Instability

A common field complaint on SIMATIC S7-313C systems using FB41 "CONT_C" to regulate a cable spooler is that the loop is stable only when the reel is full. Between empty reel and mid-build diameter, the same proportional/integral set (GAIN = 0.08, TI = 510 ms) yields visible tension oscillation, while the same settings become stable once the reel approaches its outer diameter.

The symptom is not a defective FB41 instance, nor an undersized CPU. It is the expected behavior of a fixed-gain PI regulator controlling a process whose gain is itself a function of the roll diameter. This article describes the root cause, the FB41 parameter mappings involved, and three engineering solutions: gain scheduling in the PLC, drive-integrated PID on the SIMOREG 6RA70, and the PID Self Tuner available for S7-300/S7-400.

S7-313C Hardware Reference and FB41 Block Layout

The CPU 313C (6ES7313-5BF03-0AB0 and successors in the 313C-2 DP / 313C-2 PtP family) provides 32 KB of work memory, 0.1 µs bit execution, and 16 integrated DI / 16 DO. It supports the full PID library FB41/FB42/FB43 from the Standard Library > PID Control Blocks package.

The relevant I/O for a winder loop is typically:

FB41 inputs that matter for spooler tuning:

Reference: SIMATIC S7-300 CPU 31xC Technological Functions manual (entry ID 12429336 in the Siemens Industry Online Support). Detailed FB41 description: Standard Library - PID Control Blocks, also part of the S7-300 documentation set.

Figure 1 - FB41 inside OB35 of the S7-313C closes the tension loop around a SIMOREG 6RA70 DC drive and a load-cell-fed tension process variable.

Why a Cable Winder is a Non-Linear Process

A spooler couples a DC motor (via the 6RA70) to a growing roll of cable. Three physical quantities are explicit functions of the instantaneous roll radius r:

1. Process gain (torque to tension): T = F · r. For a given tension error, the motor torque that must be added scales linearly with r.
2. Reflected inertia: J = J_core + ½ · ρ · L · (r⁴ - r_core⁴). At empty reel, J is small; at full reel, J can be 10× to 30× larger.
3. Line-speed to angular-speed ratio: ω = v / r. For the same linear cable speed the motor must run faster when the reel is empty.

The consequence is that the open-loop gain between FB41's output (torque command) and the process variable (tension) varies roughly as 1/r at constant line speed, plus an additional inertia-dependent acceleration term:

K_process(r) ≈ 1 / (r · J_total)

With the supplied PI fixed at GAIN=0.08 and TI=510 ms, the closed-loop gain GAIN × K_process exceeds stability margins on an empty reel (high K_process) but is well-damped on a full reel (low K_process). The exact crossover where oscillation appears depends on line speed, cable cross-section, and dancer stiffness, but the symptom pattern - instability at small r and stability at large r - is the diagnostic fingerprint.

Figure 2 - Closed-loop gain as a function of roll radius. Stability margin is consumed in the empty-to-mid region and recovered only at full reel.

Root Cause Analysis: Variable Process Gain

Using FB41 with constant GAIN and TI assumes the plant is linear. The cable winder is not. Three concrete observations support the diagnosis:

Because the symptom is geometric (radius dependent), the fix must be geometric as well. Three field-proven remedies follow.

Solution 1 - Gain Scheduling with Multiple PI Sets in FB41

Maintain a parameter table indexed by roll-diameter bands. Move the controller from one PI set to another in OB35 based on a measured (or computed) diameter. This is the most common retro-fit on an existing S7-313C and requires no drive changes.

Recommended parameter table stored in a global DB (e.g. DB50):

Structured-text selector inside OB35 (run at 100 ms cycle, matching FB41 CYCLE):

// OB35 - 100 ms cyclic task
CASE "DB50".band OF
    1:  "FB41".GAIN  := "DB50".gain[1];
        "FB41".TI    := "DB50".ti[1];
    2:  "FB41".GAIN  := "DB50".gain[2];
        "FB41".TI    := "DB50".ti[2];
    3:  "FB41".GAIN  := "DB50".gain[3];
        "FB41".TI    := "DB50".ti[3];
    4:  "FB41".GAIN  := "DB50".gain[4];
        "FB41".TI    := "DB50".ti[4];
    5:  "FB41".GAIN  := "DB50".gain[5];
        "FB41".TI    := "DB50".ti[5];
END_CASE;
"FB41".CYCLE := T#100ms;
"FB41"();   // call FB41 with the active PI set

To avoid bump transfers, ramp GAIN and TI linearly between bands over a few seconds (e.g. 3 s transition window). Force I_ITL_ON := TRUE and load ITN_VAL with the previous output during the transfer to prevent integrator wind-up jumps.

Figure 3 - Diameter-driven gain-scheduling state machine. Transitions are debounced (50-100 ms) to prevent hysteresis flicker near a band edge.

Solution 2 - Drive-Based PID on SIMOREG 6RA70

For new installations, the more robust solution is to push the tension loop down into the 6RA70 itself. The 6RA70 contains internal PID structures (parameter groups nXXX for speed, PXXX for current/torque) plus a configurable technology controller. Reference: the SIMOREG 6RA70 parameter list and the Siemens application note Center Winder with SIMOREG 6RA70 (entry 9716319 in the Siemens Industry Online Support).

Wiring: the 6RA70 receives the cable tension setpoint (analog 0-10 V or PROFIBUS word) and the load-cell feedback. The drive closes the loop at 1-2 ms internally; the S7-313C is reduced to supervision, recipe selection, and diameter tracking. Use the drive's free function blocks (or a structured PLC function block on the S7-313C) to compute:

r = sqrt(r_core² + (N · d_cable · 2) / π)

where N is the turn count from an encoder and d_cable the cable diameter. Feed r back to the drive as a scaling factor for P225 (gain) using the 6RA70's internal multiplier. This way the gain-scheduling is performed inside the drive's fast loop without PLC scan delay.

Solution 3 - PID Self Tuner for S7-300 / S7-400

For engineers who prefer an automatic tuning routine rather than manual band-by-band adjustment, the PID Self Tuner integrated in the TIA Portal PID control package for S7-300/S7-400 identifies the process during a controlled step and computes Kp, TI, TD. The tuning pass can be executed once per diameter band; the resulting parameters are stored in DB50 and loaded by the gain-scheduling selector described above.

Repeat steps 1-6 for each diameter band. The Self Tuner is preferable to manual Ziegler-Nichols for non-linear plants because it explicitly models the dead-time and time constant that change with r.

Tension and Torque Compensation Formulas

Regardless of which solution is chosen, the loop should apply diameter compensation explicitly. The two compensation terms added in front of the drive's torque reference are:

Implement these as look-up tables in the PLC or as 6RA70 free blocks. With compensation in place, the residual that FB41 must close is the tension error only - a small-signal linear term that is far easier to tune with a single PI set.

Step-by-Step Commissioning Procedure

1. Validate the I/O. Force PV_PER from the S7-313C and confirm in STEP 7 / TIA Portal that the load-cell signal tracks the cable tension over the full reel range.
2. Run open-loop step test. Set MAN_ON := TRUE, hold MAN at 30 %, then at 60 % of motor rated torque. Record PV on the HMI trend for two diameter bands.
3. Compute process gain. K_process = ΔPV / ΔLMN for each band. Expect K_process(empty) > 3 × K_process(full).
4. Compile a band table. Populate DB50 with five PI sets using the Kp_r = Kp_full × r_full / r as a starting rule, and TI scaled proportionally to the inverse of the natural frequency.
5. Enable gain scheduling. Implement the CASE selector inside OB35 with the same cycle as CYCLE.
6. Switch to closed loop. Set MAN_ON := FALSE; verify LMN_HLM and LMN_LLM clamp the drive within safe current limits.
7. Run a step response per band. Apply a 5 % setpoint step at each diameter. Acceptable: overshoot < 8 %, settling time < 5 s, no oscillation.
8. Run a full-reel transition test. From empty to full at constant line speed. Adjust band boundaries if a hysteresis loop forms at a band edge.
9. Persist to recipe. Save DB50 as part of the HMI recipe so the tuning is restored on power-up.
10. Document safe-state behavior. Verify that on E-stop or dancer over-travel, FB41 is frozen (I_ITL_ON := TRUE) and the drive accepts the controller inhibit command.

Verification and Field Diagnostics

After commissioning, three live checks confirm the fix is correct:

Trend the FB41 instance variables on the HMI: LMN, PV_IN, ER, and the integrator state ITN_VAL. They are all in the FB41 instance DB and can be added to the standard PID control faceplate.

Troubleshooting Matrix