Siemens FB41 PID Tuning for AGC Strip Flatness Control Loops

1. Problem Overview: FB41 Oscillation in a Hydraulic AGC Loop

The reported fault is a classical dominant-time-constant mismatch between a slow hydraulic Automatic Gauge Control (AGC) actuator and a poorly configured SIMATIC S7 FB41 "CONT_C" continuous controller. The reported symptoms are:

• Setpoint (SP_INT) fixed at 3000 µm with a starting thickness of 28000 µm (cold-start travel of ~25 mm).
• Steady-state process value (PV_IN) fluctuating between -2945 µm and +3100 µm (peak-to-peak > 6 mm).
• Output manipulated continuously with no apparent settling.
• Only GAIN and TI used. TD (derivative time) = 0 and DEADB_W (dead band) = 0.
• OB1 scan time measured between 1 s and 5 s — already an order of magnitude larger than the actuator response.

Target specification from the user is ±2 µm at the setpoint. The current peak error of >6000 µm indicates a controller that is either (a) grossly over-gained with insufficient integral action, (b) being sampled far too slowly, (c) suffering from quantization noise, or — most likely — (d) a combination of all three. The fix is rarely a single parameter change; it requires a structured re-commissioning of the FB41 instance, its sample time, its derivative block, and the hydraulic valve I/O conversion.

2. AGC System Architecture and FB41 Placement

Hydraulic AGC systems regulate strip exit thickness by closed-loop positioning of a screwdown or hydraulic roll-gap actuator against a load cell (force) and/or position transducer. The control hierarchy is typically:

1. Level 0 — Load cell / LVDT / X-ray thickness gauge (PV feedback).
2. Level 1 — SIMATIC S7-300 or S7-400 FB41 CONT_C block (PID algorithm).
3. Level 2 — Hydraulic servo-valve driver, ±10 V or 4–20 mA output (LMN scaled to engineering units).

FB41 implements the ideal, parallel (non-interacting) PID algorithm:

LMN(t) = GAIN · [ e(t) + (1/TI)·∫e(t)dt + TD·de(t)/dt ] + LMN_OFF

where e(t) = SP − PV. Because the standard FB41 supports proportional, integral, and derivative branches, a default of TD = 0 reduces the controller to a PI structure. For a stiff hydraulic position loop the PI-only branch is workable, but the derivative term should be reintroduced (with TM_LAG filter) to damp the dominant mechanical resonance that is being excited at the start of the travel and is now showing up as the 6 mm steady-state hunting.

3. Root-Cause Analysis of the ±6 mm Oscillation

A 5 s scan time on a hydraulic actuator with a 100–200 ms dominant time constant violates the Shannon sampling rule and forces the integrator to fight itself. The first concrete action is therefore to move the FB41 call out of OB1 into a dedicated OB35 (cycle interrupt) at 100 ms.

4. FB41 Parameter Reference Table

The following table lists every FB41 instance-DB parameter that matters for AGC stability. Default values shown are for a fresh CONT_C block; do not run a hydraulic AGC loop with these defaults.

Parameter reference: SIMATIC S7-300/400 Standard PID Control — Function Block Manual.

5. Sampling-Time Rule (Section 9.3.1 of the Standard PID Manual)

The Siemens "Standard PID Control" reference manual gives a direct rule for the FB41 CYCLE input:

T_sample ≤ T_dominant / 6

For a hydraulic AGC, the dominant time constant of the combined valve–cylinder–load system is typically 80–200 ms. Therefore the FB41 sample time should be set between 15 ms and 35 ms. The acceptable engineering range is 50–100 ms, which is what OB35 in the default S7-300 / S7-400 CPU configuration provides.

6. Tuning Procedure — Step Response and Ziegler–Nichols

6.1 Prerequisites

• FB41 instance DB exists and is being called in OB35 with CYCLE = T#100ms.
• PV scaling PV_FAC and PV_OFF verified by injecting a calibration thickness.
• Manual mode operational: set MAN_ON = TRUE and MAN to a fixed output (e.g. 30 %).
• Trend recorder on PV_IN, LMN, and SP_INT (use the S7 Variable Table or a WinCC trend).

6.2 Open-Loop Step Test

1. From a steady state at 28000 µm, with the controller in manual, step MAN from 0 % to 20 %.
2. Record PV_IN until a new steady state is reached. Mark on the trend:
   • Td = dead time (transport delay) — time until PV first visibly changes.
   • Tu = time constant (63 % of the total step change).
   • Kp = (ΔPV/ΔLMN) process gain in µm / %.
3. Restore MAN to the original value and allow PV to settle back.

6.3 Apply Ziegler–Nichols PI Tuning

Using the Kp, Tu, and Td measured in §6.2, calculate the initial FB41 parameters from the open-loop Ziegler–Nichols PI rule:

GAIN_Kp = 0.9 · Tu / (Kp · Td)

TI = 3.3 · Td

For example, with a measured Kp = 800 µm/%, Tu = 1.2 s, Td = 0.25 s:

GAIN = 0.9 · 1.2 / (800 · 0.25) = 0.0054

TI = 3.3 · 0.25 s = 0.825 s → T#825ms

This will be intentionally aggressive; in §6.5 it will be detuned.

6.4 Closed-Loop Detuning (Quarter-Amplitude Decay)

1. Switch the FB41 to automatic (MAN_ON = FALSE).
2. Make a 5 % setpoint step (e.g. SP_INT 3000 → 3150 µm) and observe the response.
3. Adjust by quarter-decay rules:
   • Amplitude too large, decay too slow → reduce GAIN by 25 %.
   • Persistent oscillation at constant amplitude → increase TI by 50 %.
   • Excessive overshoot, slow recovery → reduce TI by 20 %.
   • High-frequency noise superimposed → reduce TD or increase TM_LAG.
4. Repeat the step until a critically-damped or slightly underdamped response is achieved with peak overshoot < 5 % and settling time within 5 × Td.

6.5 Add Derivative Action (Critical for AGC)

AGC hydraulic systems exhibit a lightly-damped mechanical resonance in the 3–15 Hz band. Pure PI control will either be slow or, when made faster, will ring at this resonance. Adding a derivative branch stabilises the loop without raising integral gain:

TD = 0.3 · Tu

TM_LAG = 0.1 · TD (or T#100ms, whichever is larger)

The TM_LAG first-order filter is mandatory — without it, a 1 LSB step in PV will appear at the output as an impulse that can saturate the valve amplifier.

7. Dead-Band Implementation (User-Suggested Fix)

The discussion thread explicitly recommends DEADB_W for the ±2 µm target. The dead-band function inside FB41 works as:

if |e| < DEADB_W → e := 0 (controller freezes)

if |e| ≥ DEADB_W → e unchanged

Recommended settings:

8. Anti-Windup and Bumpless Transfer

Because the start-up travel is 28000 → 3000 µm (an enormous step), integrator windup is the second major cause of the over-shoot and oscillation. Configure FB41 as follows:

• Set LMN_HLM = 100.0 and LMN_LLM = -100.0 if the valve is bi-directional; otherwise 0..100.
• Wire the actual valve feedback to the FB41 LMNR_HS / LMNR_LS outputs (L or H signalled feedback) by OR-ing in the saturating branch — this is the built-in anti-windup path.
• Forced-tracking during manual mode: if MAN_ON = TRUE, FB41 automatically tracks the integrator so the auto → manual transition is bumpless. Verify in the VAR table that INT_HOLD and I_ITVAL do not jump when toggling.

A common field-fitted improvement is to pre-charge the integrator by setting the initial LMN to the manually-found steady-state value at the moment of switching from manual to auto, by writing the pre-charge value into the instance DB LMN_I prior to clearing MAN_ON.

9. Step-by-Step Re-Commissioning Procedure

1. Move FB41 to OB35. In HW Config, set OB35 period = 100 ms. Replace the call in OB1 with a call in OB35 using the same instance DB. Confirm the call is unconditional and is the only block running in OB35.
2. Set CYCLE = T#100ms on the FB41 input pin.
3. Configure output limits: LMN_HLM = 100.0, LMN_LLM = 0.0 (or -100 for bi-directional valve).
4. Run the step test in manual (§6.2) and record Kp, Tu, Td.
5. Enter the calculated GAIN, TI from §6.3 into the instance DB.
6. Add derivative: TD = 0.3 · Tu, TM_LAG = max(0.1·TD, T#100ms).
7. Switch to auto and apply a small setpoint step. Iterate §6.4 until quarter-decay behaviour is obtained.
8. Apply dead band: start at DEADB_W = 3.0 (µm). If steady state is achieved within ±2 µm, leave it. If the band is over-tame, halve to 1.5 µm and re-test.
9. Add feed-forward (optional): for material-grade changes, set DISV from a load-cell or speed reference. Section 9.3.5 of the Standard PID manual covers this.
10. Save the commissioned values to the PLC and document them in the instance-DB symbol table.

10. Verification and Acceptance Test

Acceptance is the user-stated ±2 µm at 3000 µm setpoint under steady rolling conditions. A repeatable verification procedure is:

1. Hold the line at constant speed and tension for at least 60 s.
2. Capture 600 samples of PV_IN (10 min at 1 Hz log) into a WinCC archive.
3. Compute the standard deviation σ. The peak-to-peak steady-state jitter is approximately 6σ. To meet ±2 µm, σ ≤ 0.33 µm.
4. Apply a 2 % setpoint step (3060 µm) and verify overshoot ≤ 5 % (153 µm) and 2 % settling time ≤ 4 s.
5. Disturbance rejection: simulate a roll-eccentricity pulse (5 % LMN pulse for 200 ms) and verify recovery within 6 s.

If σ is not achieved, walk the DEADB_W down and the TM_LAG down in 20 % steps, re-testing after each change. If oscillations re-appear, raise TI by 30 %.

11. Diagnostics and Online Monitoring

Open the FB41 instance DB in Monitor/Modify (TIA Portal or STEP 7 classic) and observe the following real-time variables:

Cross-reference: SIMATIC Standard PID Control — Function Block Manual (PDF, Siemens Support Entry ID 1137082) and the PID controller reference for algorithm definitions.

12. Advanced Topics and References

12.1 Alternative Controller Blocks

For a mill with multiple cascades (gauge → tension → speed) consider migrating to FB58 "TCONT_CP", which is the TIA Portal successor to FB41 and supports pulse-width-modulated outputs, two configurable PID parameter sets, and integrated self-tuning. See the FM 355 / TCONT_CP application notes for migration guidance.

12.2 Smith Predictor for Transport Delay

Long distance between the X-ray gauge and the roll gap introduces a transport delay. The standard fix is a Smith predictor, which is a structural change you can build on top of FB41 by writing the predicted PV to PV_IN. The fuzzy-PID Smith predictor variant is documented in Stability and stabilisation research for hydraulic AGC.

12.3 Higher-Level Cascade Structure

Modern AGC systems use a master–slave structure: the master (FB41) sets a position reference for a slave (FB41) regulating the hydraulic cylinder position. This isolates the slow thickness loop from the fast mechanical resonance. Honeywell's MetalsMaster AGC product and the fuzzy-PID design study for AGC both confirm the two-loop architecture.

12.4 Self-Tuning Option

If commissioning time is limited, add the Siemens PID Self-Tuner (part of the Standard PID Control library). It performs the open-loop step test automatically and writes the resulting GAIN, TI, TD into the same instance DB. Reference: Siemens PID Self-Tuner manual.

13. Field-Commissioning Summary Matrix

14. Frequently Asked Questions