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process-control
pid-controller
statistical-process-control
roller-compaction
pharmaceutical-manufacturing
time-series
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IPA Roll Compactor Control Performance Synthetic Dataset Generator v1.0
=======================================================================
Generates synthetic time-series process data simulating PID control behavior
of roll compactors during dry granulation, grounded in the control performance
concepts from:
Szappanos-Csordás, K. (2018). "Impact of material properties, process
parameters and roll compactor design on roll compaction." Chapter 3.1:
Control performance of the different types of roll compactors.
Key concepts modeled:
- PID controller behavior (P, I, D terms) for SCF and gap width control
- Settling time after setpoint changes (material- and design-dependent)
- Steady-state deviation from setpoint (mean ± SD, CV%)
- Control architecture differences:
* No gap control (AlexanderWerk BT120-type): high GW variability
* PID with GW + screw speed control (Hosokawa-type): moderate control
* PID with SCF + GW control (Bohle/Gerteis-type): best control
- Material-dependent control difficulty: MCC (plastic, compressible) is
easier to control than mannitol (brittle, less compressible)
- Overshoot, oscillation, and disturbance rejection behavior
- Twin feed screw advantage: reduced feed fluctuation → lower SCF variance
THIS IS SYNTHETIC EDUCATIONAL DATA. NOT REAL CUSTOMER OR LAB DATA.
Generated by Innovative Process Applications (IPA) for teaching process
control, PID tuning, and SPC concepts.
"""
import numpy as np
import pandas as pd
rng = np.random.default_rng(seed=2026)
# =============================================================================
# CONTROL ARCHITECTURES (from Chapter 3.1 / Table 1 of the dissertation)
# =============================================================================
CONTROL_CONFIGS = {
"no_gap_control": {
"label": "No Gap Control (HP setpoint only)",
"description": "Hydraulic pressure setpoint, no closed-loop gap control",
"has_scf_pid": False,
"has_gw_pid": False,
"scf_settling_base_s": 15.0,
"gw_settling_base_s": 50.0, # gap drifts until material equilibrates
"scf_noise_base": 0.012, # CV fraction — higher without PID
"gw_noise_base": 0.030, # high GW variability (3% CV from Table 2)
"overshoot_factor": 0.08,
"feed_type": "single_screw",
},
"pid_gw_screw": {
"label": "PID: GW + Screw Speed Control",
"description": "Gap width controlled via PID adjusting screw speed",
"has_scf_pid": False,
"has_gw_pid": True,
"scf_settling_base_s": 12.0,
"gw_settling_base_s": 20.0,
"scf_noise_base": 0.010,
"gw_noise_base": 0.015,
"overshoot_factor": 0.12, # GW PID can overshoot on fast changes
"feed_type": "single_screw",
},
"pid_scf_gw": {
"label": "PID: SCF + GW Control",
"description": "Both SCF and GW controlled via independent PID loops",
"has_scf_pid": True,
"has_gw_pid": True,
"scf_settling_base_s": 8.0,
"gw_settling_base_s": 10.0,
"scf_noise_base": 0.006, # best control performance
"gw_noise_base": 0.008,
"overshoot_factor": 0.05,
"feed_type": "single_screw",
},
"pid_scf_gw_twin_screw": {
"label": "PID: SCF + GW Control + Twin Feed Screw",
"description": "Dual PID loops with twin feed screw for uniform feeding",
"has_scf_pid": True,
"has_gw_pid": True,
"scf_settling_base_s": 6.0,
"gw_settling_base_s": 8.0,
"scf_noise_base": 0.004, # twin screw reduces feed fluctuation
"gw_noise_base": 0.006,
"overshoot_factor": 0.04,
"feed_type": "twin_screw",
},
}
# =============================================================================
# MATERIALS (control difficulty varies with deformation behavior)
# =============================================================================
MATERIALS = {
"MCC_101": {
"label": "MCC 101 (Plastic)",
"control_difficulty": 0.8, # easier — plastic deformation is smoother
"settling_multiplier": 0.9,
"disturbance_sensitivity": 0.7,
},
"Mannitol_SD": {
"label": "Mannitol (Brittle)",
"control_difficulty": 1.3, # harder — brittle fragmentation causes spikes
"settling_multiplier": 1.3,
"disturbance_sensitivity": 1.4,
},
"MCC_Mannitol_Mix": {
"label": "1:1 Mixture",
"control_difficulty": 1.0,
"settling_multiplier": 1.0,
"disturbance_sensitivity": 1.0,
},
}
# =============================================================================
# SETPOINT CHANGE SCENARIOS (from Table 2/3 patterns in the dissertation)
# =============================================================================
SCENARIOS = [
{"scf_from": 4.0, "scf_to": 4.0, "gw_from": 2.0, "gw_to": 2.0,
"label": "steady_state_baseline"},
{"scf_from": 4.0, "scf_to": 8.0, "gw_from": 2.0, "gw_to": 2.0,
"label": "scf_step_up"},
{"scf_from": 8.0, "scf_to": 4.0, "gw_from": 2.0, "gw_to": 2.0,
"label": "scf_step_down"},
{"scf_from": 6.0, "scf_to": 6.0, "gw_from": 3.0, "gw_to": 1.5,
"label": "gw_step_down"},
{"scf_from": 6.0, "scf_to": 6.0, "gw_from": 1.5, "gw_to": 3.0,
"label": "gw_step_up"},
{"scf_from": 4.0, "scf_to": 8.0, "gw_from": 3.0, "gw_to": 1.5,
"label": "simultaneous_change"},
{"scf_from": 12.0, "scf_to": 12.0, "gw_from": 2.0, "gw_to": 2.0,
"label": "high_force_steady"},
{"scf_from": 2.0, "scf_to": 2.0, "gw_from": 4.0, "gw_to": 4.0,
"label": "low_force_wide_gap"},
]
# =============================================================================
# TIME-SERIES GENERATION
# =============================================================================
SAMPLE_RATE_HZ = 2.0 # 2 samples/second (0.5s intervals)
RUN_DURATION_S = 180.0 # 3-minute runs — enough to see settling + steady state
SETPOINT_CHANGE_AT_S = 30.0 # setpoint changes at t=30s
def pid_response(t, setpoint_from, setpoint_to, change_time,
settling_time, overshoot_factor, noise_cv,
has_pid, disturbance_sensitivity, rng_local):
"""
Simulate PID controller response to a setpoint change.
Without PID: parameter drifts slowly toward equilibrium with high noise.
With PID: second-order underdamped response (overshoot + settling).
"""
n = len(t)
values = np.zeros(n)
step_size = setpoint_to - setpoint_from
for i, ti in enumerate(t):
if ti < change_time:
# Pre-change: at old setpoint with noise
base = setpoint_from
else:
elapsed = ti - change_time
if has_pid and abs(step_size) > 0.01:
# Underdamped PID: exponential decay with overshoot
tau = settling_time / 4.0 # time constant
zeta = 0.4 + rng_local.uniform(-0.05, 0.05) # damping ratio
omega_n = 1.0 / tau
omega_d = omega_n * np.sqrt(1 - zeta**2) if zeta < 1 else omega_n
decay = np.exp(-zeta * omega_n * elapsed)
oscillation = np.cos(omega_d * elapsed)
overshoot_amp = overshoot_factor * abs(step_size)
response = 1.0 - decay * (oscillation + (zeta/np.sqrt(1-zeta**2)) *
np.sin(omega_d * elapsed)) if zeta < 1 else \
1.0 - (1 + omega_n * elapsed) * np.exp(-omega_n * elapsed)
response = np.clip(response, -0.5, 1.5)
base = setpoint_from + step_size * response
elif not has_pid and abs(step_size) > 0.01:
# No PID: slow exponential approach, never quite gets there
tau = settling_time / 2.0
response = 1.0 - np.exp(-elapsed / tau)
# Steady-state offset (no integral term to eliminate it)
offset = 0.03 * step_size * disturbance_sensitivity
base = setpoint_from + step_size * response * 0.95 + offset
else:
base = setpoint_to
# Process noise (proportional to setpoint magnitude)
noise = rng_local.normal(0, noise_cv * abs(base) + 0.01)
# Occasional disturbances (feed fluctuations, powder bridging)
if rng_local.random() < 0.02 * disturbance_sensitivity:
noise += rng_local.normal(0, 0.05 * abs(base))
values[i] = base + noise
return values
def compute_run_metrics(t, scf_actual, gw_actual, scf_setpoint, gw_setpoint,
change_time):
"""Compute the control performance metrics from Chapter 3.1."""
# Steady-state region: last 60 seconds of the run
ss_mask = t >= (t[-1] - 60.0)
# Settling region: after change, before steady state
settling_mask = (t >= change_time) & (t < change_time + 90.0)
# SCF metrics
scf_ss = scf_actual[ss_mask]
scf_mean = np.mean(scf_ss)
scf_std = np.std(scf_ss)
scf_cv = (scf_std / abs(scf_mean) * 100) if abs(scf_mean) > 0.1 else 0.0
scf_deviation_pct = abs(scf_mean - scf_setpoint) / scf_setpoint * 100 \
if scf_setpoint > 0.1 else 0.0
# GW metrics
gw_ss = gw_actual[ss_mask]
gw_mean = np.mean(gw_ss)
gw_std = np.std(gw_ss)
gw_cv = (gw_std / abs(gw_mean) * 100) if abs(gw_mean) > 0.1 else 0.0
gw_deviation_pct = abs(gw_mean - gw_setpoint) / gw_setpoint * 100 \
if gw_setpoint > 0.1 else 0.0
# Settling time: time after change until value stays within ±2% of final
scf_settled_s = _find_settling_time(t, scf_actual, scf_setpoint,
change_time, tolerance=0.02)
gw_settled_s = _find_settling_time(t, gw_actual, gw_setpoint,
change_time, tolerance=0.02)
# Overshoot
post_change = scf_actual[t >= change_time]
if len(post_change) > 0 and scf_setpoint > 0.1:
scf_overshoot_pct = (max(post_change) - scf_setpoint) / scf_setpoint * 100
else:
scf_overshoot_pct = 0.0
return {
"scf_ss_mean": round(scf_mean, 3),
"scf_ss_std": round(scf_std, 4),
"scf_ss_cv_pct": round(scf_cv, 2),
"scf_deviation_from_setpoint_pct": round(scf_deviation_pct, 2),
"scf_settling_time_s": round(scf_settled_s, 1),
"scf_overshoot_pct": round(max(scf_overshoot_pct, 0), 2),
"gw_ss_mean_mm": round(gw_mean, 4),
"gw_ss_std_mm": round(gw_std, 4),
"gw_ss_cv_pct": round(gw_cv, 2),
"gw_deviation_from_setpoint_pct": round(gw_deviation_pct, 2),
"gw_settling_time_s": round(gw_settled_s, 1),
}
def _find_settling_time(t, values, setpoint, change_time, tolerance=0.02):
"""Find time after change when value stays within tolerance band."""
if abs(setpoint) < 0.1:
return 0.0
band = tolerance * abs(setpoint)
post_mask = t >= change_time
post_t = t[post_mask]
post_v = values[post_mask]
# Walk backwards from end to find last excursion outside band
for i in range(len(post_v) - 1, -1, -1):
if abs(post_v[i] - setpoint) > band:
if i < len(post_v) - 1:
return post_t[i+1] - change_time
else:
return post_t[-1] - change_time
return 0.0 # already settled
# =============================================================================
# GENERATE ALL RUNS
# =============================================================================
t = np.arange(0, RUN_DURATION_S, 1.0 / SAMPLE_RATE_HZ)
n_samples = len(t)
summary_rows = []
timeseries_rows = []
run_id = 0
for ctrl_key, ctrl in CONTROL_CONFIGS.items():
for mat_key, mat in MATERIALS.items():
for scenario in SCENARIOS:
run_id += 1
# Adjusted settling times and noise for material
scf_settling = (ctrl["scf_settling_base_s"] *
mat["settling_multiplier"])
gw_settling = (ctrl["gw_settling_base_s"] *
mat["settling_multiplier"])
scf_noise = ctrl["scf_noise_base"] * mat["control_difficulty"]
gw_noise = ctrl["gw_noise_base"] * mat["control_difficulty"]
# Twin screw reduces feed fluctuation → lower noise
if ctrl["feed_type"] == "twin_screw":
scf_noise *= 0.75
gw_noise *= 0.80
# Generate time series
scf_actual = pid_response(
t, scenario["scf_from"], scenario["scf_to"],
SETPOINT_CHANGE_AT_S, scf_settling,
ctrl["overshoot_factor"], scf_noise,
ctrl["has_scf_pid"], mat["disturbance_sensitivity"], rng
)
gw_actual = pid_response(
t, scenario["gw_from"], scenario["gw_to"],
SETPOINT_CHANGE_AT_S, gw_settling,
ctrl["overshoot_factor"] * 0.7, gw_noise,
ctrl["has_gw_pid"], mat["disturbance_sensitivity"], rng
)
# Clip to physical limits
scf_actual = np.clip(scf_actual, 0.5, 25.0)
gw_actual = np.clip(gw_actual, 0.5, 8.0)
# Roll speed: constant within a run (not PID-controlled here)
rs_setpoint = 3.0 + rng.uniform(-1, 1)
rs_actual = rs_setpoint + rng.normal(0, 0.02 * rs_setpoint, n_samples)
# Screw speed: varies if GW PID adjusts it
ss_base = 30.0 + rng.uniform(-5, 5)
if ctrl["has_gw_pid"]:
# Screw speed adapts inversely to gap error
gw_error = scenario["gw_to"] - gw_actual
ss_actual = ss_base + 5.0 * gw_error + rng.normal(0, 0.5, n_samples)
else:
ss_actual = ss_base + rng.normal(0, 0.3, n_samples)
# Store time-series (subsample to every 2s for manageable file size)
subsample = np.arange(0, n_samples, 4) # every 2 seconds
for idx in subsample:
timeseries_rows.append({
"run_id": run_id,
"time_s": round(t[idx], 1),
"scf_setpoint_kN_per_cm": scenario["scf_to"] if t[idx] >= SETPOINT_CHANGE_AT_S else scenario["scf_from"],
"scf_actual_kN_per_cm": round(scf_actual[idx], 3),
"gw_setpoint_mm": scenario["gw_to"] if t[idx] >= SETPOINT_CHANGE_AT_S else scenario["gw_from"],
"gw_actual_mm": round(gw_actual[idx], 4),
"roll_speed_rpm": round(rs_actual[idx], 2),
"screw_speed_rpm": round(ss_actual[idx], 1),
})
# Compute summary metrics
metrics = compute_run_metrics(
t, scf_actual, gw_actual,
scenario["scf_to"], scenario["gw_to"],
SETPOINT_CHANGE_AT_S
)
# Classify control quality
total_cv = metrics["scf_ss_cv_pct"] + metrics["gw_ss_cv_pct"]
if total_cv < 2.0 and metrics["scf_deviation_from_setpoint_pct"] < 1.0:
control_quality = "Excellent"
elif total_cv < 5.0 and metrics["scf_deviation_from_setpoint_pct"] < 3.0:
control_quality = "Good"
elif total_cv < 10.0:
control_quality = "Acceptable"
else:
control_quality = "Poor"
summary_rows.append({
"run_id": run_id,
"control_architecture": ctrl_key,
"control_label": ctrl["label"],
"feed_type": ctrl["feed_type"],
"has_scf_pid": ctrl["has_scf_pid"],
"has_gw_pid": ctrl["has_gw_pid"],
"material": mat_key,
"scenario": scenario["label"],
"scf_setpoint_kN_per_cm": scenario["scf_to"],
"gw_setpoint_mm": scenario["gw_to"],
**metrics,
"control_quality_grade": control_quality,
})
# =============================================================================
# SAVE
# =============================================================================
df_summary = pd.DataFrame(summary_rows)
df_timeseries = pd.DataFrame(timeseries_rows)
df_summary.to_csv("control_performance_summary_v1.0.csv", index=False)
df_timeseries.to_csv("control_performance_timeseries_v1.0.csv", index=False)
print(f"Summary: {len(df_summary)} runs, {len(df_summary.columns)} columns")
print(f"Time series: {len(df_timeseries)} rows, {len(df_timeseries.columns)} columns")
print()
print("=== Control quality distribution ===")
print(df_summary["control_quality_grade"].value_counts())
print()
print("=== Mean SCF CV% by architecture ===")
print(df_summary.groupby("control_architecture")["scf_ss_cv_pct"].mean().round(2))
print()
print("=== Mean GW CV% by architecture ===")
print(df_summary.groupby("control_architecture")["gw_ss_cv_pct"].mean().round(2))
print()
print("=== Mean SCF settling time by architecture ===")
print(df_summary.groupby("control_architecture")["scf_settling_time_s"].mean().round(1))
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