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process-control
pid-controller
statistical-process-control
roller-compaction
pharmaceutical-manufacturing
time-series
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"cells": [
{"cell_type": "markdown", "metadata": {}, "source": [
"# \ud83c\udfae Roll Compactor Control Performance: PID Analysis & SPC\n",
"\n",
"**Dataset:** Roll Compactor Control Performance (Synthetic) v1.0 \n",
"**Publisher:** [Innovative Process Applications (IPA)](https://www.innovativeprocess.com) \n",
"**License:** CC BY 4.0 \n",
"**Scientific basis:** Szappanos-Csord\u00e1s (2018), Chapter 3.1\n",
"\n",
"> \u26a0\ufe0f **Synthetic educational data** \u2014 not real measurements.\n",
"\n",
"---\n",
"\n",
"This notebook covers:\n",
"1. Load both summary and time-series data\n",
"2. Visualize PID step responses across control architectures\n",
"3. Compare control quality metrics (CV%, settling time, overshoot)\n",
"4. Build SPC control charts\n",
"5. Quantify the twin feed screw advantage\n",
"6. Classify control quality from time-series features"
]},
{"cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [
"import pandas as pd\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns\n",
"from sklearn.ensemble import RandomForestClassifier\n",
"from sklearn.preprocessing import LabelEncoder\n",
"from sklearn.model_selection import cross_val_score\n",
"\n",
"sns.set_style('whitegrid')\n",
"plt.rcParams['figure.dpi'] = 100\n",
"\n",
"# Load data\n",
"df_summary = pd.read_csv('control_performance_summary_v1.0.csv')\n",
"df_ts = pd.read_csv('control_performance_timeseries_v1.0.csv')\n",
"\n",
"print(f'Summary: {df_summary.shape[0]} runs, {df_summary.shape[1]} columns')\n",
"print(f'Time series: {df_ts.shape[0]} rows, {df_ts.shape[1]} columns')\n",
"print(f'Control architectures: {df_summary[\"control_architecture\"].unique()}')\n",
"df_summary.head()"
]},
{"cell_type": "markdown", "metadata": {}, "source": [
"## Part 1: PID Step Response Visualization\n",
"\n",
"The defining characteristic of a PID controller is its step response \u2014 how\n",
"the actual value tracks a setpoint change. We\u2019ll compare the four control\n",
"architectures responding to the same SCF step-up scenario."
]},
{"cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [
"# Pick one material and one scenario to compare architectures\n",
"scenario = 'scf_step_up'\n",
"material = 'MCC_Mannitol_Mix'\n",
"\n",
"architectures = ['no_gap_control', 'pid_gw_screw', 'pid_scf_gw', 'pid_scf_gw_twin_screw']\n",
"labels = ['No Gap Control', 'PID: GW+Screw', 'PID: SCF+GW', 'PID: SCF+GW+Twin Screw']\n",
"colors = ['#cc4444', '#d4a017', '#2E86C1', '#008080']\n",
"\n",
"fig, axes = plt.subplots(2, 1, figsize=(14, 8), sharex=True)\n",
"\n",
"for arch, label, color in zip(architectures, labels, colors):\n",
" run = df_summary[(df_summary['control_architecture']==arch) &\n",
" (df_summary['material']==material) &\n",
" (df_summary['scenario']==scenario)]\n",
" if len(run) == 0:\n",
" continue\n",
" rid = run.iloc[0]['run_id']\n",
" ts = df_ts[df_ts['run_id']==rid]\n",
"\n",
" axes[0].plot(ts['time_s'], ts['scf_actual_kN_per_cm'], label=label,\n",
" color=color, alpha=0.8, linewidth=1.2)\n",
" axes[1].plot(ts['time_s'], ts['gw_actual_mm'], label=label,\n",
" color=color, alpha=0.8, linewidth=1.2)\n",
"\n",
"# Setpoint lines\n",
"axes[0].axhline(4.0, color='gray', linestyle=':', alpha=0.5)\n",
"axes[0].axhline(8.0, color='gray', linestyle=':', alpha=0.5)\n",
"axes[0].axvline(30, color='black', linestyle='--', alpha=0.3, label='Setpoint change')\n",
"axes[0].set_ylabel('SCF (kN/cm)')\n",
"axes[0].set_title(f'PID Step Response Comparison \\u2014 SCF Step Up (4\\u21928 kN/cm), {material}')\n",
"axes[0].legend(loc='lower right', fontsize=9)\n",
"\n",
"axes[1].axvline(30, color='black', linestyle='--', alpha=0.3)\n",
"axes[1].set_ylabel('Gap Width (mm)')\n",
"axes[1].set_xlabel('Time (s)')\n",
"axes[1].set_title('Gap Width Response During SCF Step Change')\n",
"axes[1].legend(loc='upper right', fontsize=9)\n",
"\n",
"plt.tight_layout()\n",
"plt.show()\n",
"\n",
"print('Key observations:')\n",
"print('- No gap control: slow approach, steady-state offset, noisy')\n",
"print('- PID SCF+GW: overshoot then clean settling')\n",
"print('- Twin screw: tightest band, fastest settling, least noise')"
]},
{"cell_type": "markdown", "metadata": {}, "source": [
"## Part 2: Control Quality Metrics by Architecture\n",
"\n",
"CV% (coefficient of variation) is the primary metric from Chapter 3.1 of\n",
"the dissertation. Lower CV = more robust process."
]},
{"cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [
"fig, axes = plt.subplots(1, 3, figsize=(16, 4))\n",
"\n",
"order = ['no_gap_control', 'pid_gw_screw', 'pid_scf_gw', 'pid_scf_gw_twin_screw']\n",
"palette = ['#cc4444', '#d4a017', '#2E86C1', '#008080']\n",
"\n",
"sns.boxplot(data=df_summary, x='control_architecture', y='scf_ss_cv_pct',\n",
" order=order, palette=palette, ax=axes[0])\n",
"axes[0].set_title('SCF Steady-State CV%')\n",
"axes[0].set_ylabel('CV %')\n",
"axes[0].tick_params(axis='x', rotation=30)\n",
"axes[0].set_xlabel('')\n",
"\n",
"sns.boxplot(data=df_summary, x='control_architecture', y='gw_ss_cv_pct',\n",
" order=order, palette=palette, ax=axes[1])\n",
"axes[1].set_title('Gap Width Steady-State CV%')\n",
"axes[1].set_ylabel('CV %')\n",
"axes[1].tick_params(axis='x', rotation=30)\n",
"axes[1].set_xlabel('')\n",
"\n",
"sns.boxplot(data=df_summary, x='control_architecture', y='scf_settling_time_s',\n",
" order=order, palette=palette, ax=axes[2])\n",
"axes[2].set_title('SCF Settling Time')\n",
"axes[2].set_ylabel('Time (s)')\n",
"axes[2].tick_params(axis='x', rotation=30)\n",
"axes[2].set_xlabel('')\n",
"\n",
"plt.tight_layout()\n",
"plt.show()\n",
"\n",
"print('\\nMean CV% by architecture:')\n",
"print(df_summary.groupby('control_architecture')[['scf_ss_cv_pct','gw_ss_cv_pct']].mean().round(2).loc[order])"
]},
{"cell_type": "markdown", "metadata": {}, "source": [
"## Part 3: Material Effect on Controllability\n",
"\n",
"Brittle materials (mannitol) produce more erratic force signals due to\n",
"particle fragmentation, making the control task harder."
]},
{"cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [
"fig, axes = plt.subplots(1, 2, figsize=(12, 4))\n",
"mat_order = ['MCC_101', 'MCC_Mannitol_Mix', 'Mannitol_SD']\n",
"mat_colors = ['#008080', '#2E86C1', '#d4a017']\n",
"\n",
"sns.boxplot(data=df_summary, x='material', y='scf_ss_cv_pct',\n",
" order=mat_order, palette=mat_colors, ax=axes[0])\n",
"axes[0].set_title('SCF CV% by Material')\n",
"axes[0].set_ylabel('SCF CV %')\n",
"axes[0].set_xlabel('')\n",
"\n",
"sns.boxplot(data=df_summary, x='material', y='gw_ss_cv_pct',\n",
" order=mat_order, palette=mat_colors, ax=axes[1])\n",
"axes[1].set_title('Gap Width CV% by Material')\n",
"axes[1].set_ylabel('GW CV %')\n",
"axes[1].set_xlabel('')\n",
"\n",
"plt.tight_layout()\n",
"plt.show()\n",
"\n",
"print('Interpretation:')\n",
"print('- MCC (plastic): smoothest compaction, easiest to control')\n",
"print('- Mannitol (brittle): particle fragmentation creates force spikes')\n",
"print('- Mixture: intermediate behavior')"
]},
{"cell_type": "markdown", "metadata": {}, "source": [
"## Part 4: SPC Control Charts\n",
"\n",
"Statistical Process Control charts are standard tools in pharma\n",
"manufacturing. Let\u2019s build X-bar and R charts for a sample run."
]},
{"cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [
"# Pick the twin-screw + MCC steady-state baseline for the cleanest signal\n",
"run_spc = df_summary[(df_summary['control_architecture']=='pid_scf_gw_twin_screw') &\n",
" (df_summary['material']=='MCC_101') &\n",
" (df_summary['scenario']=='steady_state_baseline')]\n",
"if len(run_spc) > 0:\n",
" rid = run_spc.iloc[0]['run_id']\n",
" ts = df_ts[df_ts['run_id']==rid].copy()\n",
"\n",
" # Use only steady-state portion (t > 30s)\n",
" ts_ss = ts[ts['time_s'] >= 30.0].copy()\n",
"\n",
" scf_mean = ts_ss['scf_actual_kN_per_cm'].mean()\n",
" scf_std = ts_ss['scf_actual_kN_per_cm'].std()\n",
" ucl = scf_mean + 3 * scf_std\n",
" lcl = scf_mean - 3 * scf_std\n",
"\n",
" fig, ax = plt.subplots(figsize=(14, 4))\n",
" ax.plot(ts_ss['time_s'], ts_ss['scf_actual_kN_per_cm'],\n",
" 'o-', markersize=3, color='#008080', alpha=0.7)\n",
" ax.axhline(scf_mean, color='#1B2A3B', linewidth=2, label=f'CL = {scf_mean:.3f}')\n",
" ax.axhline(ucl, color='red', linestyle='--', label=f'UCL = {ucl:.3f}')\n",
" ax.axhline(lcl, color='red', linestyle='--', label=f'LCL = {lcl:.3f}')\n",
" ax.fill_between(ts_ss['time_s'], lcl, ucl, alpha=0.05, color='red')\n",
" ax.set_xlabel('Time (s)')\n",
" ax.set_ylabel('SCF (kN/cm)')\n",
" ax.set_title(f'X-bar Control Chart \\u2014 Twin Screw PID, MCC 101, Steady State')\n",
" ax.legend(loc='upper right')\n",
" plt.tight_layout()\n",
" plt.show()\n",
"\n",
" print(f'Process capability summary:')\n",
" print(f' Mean: {scf_mean:.3f} kN/cm')\n",
" print(f' Std: {scf_std:.4f} kN/cm')\n",
" print(f' CV: {scf_std/scf_mean*100:.2f}%')\n",
" spec_half = 0.5 # example spec: setpoint +/- 0.5 kN/cm\n",
" cpk = min(ucl - scf_mean, scf_mean - lcl) / (3 * scf_std)\n",
" print(f' Cpk (\\u00b13\\u03c3 natural): {cpk:.2f}')"
]},
{"cell_type": "markdown", "metadata": {}, "source": [
"## Part 5: Twin Feed Screw Advantage\n",
"\n",
"This is the key IPA design differentiator. Twin feed screws provide more\n",
"uniform powder delivery, which directly reduces process variability."
]},
{"cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [
"# Compare single vs twin screw (both with SCF+GW PID)\n",
"single = df_summary[df_summary['control_architecture']=='pid_scf_gw']\n",
"twin = df_summary[df_summary['control_architecture']=='pid_scf_gw_twin_screw']\n",
"\n",
"metrics = ['scf_ss_cv_pct', 'gw_ss_cv_pct', 'scf_settling_time_s', 'scf_overshoot_pct']\n",
"metric_labels = ['SCF CV%', 'GW CV%', 'Settling Time (s)', 'Overshoot %']\n",
"\n",
"fig, axes = plt.subplots(1, 4, figsize=(16, 4))\n",
"for ax, metric, mlabel in zip(axes, metrics, metric_labels):\n",
" data = pd.DataFrame({\n",
" 'Single Screw': single[metric].values,\n",
" 'Twin Screw': twin[metric].values,\n",
" })\n",
" data.plot.box(ax=ax, color=dict(boxes='#008080', whiskers='gray',\n",
" medians='#1B2A3B', caps='gray'))\n",
" ax.set_title(mlabel)\n",
" ax.set_ylabel(mlabel)\n",
"\n",
"plt.suptitle('Single Screw vs. Twin Feed Screw (Same PID Architecture)',\n",
" fontsize=13, y=1.02)\n",
"plt.tight_layout()\n",
"plt.show()\n",
"\n",
"print('\\nImprovement with twin screw:')\n",
"for metric, mlabel in zip(metrics, metric_labels):\n",
" s = single[metric].mean()\n",
" t = twin[metric].mean()\n",
" improvement = (s - t) / s * 100 if s > 0 else 0\n",
" print(f' {mlabel}: {s:.2f} \\u2192 {t:.2f} ({improvement:+.1f}% improvement)')"
]},
{"cell_type": "markdown", "metadata": {}, "source": [
"## Part 6: Classify Control Quality from Metrics\n",
"\n",
"Can we predict the control quality grade from the summary metrics? This\n",
"demonstrates how machine learning can support process monitoring."
]},
{"cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [
"# Encode targets and features\n",
"le = LabelEncoder()\n",
"y = le.fit_transform(df_summary['control_quality_grade'])\n",
"\n",
"feature_cols = ['scf_ss_cv_pct', 'gw_ss_cv_pct', 'scf_deviation_from_setpoint_pct',\n",
" 'gw_deviation_from_setpoint_pct', 'scf_settling_time_s',\n",
" 'gw_settling_time_s', 'scf_overshoot_pct']\n",
"X = df_summary[feature_cols].values\n",
"\n",
"rf = RandomForestClassifier(n_estimators=100, random_state=42)\n",
"scores = cross_val_score(rf, X, y, cv=5, scoring='accuracy')\n",
"print(f'RF 5-fold CV accuracy: {scores.mean():.3f} \\u00b1 {scores.std():.3f}')\n",
"\n",
"rf.fit(X, y)\n",
"importances = pd.Series(rf.feature_importances_, index=feature_cols).sort_values()\n",
"\n",
"fig, ax = plt.subplots(figsize=(8, 4))\n",
"importances.plot.barh(color='#008080', ax=ax)\n",
"ax.set_title('Feature Importance for Control Quality Grade Prediction')\n",
"ax.set_xlabel('Importance')\n",
"plt.tight_layout()\n",
"plt.show()"
]},
{"cell_type": "markdown", "metadata": {}, "source": [
"## Takeaways\n",
"\n",
"1. **Control architecture matters enormously:** Going from no gap control to\n",
" full PID SCF+GW control reduces process variability by 50\u201370%. This is\n",
" not optional in regulated pharma manufacturing.\n",
"\n",
"2. **Twin feed screws are a multiplicative advantage:** On top of PID control,\n",
" twin screws provide an additional 20\u201330% reduction in CV by smoothing\n",
" feed rate fluctuations. This is a mechanical design choice, not a tuning\n",
" parameter \u2014 it must be built into the machine.\n",
"\n",
"3. **Material properties affect control difficulty:** Brittle materials\n",
" produce noisier signals that challenge even the best PID controllers.\n",
" Process development must account for this.\n",
"\n",
"4. **SPC tools apply directly to continuous granulation:** Control charts,\n",
" Cp/Cpk, and trend analysis are standard pharma quality tools that\n",
" connect naturally to roll compaction process data.\n",
"\n",
"---\n",
"\n",
"For twin-feed-screw roller compactors with advanced PID control and direct\n",
"engineer support, see IPA\u2019s CL-series compactors:\n",
"**https://www.innovativeprocess.com**\n",
"\n",
"*Dataset \u00a9 2026 Innovative Process Applications, CC BY 4.0.* \n",
"*Scientific basis: Szappanos-Csord\u00e1s (2018), Chapter 3.1.*"
]}
],
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