Control System Performance Metrics
Rise Time
Time for system to go from 10% to 90% of target value.
pythondef rise_time(times, values, target): """Calculate rise time (10% to 90% of target).""" t10 = t90 = None for t, v in zip(times, values): if t10 is None and v >= 0.1 * target: t10 = t if t90 is None and v >= 0.9 * target: t90 = t break if t10 is not None and t90 is not None: return t90 - t10 return None
Overshoot
How much response exceeds target, as percentage.
pythondef overshoot_percent(values, target): """Calculate overshoot percentage.""" max_val = max(values) if max_val <= target: return 0.0 return ((max_val - target) / target) * 100
Steady-State Error
Difference between target and final settled value.
pythondef steady_state_error(values, target, final_fraction=0.1): """Calculate steady-state error using final portion of data.""" n = len(values) start = int(n * (1 - final_fraction)) final_avg = sum(values[start:]) / len(values[start:]) return abs(target - final_avg)
Settling Time
Time to stay within tolerance band of target.
pythondef settling_time(times, values, target, tolerance=0.02): """Time to settle within tolerance of target.""" band = target * tolerance lower, upper = target - band, target + band settled_at = None for t, v in zip(times, values): if v < lower or v > upper: settled_at = None elif settled_at is None: settled_at = t return settled_at
Usage
pythontimes = [row['time'] for row in results] values = [row['value'] for row in results] target = 30.0 print(f"Rise time: {rise_time(times, values, target)}") print(f"Overshoot: {overshoot_percent(values, target)}%") print(f"SS Error: {steady_state_error(values, target)}")
