Control System Performance Metrics
Rise Time
Time for system to go from 10% to 90% of target value.
def 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.
def 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.
def 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.
def 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
times = [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)}")
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