fix: split inner-loop yi_max clamp to fix HOLD-state windup overshoot

Renames pid_hold/pid_heat/pid_cool to pid_outer/pid_inner/pid_inner_cool
to match what actually runs when, and splits inner-loop config into
Inner.Heat/Inner.Hold/Inner.Cool so the same PID instance gets a tight
yi_max ceiling only while HOLD drives it, without capping legitimate
1.5 K/min ramps. Fixes the overshoot from docs/overshoot_hold_windup.md
where a cold-water disturbance during HOLD wound up pid_heat's integral
term with no anti-windup engagement, taking ~35s+ to unwind naturally.

Breaking config change: Hold/Heat/Cool -> Outer/Inner.{Heat,Hold,Cool}
in config.json, both .tpl templates, the pid/sud demo scripts, and
replay_sim.py's CLI flags. Adds tests/components/pid/ (stdlib unittest)
covering the Pid clamp/recovery behavior and closed-loop disturbance,
ramp, and HOLD<->HEAT transition cases.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01DGQhVQ2Y3yXAQTXhrxVd5u

utils/replay_sim.py

@@ -45,13 +45,21 @@ from components.pid import PidFactory
 from components.plant.pot import Pot
 
 
+GAIN_SECTIONS = (('Outer', 'outer'), ('Inner.Heat', 'inner-heat'),
+                 ('Inner.Hold', 'inner-hold'), ('Inner.Cool', 'inner-cool'))
+
+
 def _apply_gain_overrides(params, args):
     p = copy.deepcopy(params)
-    for section, prefix in (('Hold', 'hold'), ('Heat', 'heat'), ('Cool', 'cool')):
+    for section, prefix in GAIN_SECTIONS:
         for gain in ('kp', 'ki', 'kd', 'kt'):
-            val = getattr(args, '{}_{}'.format(prefix, gain))
+            val = getattr(args, '{}_{}'.format(prefix.replace('-', '_'), gain))
             if val is not None:
-                p[section][gain] = val
+                if '.' in section:
+                    outer, inner = section.split('.')
+                    p[outer][inner][gain] = val
+                else:
+                    p[section][gain] = val
     return p
 
 
@@ -63,7 +71,7 @@ def _infer_max_power(samples):
 def _infer_heatrate_soll_set(samples):
     """Estimate heatrate_soll_set from the log.
 
-    rate_soll = heatrate_soll_set * pid_hold.get_y(); when the hold PID is
+    rate_soll = heatrate_soll_set * pid_outer.get_y(); when the outer PID is
     saturated at 1.0 during active heating the two are equal, so the max
     rate_soll seen while the heater is on is a good upper bound."""
     candidates = [s['rate_soll'] for s in samples if s['power_set'] > 0]
@@ -211,12 +219,12 @@ def main():
     parser.add_argument('--plant-L',  type=float, default=None, metavar='W/kgK', help='Heat loss coeff [W/(kg·K)]')
     parser.add_argument('--plant-Td', type=float, default=None, metavar='s',     help='Transport delay [s]')
 
-    for section, prefix in (('Hold', 'hold'), ('Heat', 'heat'), ('Cool', 'cool')):
+    for section, prefix in GAIN_SECTIONS:
         for gain in ('kp', 'ki', 'kd', 'kt'):
             parser.add_argument(
                 '--{}-{}'.format(prefix, gain),
                 type=float, default=None,
-                dest='{}_{}'.format(prefix, gain),
+                dest='{}_{}'.format(prefix.replace('-', '_'), gain),
                 metavar='VAL',
                 help='Override TempCtrl.{}.{}'.format(section, gain),
             )
@@ -265,8 +273,8 @@ def main():
     ambient      = args.ambient   if args.ambient   is not None else config.get('ambient_temperature', 20.0)
 
     any_override = any(
-        getattr(args, '{}_{}'.format(p, g)) is not None
-        for p in ('hold', 'heat', 'cool')
+        getattr(args, '{}_{}'.format(prefix.replace('-', '_'), g)) is not None
+        for _, prefix in GAIN_SECTIONS
         for g in ('kp', 'ki', 'kd', 'kt')
     )
     config_source = 'log' if log.get('Config') else 'file'
@@ -281,8 +289,12 @@ def main():
     print('Params: {} ({})'.format('overridden' if any_override else 'from {}'.format(config_source),
                                    'log' if log_plant else 'defaults'))
     print()
-    for section in ('Hold', 'Heat', 'Cool'):
-        p = pid_params[section]
+    for section, _ in GAIN_SECTIONS:
+        if '.' in section:
+            outer, inner = section.split('.')
+            p = pid_params[outer][inner]
+        else:
+            p = pid_params[section]
         print('  {}: kp={kp}  ki={ki}  kd={kd}  kt={kt}'.format(section, **p))
 
     replay = run_replay(samples, pid_type, pid_params, rate_soll, plant_params, param_events,