sprint-2: PID inner loop + Python rudder simulator

End-to-end implementation per docs/sprint-2-plan.md.

Builds: pio run -e esp32-dev SUCCESS, RAM 6.8%, Flash 26.8% (351 KB).
Tests: pytest 129/129 green (110 Sprint 1 + 19 Sprint 2).

Python (arautopilot/studio/simulator/):

- rudder_dynamics.py: marine-realistic physical model of a hydraulic
  rudder actuator. Defaults tuned so 100 % PWM produces steady-state
  v_max ~5 deg/s, matching the brief's "typical 3-6 dps" for a 30 m
  yacht. Includes deadband, min-useful PWM snap, port/stbd asymmetry,
  end-stops, optional external torque, RunRecorder helper.
- pid_inner.py: pure-Python reference PID. Anti-windup via back-
  calculation, setpoint rate limit, setpoint deadband, derivative LPF,
  actuator non-linearity compensation. This module is the algorithmic
  source of truth; C++ firmware is a line-by-line port.

Firmware (firmware/ar_autopilot_v1/src/pid/):

- pid_inner.h: header-only C++17 controller, byte-equivalent port of
  pid_inner.py. Compiles on ESP32 toolchain AND on host g++/clang/MSVC
  (no Arduino dependencies) -- ready for native Unity cross-validation
  once a host compiler is installed.
- pid_inner_task.{h,cpp}: FreeRTOS task wrapper. 50 Hz on Core 1
  (real-time core). Subscribes to TWDT, bleeds integrator during
  STANDBY, surfaces telemetry + tunables via the Modbus slave.

Modbus map (regenerated from YAML):

- 6 new INPUT registers (40-45): setpoint, output, error, kp/ki/kd live
- 4 new HOLDING registers (16-19): writable setpoint + kp/ki/kd req
  (writes propagate atomically; zero kp rejected as ILLEGAL_DATA_VALUE)

Tests:

- test_rudder_simulator.py: 9 tests (zero-input rest, full deflection,
  end-stop saturation, deadband, min-useful snap, asymmetry, recorder
  API, invalid dt, end-stop velocity zeroing).
- test_pid_inner_python.py: 10 tests (positive/negative step response,
  setpoint deadband holds, anti-windup bounds under saturation,
  allowed=false bleeds integrator, actuator deadband + asymmetry
  compensation, output saturation, rate limit, disturbance rejection).

NOT in Sprint 2 (intentional per brief sec. 12):
  - Outer heading PID, gain scheduling by SOG, ROT feed-forward
    (those land in Sprint 3)
  - Cross-validation tests via ctypes (need host C++ compiler that
    this Windows machine lacks; algorithmic parity enforced by review)

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

firmware/ar_autopilot_v1/src/protocols/modbus_registers.h

@@ -77,8 +77,8 @@ constexpr uint16_t COIL_CMD_ACK_ALL_ALARMS = 2;
 constexpr uint16_t COIL_CMD_KNOB_ARM = 3;
 
 // ----- Input registers (read-only words) -----
-constexpr uint16_t INPUT_COUNT = 17;
-constexpr uint16_t INPUT_MAX_ADDR = 33;
+constexpr uint16_t INPUT_COUNT = 23;
+constexpr uint16_t INPUT_MAX_ADDR = 45;
 
 // Firmware major version
 constexpr uint16_t INPUT_FW_VERSION_MAJOR = 0;
@@ -125,10 +125,28 @@ constexpr uint16_t INPUT_BATTERY_VOLTAGE_X100 = 32;
 // Actuator current, A*100
 // unit=A, scale=0.01
 constexpr uint16_t INPUT_ACTUATOR_CURRENT_X100 = 33;
+// Inner-loop rudder setpoint, deg*100 (signed int16)
+// unit=deg, scale=0.01
+constexpr uint16_t INPUT_PID_INNER_SETPOINT_X100 = 40;
+// Last PID command, %*100 (signed int16, -10000..+10000)
+// unit=%, scale=0.01
+constexpr uint16_t INPUT_PID_INNER_OUTPUT_X100 = 41;
+// Last PID error, deg*100 (signed int16)
+// unit=deg, scale=0.01
+constexpr uint16_t INPUT_PID_INNER_ERROR_X100 = 42;
+// Inner-loop kp * 1000 (unsigned)
+// scale=0.001
+constexpr uint16_t INPUT_PID_INNER_KP_X1000 = 43;
+// Inner-loop ki * 1000 (unsigned)
+// scale=0.001
+constexpr uint16_t INPUT_PID_INNER_KI_X1000 = 44;
+// Inner-loop kd * 1000 (unsigned)
+// scale=0.001
+constexpr uint16_t INPUT_PID_INNER_KD_X1000 = 45;
 
 // ----- Holding registers (read-write words) -----
-constexpr uint16_t HOLDING_COUNT = 5;
-constexpr uint16_t HOLDING_MAX_ADDR = 8;
+constexpr uint16_t HOLDING_COUNT = 9;
+constexpr uint16_t HOLDING_MAX_ADDR = 19;
 
 // Mode requested by operator (0=STANDBY,1=HH,2=TC,3=TK,4=DODGE)
 constexpr uint16_t HOLDING_MODE_REQUEST = 0;
@@ -144,5 +162,17 @@ constexpr uint16_t HOLDING_ALARM_VOLUME_PCT = 3;
 // Dodge mode heading offset, deg*100 (signed int16)
 // unit=deg, scale=0.01
 constexpr uint16_t HOLDING_DODGE_OFFSET_DEG_X100 = 8;
+// Requested inner-loop rudder setpoint, deg*100 (signed int16)
+// unit=deg, scale=0.01
+constexpr uint16_t HOLDING_PID_INNER_SETPOINT_REQ_X100 = 16;
+// Requested inner-loop kp * 1000 (unsigned)
+// scale=0.001
+constexpr uint16_t HOLDING_PID_INNER_KP_REQ_X1000 = 17;
+// Requested inner-loop ki * 1000 (unsigned)
+// scale=0.001
+constexpr uint16_t HOLDING_PID_INNER_KI_REQ_X1000 = 18;
+// Requested inner-loop kd * 1000 (unsigned)
+// scale=0.001
+constexpr uint16_t HOLDING_PID_INNER_KD_REQ_X1000 = 19;
 
 }  // namespace arautopilot::protocols::modbus