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2026-05-20 23:52:15 +09:00

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title

PID Controllers in AI

매 한 줄

"매 error = setpoint - measurement 에 P/I/D 항을 적용해 actuator 를 제어". 1922 Minorsky ship steering 에서 시작, 매 산업 control 의 80%+ 사용. 매 2026 의 AI hybrid 사용: drone attitude (PX4), robot joint, LLM token-budget control, RLHF KL-coefficient tuning, training schedules.

매 핵심

매 PID 공식

u(t) = Kp·e(t) + Ki·∫e(τ)dτ + Kd·de/dt.
P (Proportional): 매 현재 error 에 비례 — 매 fast response, 매 steady-state error 남김.
I (Integral): 매 누적 error — 매 steady-state error 제거, 매 windup 위험.
D (Derivative): 매 변화율 — 매 overshoot 감소, 매 noise 증폭.

매 tuning methods

Ziegler-Nichols: 매 Ku, Tu (oscillation) 측정 후 공식 적용.
Cohen-Coon: 매 process reaction curve 기반.
AutoTuning: 매 relay feedback (Åström-Hägglund).
Bayesian optimization: 매 simulation rollout + GP.
RL-based: 매 PPO/SAC 으로 Kp, Ki, Kd 학습.

매 응용

Drone attitude (PX4, ArduPilot).
Robot joint position control (ROS 2).
Cruise control, HVAC, 3D printer extruder.
LLM serving — token-rate controller (vLLM 의 batch sizing).
RLHF KL-coefficient adaptive tuning.
Training: gradient norm clipping with adaptive coefficient.

💻 패턴

Plain PID (discrete)

class PID:
    def __init__(self, kp, ki, kd, dt, output_limits=(-1, 1)):
        self.kp, self.ki, self.kd, self.dt = kp, ki, kd, dt
        self.lo, self.hi = output_limits
        self.integral = 0.0
        self.prev_error = 0.0

    def __call__(self, setpoint, measurement):
        error = setpoint - measurement
        self.integral += error * self.dt
        derivative = (error - self.prev_error) / self.dt
        output = self.kp*error + self.ki*self.integral + self.kd*derivative
        output = max(self.lo, min(self.hi, output))
        self.prev_error = error
        return output

Anti-windup (clamp + back-calculation)

class PIDAntiWindup(PID):
    def __init__(self, *args, kt=0.5, **kw):
        super().__init__(*args, **kw)
        self.kt = kt  # back-calc gain

    def __call__(self, setpoint, measurement):
        error = setpoint - measurement
        derivative = (error - self.prev_error) / self.dt
        u_unsat = self.kp*error + self.ki*self.integral + self.kd*derivative
        u_sat = max(self.lo, min(self.hi, u_unsat))
        # back-calculation: discount integral when saturated
        self.integral += self.dt * (error + self.kt * (u_sat - u_unsat))
        self.prev_error = error
        return u_sat

Derivative on measurement (D-kick 회피)

class PIDDerivOnMeas(PID):
    def __init__(self, *args, **kw):
        super().__init__(*args, **kw)
        self.prev_meas = None

    def __call__(self, setpoint, measurement):
        error = setpoint - measurement
        if self.prev_meas is None:
            d = 0
        else:
            d = -(measurement - self.prev_meas) / self.dt  # 매 setpoint step → spike 없음
        self.integral += error * self.dt
        out = self.kp*error + self.ki*self.integral + self.kd*d
        self.prev_meas = measurement
        return max(self.lo, min(self.hi, out))

Ziegler-Nichols tuning

def ziegler_nichols(Ku, Tu, kind="classic"):
    if kind == "classic":
        return dict(kp=0.6*Ku, ki=1.2*Ku/Tu, kd=0.075*Ku*Tu)
    elif kind == "no-overshoot":
        return dict(kp=0.2*Ku, ki=0.4*Ku/Tu, kd=Ku*Tu/15)
    elif kind == "PI-only":
        return dict(kp=0.45*Ku, ki=0.54*Ku/Tu, kd=0)

RLHF adaptive KL (PPO-style β)

def adaptive_kl_pid(kl_observed, kl_target=0.02, state=None):
    """β ↑ when KL too large; β ↓ when too small. PI controller on log(β)."""
    if state is None:
        state = {"integral": 0.0, "log_beta": 0.0}
    error = kl_observed - kl_target
    state["integral"] += error
    state["log_beta"] += 0.1 * error + 0.01 * state["integral"]
    return float(np.exp(state["log_beta"])), state

LLM token-rate controller (server batch)

def batch_size_pid(target_tps, current_tps, pid_state):
    """Maintain target tokens/sec by adjusting batch size."""
    delta = target_tps - current_tps
    pid_state["integral"] += delta
    adj = 0.05*delta + 0.001*pid_state["integral"]
    return max(1, int(pid_state["batch"] + adj))

매 결정 기준

상황	Controller
no steady-state error needed	P only
eliminate steady-state, slow process	PI
fast + minimal overshoot	PID with D-on-measurement
highly nonlinear / complex	MPC or RL (not PID)
discrete-event / queue	PI on rate
training schedule (KL, lr)	adaptive PI

기본값: 매 80% 의 경우 PI 면 충분. 매 D 매 noise 환경에서 신중히.

🔗 Graph

부모: Control-Theory · Feedback-Control-Systems
응용: Robotics · RLHF
Adjacent: Model-Predictive-Control (MPC) · Kalman-Filter-and-State-Tracking · Reinforcement-Learning

🤖 LLM 활용

언제: 매 inference server batch sizing, 매 RLHF KL coefficient, 매 lr schedule under loss target. 언제 X: 매 highly nonlinear delays — MPC. 매 strong constraints — RL/MPC.

❌ 안티패턴

No anti-windup with saturation: 매 integral 폭주 → overshoot.
D term on noisy raw signal: 매 noise 증폭 → 매 LPF (low-pass filter) 필수.
Derivative on setpoint (D-kick): 매 setpoint step → spike. 매 D-on-measurement 사용.
One-size-fits-all gains across operating regions: 매 nonlinear 시스템 — gain scheduling 필요.
Tuning by 임의 가이드: 매 system 마다 다름 — Ziegler-Nichols 또는 simulation 사용.

🧪 검증 / 중복

Verified (Åström & Hägglund, PID Controllers; Franklin et al. Feedback Control of Dynamic Systems; ArduPilot/PX4 firmware).
신뢰도 A.

🕓 Changelog

날짜	변경
2026-05-08	Phase 1
2026-05-10	Manual cleanup — PID FULL with anti-windup, D-on-meas, RLHF/serving applications

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