2nd/10_Wiki/Topics/Architecture/Control_Systems_Engineering.md

id, title, category, status, canonical_id, aliases, duplicate_of, source_trust_level, confidence_score, verification_status, tags, raw_sources, last_reinforced, github_commit, tech_stack

id	title	category	status	canonical_id	aliases	duplicate_of	source_trust_level	confidence_score	verification_status	tags	raw_sources	last_reinforced	github_commit	tech_stack
wiki-2026-0508-control-systems-engineering	Control Systems Engineering	10_Wiki/Topics	verified	self	control-systems feedback-control PID-control	none	A	0.9	applied	control-systems pid mpc feedback		2026-05-10	pending	language framework python do-mpc/control

Control Systems Engineering

매 한 줄

"매 control 의 매 measure → compare → actuate 의 closed loop". 매 PID (1922 Minorsky) 가 매 95% industrial loops, 매 MPC (Model Predictive Control) 가 매 multivariable + constrained problems 의 dominant. 2026 의 매 RL-augmented control + neural ODEs 가 매 emerging — 매 Boston Dynamics, Tesla Autopilot, NVIDIA GR00T 가 hybrid.

매 핵심

매 building blocks

• Plant — 매 controlled system (motor, reactor, drone).
• Sensor — 매 measurement (encoder, IMU, thermocouple).
• Controller — 매 algorithm (PID, MPC, LQR).
• Actuator — 매 output (PWM, valve, voltage).
• Reference / setpoint — 매 desired state.

매 stability

• Open-loop: 매 simple, 매 no feedback — 매 disturbance 에 fragile.
• Closed-loop: 매 feedback — 매 disturbance reject + setpoint track.
• Stability criteria: Routh-Hurwitz, Nyquist, Bode (gain margin > 6 dB, phase margin > 45°).

매 controller spectrum

1. Bang-bang — 매 thermostat.
2. PID — 매 95% loops.
3. State-space (LQR / pole placement) — MIMO linear.
4. MPC — 매 constrained, predictive.
5. Adaptive / gain scheduling — 매 nonlinear plants.
6. RL / learned policy — 매 high-dim, 매 simulation 의 train.
7. Robust H∞ — 매 worst-case guarantees.

💻 패턴

Discrete PID with anti-windup

class PID:
    def __init__(self, kp, ki, kd, dt, u_min, u_max):
        self.kp, self.ki, self.kd, self.dt = kp, ki, kd, dt
        self.u_min, self.u_max = u_min, u_max
        self.i, self.prev_e = 0.0, 0.0

    def step(self, setpoint, measurement):
        e = setpoint - measurement
        self.i += e * self.dt
        d = (e - self.prev_e) / self.dt
        u = self.kp*e + self.ki*self.i + self.kd*d
        u_clamped = max(self.u_min, min(self.u_max, u))
        # 매 anti-windup: 매 saturate 시 integrator 의 back-calc
        if u != u_clamped:
            self.i -= (u - u_clamped) / self.ki if self.ki else 0
        self.prev_e = e
        return u_clamped

Ziegler-Nichols 의 tune

def ziegler_nichols(Ku, Tu, kind='PID'):
    if kind == 'PID':
        return dict(kp=0.6*Ku, ki=1.2*Ku/Tu, kd=0.075*Ku*Tu)
    if kind == 'PI':
        return dict(kp=0.45*Ku, ki=0.54*Ku/Tu, kd=0)

State-space LQR (CartPole)

import numpy as np
from scipy.linalg import solve_continuous_are
A = np.array([[0,1,0,0],[0,0,-mp*g/M,0],[0,0,0,1],[0,0,(M+mp)*g/(M*l),0]])
B = np.array([[0],[1/M],[0],[-1/(M*l)]])
Q = np.diag([1, 1, 10, 10]); R = np.array([[0.1]])
P = solve_continuous_are(A, B, Q, R)
K = np.linalg.inv(R) @ B.T @ P
u = -K @ x  # state feedback

MPC with do-mpc

import do_mpc
model = do_mpc.model.Model('continuous')
x = model.set_variable('_x', 'x', shape=(2,1))
u = model.set_variable('_u', 'u')
model.set_rhs('x', np.array([[x[1]],[u - 0.1*x[1]]]))
model.setup()
mpc = do_mpc.controller.MPC(model)
mpc.set_param(n_horizon=20, t_step=0.1)
mpc.set_objective(mterm=x[0]**2, lterm=x[0]**2 + 0.01*u**2)
mpc.bounds['lower','_u','u'] = -5; mpc.bounds['upper','_u','u'] = 5
mpc.setup()

Kalman filter (state estimation)

def kalman_step(x, P, u, z, A, B, H, Q, R):
    x_pred = A @ x + B @ u
    P_pred = A @ P @ A.T + Q
    K = P_pred @ H.T @ np.linalg.inv(H @ P_pred @ H.T + R)
    x = x_pred + K @ (z - H @ x_pred)
    P = (np.eye(len(x)) - K @ H) @ P_pred
    return x, P

RL policy (PPO via stable-baselines3)

from stable_baselines3 import PPO
import gymnasium as gym
env = gym.make("Pendulum-v1")
model = PPO("MlpPolicy", env, verbose=1)
model.learn(total_timesteps=200_000)

Real-time loop (Linux PREEMPT_RT)

import time, os
os.sched_setscheduler(0, os.SCHED_FIFO, os.sched_param(80))
T = 0.001  # 1 kHz
while True:
    t0 = time.perf_counter()
    u = pid.step(setpoint, sensor.read())
    actuator.write(u)
    while time.perf_counter() - t0 < T: pass

매 결정 기준

상황	Approach
매 SISO + linear	PID
매 MIMO + linear	LQR / state-space
Constrained + slow plant	MPC
Nonlinear + simulator 가능	RL (PPO, SAC)
Safety-critical + uncertain	Robust H∞ / sliding mode
매 very fast (>10 kHz)	Hardware PID (FPGA)

기본값: PID with proper tuning + anti-windup; escalate to MPC if multivariable or constrained.

🔗 Graph

• 부모: Cyber-Physical-Systems · Robotics
• 변형: PID · MPC
• 응용: Digital-Twin
• Adjacent: Kalman-Filter-and-State-Tracking · Reinforcement-Learning

🤖 LLM 활용

언제: 매 controller derivation explanation, 매 transfer function manipulation, 매 tuning suggestion based on step response, 매 simulation script generation. 언제 X: 매 actual real-time loop (deterministic 코드 / FPGA). 매 safety certification (formal verification 필요).

❌ 안티패턴

• No anti-windup: 매 actuator saturate 시 integral runaway → overshoot.
• Derivative on error (vs measurement): 매 setpoint step 시 derivative kick — derivative-on-PV 사용.
• Tune via trial-and-error only: 매 system identification 의 사용 (Ziegler-Nichols, FOPDT fit).
• MPC without warm-start: 매 solve time 의 explode — previous solution 의 reuse.
• No filter on derivative: 매 measurement noise 가 D term 의 amplify.
• RL on real hardware first: 매 sim-to-real 의 가야 — safe exploration.

🧪 검증 / 중복

• Verified (Åström & Murray "Feedback Systems", Skogestad MIMO control, do-mpc docs, IEEE control textbooks).
• 신뢰도 A.

🕓 Changelog

날짜	변경
2026-05-08	Phase 1
2026-05-10	Manual cleanup — control engineering: PID, LQR, MPC, RL, Kalman