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이름만 다른(표기 변형) [[위키링크]]를 대상 문서의 canonical 제목으로 치환해 끊겼던 1,200개 링크를 연결. 제목/파일명 정규화 일치만 적용하고 별칭 매칭은 과병합 위험으로 제외(애매성 가드). 원본은 _link_reconcile_backup/ 에 백업. 도구: Datacollect/scripts/link_reconcile_apply.mjs Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
179 lines
6.2 KiB
Markdown
179 lines
6.2 KiB
Markdown
---
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id: wiki-2026-0508-control-systems-engineering
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title: Control Systems Engineering
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category: 10_Wiki/Topics
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status: verified
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canonical_id: self
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aliases: [control-systems, feedback-control, PID-control]
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duplicate_of: none
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source_trust_level: A
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confidence_score: 0.9
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verification_status: applied
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tags: [control-systems, pid, mpc, feedback]
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raw_sources: []
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last_reinforced: 2026-05-10
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github_commit: pending
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tech_stack:
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language: python
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framework: do-mpc/control
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---
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# Control Systems Engineering
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## 매 한 줄
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> **"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.
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## 매 핵심
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### 매 building blocks
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- **Plant** — 매 controlled system (motor, reactor, drone).
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- **Sensor** — 매 measurement (encoder, IMU, thermocouple).
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- **Controller** — 매 algorithm (PID, MPC, LQR).
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- **Actuator** — 매 output (PWM, valve, voltage).
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- **Reference / setpoint** — 매 desired state.
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### 매 stability
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- **Open-loop**: 매 simple, 매 no feedback — 매 disturbance 에 fragile.
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- **Closed-loop**: 매 feedback — 매 disturbance reject + setpoint track.
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- **Stability criteria**: Routh-Hurwitz, Nyquist, Bode (gain margin > 6 dB, phase margin > 45°).
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### 매 controller spectrum
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1. **Bang-bang** — 매 thermostat.
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2. **PID** — 매 95% loops.
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3. **State-space (LQR / pole placement)** — MIMO linear.
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4. **MPC** — 매 constrained, predictive.
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5. **Adaptive / gain scheduling** — 매 nonlinear plants.
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6. **RL / learned policy** — 매 high-dim, 매 simulation 의 train.
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7. **Robust H∞** — 매 worst-case guarantees.
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## 💻 패턴
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### Discrete PID with anti-windup
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```python
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class PID:
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def __init__(self, kp, ki, kd, dt, u_min, u_max):
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self.kp, self.ki, self.kd, self.dt = kp, ki, kd, dt
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self.u_min, self.u_max = u_min, u_max
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self.i, self.prev_e = 0.0, 0.0
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def step(self, setpoint, measurement):
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e = setpoint - measurement
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self.i += e * self.dt
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d = (e - self.prev_e) / self.dt
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u = self.kp*e + self.ki*self.i + self.kd*d
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u_clamped = max(self.u_min, min(self.u_max, u))
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# 매 anti-windup: 매 saturate 시 integrator 의 back-calc
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if u != u_clamped:
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self.i -= (u - u_clamped) / self.ki if self.ki else 0
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self.prev_e = e
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return u_clamped
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```
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### Ziegler-Nichols 의 tune
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```python
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def ziegler_nichols(Ku, Tu, kind='PID'):
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if kind == 'PID':
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return dict(kp=0.6*Ku, ki=1.2*Ku/Tu, kd=0.075*Ku*Tu)
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if kind == 'PI':
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return dict(kp=0.45*Ku, ki=0.54*Ku/Tu, kd=0)
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```
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### State-space LQR (CartPole)
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```python
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import numpy as np
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from scipy.linalg import solve_continuous_are
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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]])
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B = np.array([[0],[1/M],[0],[-1/(M*l)]])
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Q = np.diag([1, 1, 10, 10]); R = np.array([[0.1]])
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P = solve_continuous_are(A, B, Q, R)
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K = np.linalg.inv(R) @ B.T @ P
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u = -K @ x # state feedback
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```
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### MPC with do-mpc
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```python
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import do_mpc
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model = do_mpc.model.Model('continuous')
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x = model.set_variable('_x', 'x', shape=(2,1))
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u = model.set_variable('_u', 'u')
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model.set_rhs('x', np.array([[x[1]],[u - 0.1*x[1]]]))
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model.setup()
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mpc = do_mpc.controller.MPC(model)
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mpc.set_param(n_horizon=20, t_step=0.1)
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mpc.set_objective(mterm=x[0]**2, lterm=x[0]**2 + 0.01*u**2)
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mpc.bounds['lower','_u','u'] = -5; mpc.bounds['upper','_u','u'] = 5
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mpc.setup()
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```
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### Kalman filter (state estimation)
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```python
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def kalman_step(x, P, u, z, A, B, H, Q, R):
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x_pred = A @ x + B @ u
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P_pred = A @ P @ A.T + Q
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K = P_pred @ H.T @ np.linalg.inv(H @ P_pred @ H.T + R)
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x = x_pred + K @ (z - H @ x_pred)
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P = (np.eye(len(x)) - K @ H) @ P_pred
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return x, P
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```
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### RL policy (PPO via stable-baselines3)
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```python
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from stable_baselines3 import PPO
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import gymnasium as gym
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env = gym.make("Pendulum-v1")
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model = PPO("MlpPolicy", env, verbose=1)
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model.learn(total_timesteps=200_000)
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```
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### Real-time loop (Linux PREEMPT_RT)
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```python
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import time, os
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os.sched_setscheduler(0, os.SCHED_FIFO, os.sched_param(80))
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T = 0.001 # 1 kHz
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while True:
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t0 = time.perf_counter()
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u = pid.step(setpoint, sensor.read())
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actuator.write(u)
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while time.perf_counter() - t0 < T: pass
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```
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## 매 결정 기준
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| 상황 | Approach |
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|---|---|
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| 매 SISO + linear | PID |
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| 매 MIMO + linear | LQR / state-space |
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| Constrained + slow plant | MPC |
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| Nonlinear + simulator 가능 | RL (PPO, SAC) |
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| Safety-critical + uncertain | Robust H∞ / sliding mode |
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| 매 very fast (>10 kHz) | Hardware PID (FPGA) |
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**기본값**: PID with proper tuning + anti-windup; escalate to MPC if multivariable or constrained.
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## 🔗 Graph
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- 부모: [[Cyber-Physical-Systems]] · [[Robotics]]
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- 변형: [[PID]] · [[MPC]]
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- 응용: [[Digital Twin]]
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- Adjacent: [[Kalman-Filter-and-State-Tracking|Kalman-Filter]] · [[Reinforcement-Learning]]
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## 🤖 LLM 활용
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**언제**: 매 controller derivation explanation, 매 transfer function manipulation, 매 tuning suggestion based on step response, 매 simulation script generation.
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**언제 X**: 매 actual real-time loop (deterministic 코드 / FPGA). 매 safety certification (formal verification 필요).
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## ❌ 안티패턴
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- **No anti-windup**: 매 actuator saturate 시 integral runaway → overshoot.
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- **Derivative on error (vs measurement)**: 매 setpoint step 시 derivative kick — derivative-on-PV 사용.
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- **Tune via trial-and-error only**: 매 system identification 의 사용 (Ziegler-Nichols, FOPDT fit).
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- **MPC without warm-start**: 매 solve time 의 explode — previous solution 의 reuse.
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- **No filter on derivative**: 매 measurement noise 가 D term 의 amplify.
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- **RL on real hardware first**: 매 sim-to-real 의 가야 — safe exploration.
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## 🧪 검증 / 중복
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- Verified (Åström & Murray "Feedback Systems", Skogestad MIMO control, do-mpc docs, IEEE control textbooks).
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- 신뢰도 A.
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## 🕓 Changelog
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| 날짜 | 변경 |
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|---|---|
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| 2026-05-08 | Phase 1 |
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| 2026-05-10 | Manual cleanup — control engineering: PID, LQR, MPC, RL, Kalman |
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