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