Lesson 8: PID Control¶

Goal / 目標¶

Add Integral (I) and Derivative (D) terms to the P controller from Lesson 5. Eliminate steady-state error and reduce overshoot.

レッスン5のP制御に積分(I)項と微分(D)項を追加する。定常偏差を除去し、オーバーシュートを低減する。

Prerequisites / 前提条件¶

Lesson 5 completed (P-control working, first flight achieved)
Lesson 6 completed (System Modeling, model-based Kp design)
Lesson 7 completed (System Identification, flight data analysis)

Key Concept: PID Control / PID制御¶

Block Diagram / ブロック図¶

                              +-->[Kp * e]----------+
                              |                      |
target -->(+)--> error(e) ----+-->[Ki * integral]--->+--> output --> mixer
            ^(-)              |                      |
            |                 +-->[Kd * de/dt]------>+
       gyro (actual)

Three Terms / 3つの項¶

Term	Formula	Role	役割
P (Proportional)	`Kp * error`	React to current error	現在の誤差に反応
I (Integral)	`Ki * sum(error * dt)`	Eliminate steady-state error	定常偏差を除去
D (Derivative)	`Kd * (error - prev_error) / dt`	Dampen overshoot	オーバーシュートを抑制

What Each Term Does / 各項の役割¶

P only:     Fast response but steady-state error remains
            速い応答だが定常偏差が残る

P + I:      Eliminates steady-state error but may overshoot
            定常偏差を除去するが、オーバーシュートの可能性

P + I + D:  Best response - fast, accurate, and well-damped
            最良の応答 - 速く、正確で、よく減衰する

Anti-Windup / アンチワインドアップ¶

The integral term accumulates error over time. Without limits, it can grow very large ("wind up") and cause dangerous overshoot.

積分項は時間とともに誤差を蓄積する。制限がないと非常に大きくなり（「ワインドアップ」）、危険なオーバーシュートを引き起こす。

Solution: Clamp the integral accumulator
解決策: 積分累積値をクランプする

  roll_integral += roll_error * dt;
  if (roll_integral >  0.5f) roll_integral =  0.5f;  // Anti-windup
  if (roll_integral < -0.5f) roll_integral = -0.5f;   // アンチワインドアップ

Why this matters: If you hold the drone still while armed, the integral accumulates. When released, all that stored energy causes a violent snap. Anti-windup prevents this.

なぜ重要か: アーム状態でドローンを手で押さえると積分値が蓄積する。離すと蓄積されたエネルギーで急激に動く。アンチワインドアップはこれを防ぐ。

State Reset on Disarm / ディスアーム時の状態リセット¶

Always reset integral and previous error when disarmed:

ディスアーム時は必ず積分値と前回誤差をリセットする:

if (!ws::is_armed()) {
    roll_integral = 0.0f;
    roll_prev_error = 0.0f;
    // ... same for pitch and yaw
}

PID Gains / PIDゲイン¶

Recommended Starting Values / 推奨初期値¶

Axis	Kp	Ki	Kd
Roll	0.25	0.3	0.005
Pitch	0.36	0.3	0.005
Yaw	2.0	0.5	0.01

Tuning Guide / チューニングガイド¶

Step 1: Start with P-only (Ki=0, Kd=0). Find a Kp that gives fast response with mild oscillation.

Step 2: Add D term to dampen the oscillation. Increase Kd until oscillation stops.

Step 3: Add I term to eliminate steady-state error. Start small (Ki=0.1) and increase slowly.

Symptom	Adjustment	調整
Slow response	Increase Kp	Kp を増やす
Oscillation (fast)	Increase Kd or decrease Kp	Kd を増やす or Kp を減らす
Steady-state drift	Increase Ki	Ki を増やす
Slow oscillation	Decrease Ki	Ki を減らす
Motor buzz/vibration	Decrease Kd	Kd を減らす

API / 使用するAPI¶

Function	Description
`ws::gyro_x/y/z()`	Angular rate [rad/s]
`ws::rc_roll/pitch/yaw()`	Stick inputs [-1, +1]
`ws::rc_throttle()`	Throttle [0, 1]
`ws::motor_mixer(T,R,P,Y)`	Apply control
`ws::telemetry_send(name, val)`	Send telemetry

Steps / 手順¶

sf lesson switch 8
Add I and D terms to each axis in student.cpp
Implement anti-windup (clamp integral to +/-0.5)
Add output limiting (clamp output to +/-1.0)
Reset state on disarm
Build, flash, and test: sf lesson build && sf lesson flash
Start with recommended gains, then tune

Challenge / チャレンジ¶

Add telemetry for P, I, D terms separately and observe with sf log wifi
Try flying without the D term. What happens?
Try flying without anti-windup. What happens when you hold the drone and release?
Can you achieve a stable 10-second hover?