this documents explains the fundamental classical control algorithms used in robotics and automation-focusing on how they process error signals to stabiliz or control system.
- P (Proportional)
- PI (Proportional-Integral)
- PD (Proportional-Derivative)
- PID (Proportional-Integral-Derivative)
the proportional controller produces an output that is directly proportional to the current error between the desired setpoint and sensor value process variable.
P = Error * Kp
- error : sensor value - setpoint
- Kp : proportional gain
- Fast respons
- Simple implementation.
the Pi controls adds an integral term to remove the steady state error by accumulating past errors.
PI = (KpError)+(Kisum(error)*dt
- Ki : integral gain (eliminates persistent offset)
- Zero steady-state error
- Smoother oytput than p
- Slow reaction due to the integral term.
the PD controllers prediccts future error by considering the rate of charg of the error.
PD = (KpError)+(Kd(de(t)/dt)
- Ki : integral gain (eliminates persistent offset)
- Zero steady-state error
- Smoother oytput than p
- Slow reaction due to the integral term.
the PID controllers combines the proportional,integral and derivative terms.
it is most widely used control algorithm in industry and robotics.
PID = (KpError)+(Kisum(errordt))+(Kd(de(t)/dt)
- Kp : proportional gain
- Ki : integral gain (eliminates persistent offset)
- Kd : derivative gain (anticipates future behaviors)
- Precise and stable
- Handles disturbances effectively
- Requires careful tuning of Kp,Ki and Kd
| Controller | Advantages | Disadvantages |
|---|---|---|
| P (Proportional) | ⚡ Simple and easy to implement ⚙️ Fast response to changes 🧩 Requires minimal tuning |
❌ Cannot eliminate steady-state error 📉 May cause oscillation or overshoot 🔊 Sensitive to system gain variations |
| PI (Proportional + Integral) | ✅ Eliminates steady-state error 🔄 Smooth and stable output 📈 Improves accuracy for constant disturbances |
🐢 Slower response than P 🧮 Integral term can cause “windup” if not limited |
| PD (Proportional + Derivative) | 🚀 Faster and more stable than P 🧠 Predicts future error trends 📉 Reduces overshoot effectively |
❌ Does not eliminate steady-state error 🔊 Very sensitive to measurement noise ⚙️ Requires careful tuning of Kd |
| PID (Proportional + Integral + Derivative) | 🌟 Combines all benefits: fast, accurate, stable 🎯 Eliminates steady-state error ⚙️ Excellent for most control systems |
💻 Computationally more demanding 🧩 Over-tuning can cause instability |