From Fundamentally Misguided Position Control to Physically Correct Energy Control

Introduction

Classical PID control has existed for more than a century and is still widely taught today. However, in modern servo systems — especially industrial servos — continuing to apply classical PID in a dogmatic way is not merely suboptimal; in many cases, it is fundamentally unusable.

This article does not aim to deny the historical value of PID. Instead, it states a technical reality that must be confronted:

Classical PID has no common language with industrial servo systems.

The root cause is not poor tuning, but a mismatch at the mathematical and physical level of the control problem itself.

1. RC Servos and the Illusion That “PID Works”

RC servos provide position-only control.
The user sends a target angle (e.g., 120°), and the servo moves toward it using its internal electromechanical characteristics.

In this context, classical PID is typically applied as follows:

• At each control cycle:
  • Compute position error
  • Output an Output_Angle
  • Call myServo.write(Output_Angle)

The servo eventually reaches the target, which creates the illusion that PID is working correctly.

But the fundamental question remains:

What is the mathematical foundation of the integral term in classical PID?

2. The Integral Term of Classical PID: No Physical Meaning

In classical PID:$$I(t) = \int K_i\, e(t)\, dt$$

where:

• $e(t)$ is position error
• The PID output is used to influence system energy (velocity, acceleration, torque)

This means we are:

• Integrating meters, degrees, or pulses
• To control energy-related quantities

👉 A dimensional mismatch from the very beginning.

PID appears to “work” for RC servos only because of slow mechanics and strong internal constraints — not because the model is correct.

3. Overshoot Is Not an Accident — It Is Inevitable

Consider a simple case:

• Setpoint = 120°
• Initial position = 0°

Early phase:

• Large error → large positive P
• $e > 0$ for many cycles → I accumulates a large positive value

Near the setpoint:

• P decreases
• I remains large
• D (if present) is a small negative term, insufficient to cancel I

What happens?

👉 Overshoot is unavoidable.

Not possible — inevitable.

What is often described as “oscillation around the setpoint” is actually:

• The system dumping incorrectly accumulated energy
• By swinging back and forth until dissipation completes

In an era of:

• nano-scale precision
• industrial reliability
• long-term stability

👉 Such behavior is unacceptable.

4. Industrial Servos: Position Is the Destination, Speed Is the Path

Industrial servos do support position control, but:

Position defines the destination.
Speed defines how you get there.

If you:

• Send a pos_cmd
• Without actively controlling speed

The servo will:

• Move at a constant internal speed
• Toward a continuously changing destination
• With no direct relationship to the original setpoint

Tracking requires explicit speed control.

This is where classical PID loses its language:

• PID outputs position
• Industrial servos require speed

Any attempt to “convert position commands into speed commands” is:

• non-transparent
• mathematically unsupported
• an ad-hoc workaround

5. Energy-Based Control: Choosing the Correct Control Variable

In modern servo systems, the correct control variable is:

Speed — or more fundamentally — system energy.

Define velocity error:$$E_v = V_{target} – V_{actual}$$

Its integral from $t_0$​ to $t$:$$\int_{t_0}^{t} E_v(\tau)\, d\tau$$

Directly yields:$$= pos_{cmd} – pos_{cur} = e$$

👉 Position error e is the integral of velocity error.

No artificial integration with $dt$.
No wind-up.
No tricks.

6. Physical Meaning of eee

• Large $e$ → system is far → more energy is required
• Smoothly decreasing $e$ → correct energy injection → stable system
• Abrupt changes in $e$ → sudden energy impulses → irregular behavior

Irregularity can be naturally defined as:

r = fabsf(e - e_last) / (fabsf(e_last) + Efloor);

This does not measure error oscillation —
It measures energy impulses.

7. Pursuit vs Tracking Is Not an Integral Problem

A common question is:

“What if the servo and target do not start from the same position?”

The answer is straightforward:

Whether the system is in ‘pursuit’ or ‘tracking’ mode is not a property of the integral model, but a strategic decision at a higher control layer.

For example:

• Far away → allow Vcmd to saturate at Vmax (pursuit)
• Near target → switch to smooth tracking

👉 The energy-based model remains unchanged.

8. Conclusion

Classical PID:

• is historically important
• but fundamentally incompatible with modern industrial servos

Overshoot:

• is not a tuning failure
• but an inevitable consequence of an incorrect model

Energy-Based Control:

• targets the correct physical variable
• has clear physical meaning
• requires no corrective patches
• and speaks the native language of industrial servos