Active Disturbance Rejection Control (ADRC)

The Extended State Observer is the core estimation engine of ADRC. Unlike a traditional Luenberger observer that only estimates the internal state of a known plant, the ESO treats the combined effect of internal non-linearities and external disturbances as an additional, augmented state variable—the 'total disturbance'. It estimates both the system's internal states and this lumped disturbance in real-time using only the system's input and output signals. This eliminates the need for a precise dynamic model.

ADRC fundamentally operates on a canonical cascade-integral form rather than a specific high-fidelity process model. The controller assumes the plant can be reduced to a simple chain of integrators. Any deviation from this simple form—whether non-linear friction, parameter drift, or an external load—is mathematically lumped into the total disturbance and actively canceled. This makes the controller inherently robust and eliminates the labor-intensive system identification phase required by Model Predictive Control.

The control law in ADRC is a two-stage process:

• Disturbance Rejection: The control signal is augmented to dynamically subtract the total disturbance estimated by the ESO. This effectively linearizes the plant in real-time.
• Proportional-Derivative Control: Once the plant is reduced to a simple integrator chain, a simple PD controller (not PID) is sufficient to drive the output to the setpoint. The integral term is unnecessary because the ESO handles steady-state error by canceling constant disturbances.

To simplify tuning for industrial engineers, ADRC is often parameterized using a bandwidth concept. All observer and controller gains are analytically calculated as functions of two intuitive tuning knobs:

• Observer Bandwidth (ω₀): Determines how quickly the ESO tracks the system states and the total disturbance. A higher value provides faster estimation but increases noise sensitivity.
• Controller Bandwidth (ωc): Determines the speed of the closed-loop response. This reduces complex multi-gain tuning to a transparent trade-off between speed and noise immunity.

In Multi-Input Multi-Output (MIMO) systems, cross-coupling between loops is a major challenge. ADRC treats the dynamic coupling from one loop acting on another not as a complex interaction matrix to be modeled, but as a component of the total disturbance. Each control channel has its own ESO that estimates and cancels the cross-coupling in real-time. This allows a complex MIMO plant to be controlled as a set of independent Single-Input Single-Output (SISO) loops, drastically simplifying the control architecture.

ADRC is often described as the natural evolution of the PID controller to meet the demands of modern digital control. It resolves PID's fundamental limitations:

• Error Computation: Unlike PID, which computes error on a potentially noisy step-change in setpoint, ADRC uses a smooth transition profile to avoid overshoot.
• Disturbance Rejection: ADRC's ESO provides a more efficient and proactive disturbance rejection mechanism than the PID's integral term, which can cause windup and phase lag.
• Noise Differentiation: The ESO provides a filtered derivative of the output, avoiding the noise amplification of a direct differentiator on the error signal.