Disturbance Observer-Based Control (DOBC)

Updated 9 December 2025

Disturbance Observer-Based Control (DOBC) is a robust control strategy that integrates a dedicated observer within a two-degree-of-freedom framework to estimate and compensate for unknown disturbances and modeling uncertainties.
It employs a low-pass filter (Q-filter) in conjunction with a nominal plant model to balance disturbance rejection, robustness, and noise sensitivity in both linear and nonlinear systems.
DOBC has been successfully applied in motion control, process industries, power grids, and automotive systems, yielding improvements such as reduced settling times, lower overshoot, and enhanced stability margins.

Disturbance Observer-Based Control (DOBC) is a robust control methodology that enhances system performance in the presence of plant uncertainty and external disturbances by embedding a disturbance observer (DOB) within a two-degree-of-freedom (2-DOF) feedback control structure. The central idea is to estimate and compensate for the lumped effect of unknown disturbances and modeling errors using a dedicated observer, typically implemented as an inner loop around an outer "baseline" controller. This structure renders the closed-loop system behavior close to the nominal closed-loop (controller–nominal-plant) in both steady-state and transients, while maintaining or even improving classical gain and phase margins. DOBC is highly influential and broadly deployed across domains including motion control, process industry, power grids, automotive systems, and safety-critical control for nonlinear and distributed parameter systems (Shim, 2021, Sariyildiz et al., 2019, Sariyildiz et al., 2019, Kadam, 2017).

1. Fundamental Architecture and Theoretical Principles

The canonical DOBC architecture consists of an outer-loop baseline controller $C(s)$ (such as PD or PID) and an inner-loop disturbance observer constructed using a nominal plant model $P_n(s)$ and a low-pass filter $Q(s)$ . The DOB estimates the lumped disturbance—comprising unmodeled dynamics, parametric errors, and external inputs—by forming the quantity: $\hat{d}(s) = Q(s)\, [\, y(s) - P_n(s)u(s) \,]$ and injecting $-\hat{d}(s)$ at the plant input. As a result, the plant input becomes $u(s) = u_c(s) - \hat{d}(s)$ , where $u_c(s)$ is the output of the baseline controller. The observer enables the plant output $y(s)$ to follow the nominal closed-loop behavior within the bandwidth of $Q(s)$ . The disturbance estimation dynamics and the design of $Q(s)$ (often a first- or higher-order low-pass filter) set the trade-offs between disturbance rejection, robustness, and noise sensitivity (Shim, 2021, Sariyildiz et al., 2019, Sariyildiz et al., 2019).

For integrating plus dead-time (IPDT) processes—a representative class of challenging systems where integral action is essential for disturbance rejection—a parallel disturbance observer is paired with a well-tuned PD controller to provide integral-like disturbance suppression without degrading servo response or unnecessarily increasing actuator activity (Kadam, 2017).

2. DOBC in Linear and Nonlinear Systems: Observer Construction and Analysis

For linear time-invariant plants, the DOB is typically constructed using the nominal inverse $P_n^{-1}(s)$ cascaded with $Q(s)$ , with the filter order chosen to ensure properness ( $\deg Q(s) \geq \deg \mathrm{den}\,P_n(s)-\deg \mathrm{num}\,P_n(s)$ ). The closed-loop input-output relationship becomes: $y(s) = \frac{P_n(s)P(s)\,C(s)}{D(s)}\,r(s) + \frac{P_n(s)P(s)[1-Q(s)]}{D(s)}\,d(s) - \frac{P(s)[Q(s) + P_n(s)C(s)]}{D(s)}\,n(s)$ where $D(s)$ collects all direct and observer-dependent terms (Shim, 2021). At low frequencies ( $Q(s) \approx 1$ ), the nominal closed-loop dynamics with disturbance rejection are recovered.

Robust stability is classically established via small-gain or singular perturbation arguments and, for parametric uncertainty classes, via the circle criterion by relating the DOB's sensitivity and complementary sensitivity functions to uncertainty bounds. When plant models have delay, minimum-phase zeros or unstable poles, precise upper and lower bounds on the DOB bandwidth are derived analytically by leveraging Bode and Poisson integral formulas (Sariyildiz et al., 2019).

In nonlinear systems, DOBC is implemented through observer forms adapted to the system's structure, such as matched and mismatched disturbance settings, filtered-regressor forms (avoiding state derivative measurement), and extended state observers. Adaptive and finite-time variants have been developed, including observers equipped with experience-replay to foster fast convergence and with rigorous Lyapunov-based stability and convergence guarantees, even in the absence of explicit knowledge of disturbance dynamics (Li et al., 2020, Wang et al., 2022).

3. Design, Implementation, and Tuning Guidelines

DOBC design proceeds as follows:

Nominal Model Identification: Establish $P_n(s)$ via process identification or physical modeling, ensuring accurate estimation of dominant parameters (e.g., plant gain, dead time, inertia, torque constant) (Shim, 2021, Kadam, 2017).
Q-Filter Selection: Choose filter order to make $Q(s)P_n^{-1}(s)$ proper. Set its bandwidth to envelop the disturbance frequencies but avoid overlapping with measurement noise or unmodeled high-frequency dynamics. This is often achieved by targeting the −3 dB bandwidth above the disturbance region but below the resonance or sampling limits (Grover et al., 2022, Sariyildiz et al., 2019, Kwon et al., 2022).
Baseline Controller Tuning: Use classical design methods to ensure the outer-loop controller achieves the desired set-point tracking and stability margins for the nominal model. In certain applications, direct time-domain–frequency-domain links facilitate controller tuning via settling time, gain and phase margins (Kadam, 2017).
Observer Gain Adjustment: For estimator gains in nonlinear or state-space observers, tune to ensure rapid disturbance tracking while avoiding amplification of sensor noise. Often, a trade-off dictates a moderate gain just high enough for tight disturbance rejection (Alan et al., 2022, Kadam, 2017).
Simulation-Driven Validation: Confirm through closed-loop simulation that performance, robustness, and disturbance rejection requirements are met, especially under model mismatch, parameter drift, or communication delays (Grover et al., 2022, Grover et al., 2022, Kadam, 2017).

In digital implementations, discrete-time equivalents of Bode’s integral theorem and root-locus analysis reveal tighter bounds for DOB bandwidths and allowable plant-model mismatch than continuous-time intuition predicts. These stricter constraints, specified in terms like $0 < a\,g_D\,T_s < 2$ for first-order systems (where $a$ is the nominal/true parameter ratio, $g_D$ observer gain, $T_s$ sample time), are vital to prevent instability or excessive noise sensitivity (Sariyildiz, 2022, Sariyildiz, 2021, Sariyildiz et al., 2020).

4. Application Domains and Performance Comparisons

DOBC has achieved broad impact across sectors:

Process Control: For IPDT processes, DOBC with PD control yields dramatically reduced settling times, overshoot, and performance indices (ISE, IAE, control energy) compared to legacy PID and model-tuned alternatives. For example, a PD-DOBC setup exhibited step response with settling time 28.1 s and overshoot 0.19%, outperforming rivals (settling time >47 s, overshoot >23%) (Kadam, 2017).
Power Systems: DOBC in frequency and voltage regulation for hybrid microgrids and RES-integrated power systems achieved far lower frequency deviation, superior disturbance rejection under worst-case uncertainty, and robustness to stochastic variability and communication delays (Grover et al., 2022, Grover et al., 2022).
Mechatronics and Robotics: In acceleration-based robot position control, inner-loop DOBC decouples disturbance rejection from performance shaping. Ultimate error bounds shrink with higher observer bandwidths and nominal inertia choices, yet practical robustness constraints (noise sensitivity, actuator saturation) remain (Sariyildiz et al., 2019).
Motion Control and Actuation: Discrete-time DOBC in motion controllers provides regulation and tracking performance robust against model variation and quantifiable noise peaks. Detailed design inequalities guarantee robust stability and performance (Sariyildiz, 2021, Sariyildiz et al., 2020).
Safety-Critical and Nonlinear Control: DOBC integrated with control barrier functions (CBF) yields provably safe controllers with quantifiable error bounds, enabling less conservative performance than worst-case robustification (Alan et al., 2022, Wang et al., 2022).
Industrial and Energy Systems: FPGA-implemented DOBC in high-power RF amplifiers (LANSCE LINAC SSPA) provides real-time feed-forward cancellation of temperature-induced phase drifts, reducing residual phase errors from ±20–40° to a few degrees with no modification of the outer-loop PI controller (Kwon et al., 2022).

Performance improvements consistently include lower IAE/ISE, reduced control energy, faster response, tighter regulation under disturbance, and in many cases, reduced actuator wear by activating compensation only when necessary (Kadam, 2017, Grover et al., 2022, Kwon et al., 2022).

5. Robustness–Performance–Noise Trade-Offs and Limitations

A defining feature of DOBC is the balancing of disturbance-rejection bandwidth against robustness margins and sensor noise sensitivity—a direct consequence of Bode’s integral and the “waterbed” phenomenon:

Disturbance Rejection vs. Noise Sensitivity: As DOB bandwidth increases, low-frequency disturbance rejection improves, but mid-band complementary sensitivity peaks grow, amplifying measurement noise or destabilizing feedback in the presence of lightly-damped or non-minimum-phase dynamics (Sariyildiz et al., 2019, Sariyildiz, 2022, Sariyildiz, 2021, Sariyildiz et al., 2020).
Robustness Constraints: Upper and lower bandwidth bounds, imposed by plant right-half-plane zeros and poles or delays, must not be violated. Discrete-time constraints are stricter, with tight bounds such as $a\,\omega_d\,T_s < 2$ crucial for stable digital implementation (Sariyildiz, 2022, Sariyildiz et al., 2020).
Observer Model Accuracy: Performance degrades if the nominal model differs substantially from the true plant or if unmodeled high-frequency dynamics are present (Kadam, 2017, Kwon et al., 2022).
Integral-Action Limitations: Pure PD control cannot reject constant disturbances; the disturbance observer must be implemented in parallel to restore integral-like regulation (Kadam, 2017).

Practical guidelines include careful nominal model selection (favoring overestimation to maintain robustness), moderate filter bandwidth, and system identification to minimize modeling errors (Sariyildiz et al., 2021).

6. Extensions, Trends, and Open Directions

Recent research continues to extend DOBC:

Finite-Time and Adaptive DOB: Observers exploiting filtered regressor approaches, experience-replay, and adaptive laws develop rigorous finite-time convergence and relax derivative measurement requirements (Li et al., 2020).
Distributed and Safety-Critical DOBC: Integration with control barrier functions (CBF) yields formal safety guarantees for complex, disturbance-prone systems under online convex optimization (Alan et al., 2022, Wang et al., 2022).
Implementation in Complex Systems: FPGA-embedded DOBC for RF systems, real-time microgrid controls, and nonlinear model predictive control (MPC) for aerial vehicles—combined with EKF-based disturbance estimation—demonstrate successful deployment and new application frontiers (Kwon et al., 2022, Grover et al., 2022, Cheung et al., 21 Sep 2024).
Analytical Design and Tool Support: Unified integral-formula–constrained design procedures, analytic synthesis of discrete-time DOb parameters, and verification of system-level performance are increasingly standard (Sariyildiz et al., 2019, Sariyildiz, 2021, Sariyildiz et al., 2020).

Challenges include further unification for MIMO/multi-agent systems, high-order Q-filter design, systematic tuning under digital constraints, generalization to mismatched disturbances, and integration with learning-based estimation and inference techniques (Sariyildiz et al., 2019, Sariyildiz et al., 2019).

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