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Disturbance Observer-based Robust Control and Its Applications: 35th Anniversary Overview
Emre Sariyildiz, Roberto Oboe, Kouhei Ohnishi
TL;DR
Robust control must address plant uncertainties and external disturbances, motivating disturbance estimation and cancellation when direct disturbance measurement is unavailable. This paper surveys DOb’s origins, applications, and linear and nonlinear analysis and synthesis within a unified framework. It presents DOb as a widely used practical robust-control approach, while noting that parameter tuning still often relies on designer experience and lacks sufficiently practical analysis and synthesis techniques.
Problem
Plant uncertainties and external disturbances are difficult to cancel directly because they are often unknown or unmeasurable, motivating observer-based robust control.
Method
The paper surveys DOb-based robust control and explains its linear and nonlinear analysis and synthesis using a unified framework.
Results
DOb-based robust control is presented as a widely used approach whose disturbance estimates support robustness across many engineering applications.
Takeaways & Limitations
DOb’s two-degree-of-freedom structure supports intuitive robust-controller synthesis while allowing disturbance-observer and performance-controller tuning to be adjusted separately.
Takeaways & Limitations
Design parameters are generally tuned by trial and error, so performance depends heavily on designers’ experience; practical analysis and synthesis techniques remain lacking.
Abstract
from arXiv · showhide
Disturbance Observer has been one of the most widely used robust control tools since it was proposed in 1983. This paper introduces the origins of Disturbance Observer and presents a survey of the major results on Disturbance Observer-based robust control in the last thirty-five years. Furthermore, it explains the analysis and synthesis techniques of Disturbance Observer-based robust control for linear and nonlinear systems by using a unified framework. In the last section, this paper presents concluding remarks on Disturbance Observer-based robust control and its engineering applications.
I. INTRODUCTION
The paper frames Disturbance Observer-based robust control as a simple, flexible, and effective response to plant uncertainties and external disturbances, then surveys its origins, developments, synthesis, and applications.
- DOb estimates internal and external disturbances using identified plant dynamics and measurable states, then feeds those estimates back to achieve robustness.
- DOb is presented as a widely used robust control tool because of its simplicity, flexibility, and efficacy.
- The paper surveys DOb-based robust control from its origins through major results, analysis and synthesis techniques, two-degree-of-freedom control, and engineering applications.
II. ORIGINS OF DISTURBANCE OBSERVER
DOb emerged from efforts to address plant uncertainties and unmeasured disturbances, evolving from robust observers and unknown-input estimation toward Ohnishi’s 1983 disturbance observer.
- A. Birth of Robust Control (1960s – 1980s): Robust control arose to address inevitable plant uncertainties and external disturbances, while classical feedback methods offered limited disturbance suppression.
- A. Birth of Robust Control (1960s – 1980s): Feedback-based suppression can be complex, slow against strong disturbances, and conservative, whereas feedforward cancellation is impractical when disturbances are unknown.
- B. Birth of DOb (1960s – 1980s): Robust state observers and unknown-input observers were developed in the 1960s and 1970s to handle unmeasured inputs and estimate external disturbances.
- B. Birth of DOb (1960s – 1980s): Johnson used disturbance estimates in robust control during the late 1960s and 1970s, including the Disturbance Accommodating Controller.
- B. Birth of DOb (1960s – 1980s): Ohnishi proposed the Disturbance Observer in 1983 to estimate external disturbances in a servo system using Gopinath’s reduced-order observer design method.
III. DEVELOPMENT OF DOB-BASED ROBUST CONTROL
DOb-based robust control expanded from servo applications into many engineering fields, while increasingly rigorous linear and nonlinear analyses developed around its flexible two-degree-of-freedom structure.
- A. DOb-based Robust Control (1990s): During the 1990s, DOb spread from servo and CNC motion control to power electronics, system identification, and fault diagnosis, alongside nonlinear and advanced controller developments.
- Observer-based Robust Control and Applications: DOb was applied across automobiles, trains, networks, missile seekers, spacecraft, motion systems, robotics, and power electronics.
- B. DOb-based Robust Control (2000s): In the 2000s, researchers strengthened analysis by considering low-pass-filter dynamics, nominal plant models, outer-loop controllers, nonminimum-phase dynamics, and time delays.
- B. DOb-based Robust Control (2000s): Nonlinear DOb synthesis and nonlinear nominal models were introduced to improve disturbance-estimation performance and robustness.
- Observer-based Robust Control and Applications: Motion-control applications include position, force, and compliance control, with Reaction Force Observers also estimating contact force or torque as a force sensor.
- Observer-based Robust Control and Applications: The 2-DoF structure permits independent synthesis of the performance controller and DOb, although advanced robust-controller analysis and synthesis remain complicated.
- Observer-based Robust Control and Applications: DOb-based robust control has inspired related observer-based controllers, including PO, EID, UDE, GPIO, ESO, and EHGO, sharing disturbance estimation, cancellation or suppression, and nominal-model-based performance tuning.
IV. ANALYSIS AND SYNTHESIS OF DOB
The paper analyzes DOb-based robust control in frequency, time, and state-space domains, showing how observer bandwidth, nominal plant dynamics, and observer gains shape disturbance rejection, stability, and performance. It also identifies practical limits from noise, plant dynamics, disturbance-model assumptions, and estimation-error behavior.
- Frequency-domain analysis: A DOb estimates internal and external disturbances using identified plant dynamics and measurable states, then compensates them through feedback.
- Frequency-domain analysis: With sufficiently large DOb bandwidth, disturbance estimates approach the actual disturbances, allowing the performance controller to be designed around nominal plant dynamics.This approximation underlies the widespread use of frequency-domain DOb analysis and synthesis.
- Frequency-domain analysis: Sensitivity and complementary sensitivity approach ideal low- and high-frequency limits, while their middle-frequency behavior depends on plant uncertainties and the DOb low-pass filter.Tuning DOb bandwidth or nominal plant dynamics therefore adjusts robustness, stability, and performance.
- Frequency-domain analysis: At low frequencies, disturbance robustness improves by increasing DOb bandwidth or the parameter α, but larger values increase noise sensitivity and middle-frequency sensitivity peaks.The parameter α increases with nominal inertia and decreases with the nominal thrust coefficient.
- State-space synthesis: State-space DOb design augments the system with a disturbance model and uses an observer, with stability depending on positive observer conditions and disturbance regularity.A constant disturbance model can estimate variable disturbances in practice, while better disturbance-model approximations can improve estimation.
- State-space synthesis: For nonlinear systems, positive-definite observer conditions provide disturbance-estimation stability, and observer gains adjust estimation stability and performance.Under bounded disturbance derivatives, uniformly ultimately bounded estimation error can be achieved; asymptotic stability requires stronger derivative conditions.
V. 2-DOF ROBUST CONTROLLER SYNTHESIS
The paper synthesizes 2-DoF robust controllers by combining an inner-loop Disturbance Observer with an outer-loop performance controller, for linear and nonlinear systems. It analyzes stability, disturbance-estimation effects, and practical limitations including mismatched disturbances and finite observer bandwidth.
- 2-DoF structure: A DOb-based robust controller uses a performance controller in the outer loop and disturbance estimation in the inner loop.The block diagram includes the performance controller C(s) and reference input, while the DOb handles disturbance compensation.
- 2-DoF structure: Robustness and performance can be independently adjusted by tuning the DOb and performance controller, respectively.This separation motivates the 2-DoF designation, although imperfect disturbance estimation can couple inner-loop behavior to overall stability and performance.
- Scope and limitations: The ideal decoupling of plant-model mismatch and disturbance estimation requires infinite DOb bandwidth or zero disturbance frequency, assumptions that are impractical or restrictive.DOb filter dynamics, unstructured uncertainties, the nominal plant model, and the performance controller all influence the robust system’s characteristic polynomial.
- Linear synthesis: Increasing α improves the phase margin and stability of the robust position-control system when velocity-measurement filtering is neglected.The acceleration-based controller treats α as an inner-loop tuning parameter and analyzes its effect using a root-locus.
- State-space stability: For matched disturbances, Lyapunov analysis shows that system states ultimately enter a compact set whose bound shrinks as disturbance-estimation accuracy improves.The bound also depends on the performance-controller matrices P and Q and the disturbance-estimation error.
- Scope and limitations: Mismatched disturbances cannot be directly cancelled through DOb estimates, requiring different control techniques; reconstructing states with successive derivatives also increases noise sensitivity.For nonlinear systems, a general 2-DoF structure is difficult because different observers and nonlinear controllers are synthesized in the two loops.
VI. CONCLUDING REMARKS
The paper surveys DOb-based robust control, tracing its origins and broad engineering adoption while clarifying time-domain and nonlinear-system applicability. It also identifies practical design limitations and the need for standardized analysis and synthesis tools.
- DOb-based robust control originated in 1983 as a state-space method for improving the robustness of a Linear Quadratic Regulator.
- DOb-based robust control has been widely adopted because it can be synthesized intuitively and implemented with a simple microcontroller, especially in motion control and power electronics.
- Its applications span fields including chemical, telecommunications, automotive, aerospace, biomedical, renewable-energy, nuclear, biological, electrical, electronic, and mechanical engineering.
- The method’s main practical drawback is that key design parameters are generally tuned by trial and error, making performance highly dependent on designer experience.
- Robust stability and performance still require further investigation for higher-order DOb filters, nonminimum-phase nominal plants, and complex dynamics.
- Standardized analysis and synthesis tools, including the DO_DAT MATLAB toolbox, are being developed to support broader adoption of DOb-based control.