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Stability and Robustness of Disturbance Observer based Motion Control Systems

Emre Sariyildiz, Kouhei Ohnishi

arXiv:1912.05046v1eess.SY

TL;DR

The paper addresses gaps caused by idealized velocity measurements in DOB analysis and oversimplified feed-forward models of RTOB-based force control. It develops practical robustness and stability analyses with new design methods, and reports validation through simulation and experiments. The results show that filtered velocity measurements constrain DOB design, while RTOB parameters and identification errors substantially affect force-control stability and performance.

  • Problem

    Conventional DOB analysis assumes ideal velocity measurement, while RTOB force-control analysis overlooks feedback-related stability effects.

  • Method

    The paper proposes robustness and stability analyses and design criteria for DOB- and RTOB-based robust motion and force control systems.

  • Results

    The analyses and proposed designs are validated by simulation and experimental results for robust motion and force control.

  • Takeaways & Limitations

    DOB robustness requires accounting for velocity measurement, while RTOB force-control design must account for bandwidth and parameter identification effects on stability.

Abstract

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This paper analyzes the robustness and stability of a disturbance observer (DOB) and a reaction torque observer (RTOB) based robust motion control systems. Conventionally, a DOB is analyzed by using an ideal velocity measurement that is obtained without using a low-pass-filter (LPF); however, it is impractical due to noise constraints. An LPF of velocity measurement changes the robustness of a DOB significantly and puts a new design constraint on the bandwidth of a DOB. An RTOB, which is used to estimate environmental impedance, is an application of a DOB. The stability of an RTOB based robust force control system has not been reported yet since its oversimplified model is derived by assuming that an RTOB has a feed-forward control structure. However, in reality, it has a feed-back control structure; therefore, not only the performance but also the stability is affected by the design parameters of a RTOB. A new practical stability analysis method is proposed for a RTOB based robust force control system. Besides that novel and practical design methods, which improve the robustness of a DOB and the stability and performance of an RTOB based robust force control system, are proposed by using the new analysis methods. The validity of the proposals is verified by simulation and experimental results.

I. INTRODUCTION

The paper motivates practical robustness and stability analysis for DOB- and RTOB-based motion control. It accounts for filtered velocity measurements and feedback effects in RTOB-based force control, then proposes new analysis and design methods validated experimentally and by simulation.

  • Motivation: DOBs provide intuitive robustness adjustment within a desired bandwidth and are widely used in motion control applications.They estimate external disturbances and system uncertainties and feed the estimates back through an inner loop.
  • Motivation: Velocity-measurement LPFs are practical for noise suppression but significantly alter DOB robustness and impose additional design constraints.The paper identifies this omission in conventional simplified analyses.
  • Motivation: RTOBs estimate environmental impedance but require stability analysis because their feedback structure makes design parameters affect both performance and stability.Earlier methods commonly focused on performance and often matched DOB and RTOB bandwidths.
  • Contributions: The paper proposes new robustness and stability analyses for DOB-based motion control and RTOB-based robust force control systems.The proposed methods address filtered velocity measurements and the feedback structure of RTOBs.
  • Validation: Simulation and experimental results are used to verify the proposed analysis and design methods.The paper presents analyses, design criteria, and experimental results in later sections.

A. Disturbance Observer

This section analyzes how finite velocity-measurement bandwidth changes DOB dynamics, robustness, and design trade-offs. It derives transfer-function constraints showing that robustness, stability, and performance cannot all be adjusted independently.

  • DOB structure: A DOB estimates external disturbances and system uncertainties, then feeds their estimates back to achieve robust motion control.The estimated disturbances include loading, friction, inertia variation, and other system uncertainties.
  • DOB structure: A disturbance can be estimated precisely when it remains within the DOB bandwidth.The DOB cutoff frequency is a fundamental design parameter.
  • Finite velocity measurement: Finite velocity-measurement bandwidth increases the relative degree of the DOB loop from one to two.This changes the attainable shaping of sensitivity and co-sensitivity responses.
  • Finite velocity measurement: High-frequency sensitivity peaks increase as low-frequency sensitivity reduction increases when the DOB loop relative degree exceeds one.The Bode integral theorem therefore limits free adjustment of the DOB parameter alpha and cutoff frequency.
  • Design trade-off: Equation (7) imposes a new DOB design constraint when an LPF is used in velocity measurement.Increasing the lower damping constraint improves robustness but tightens upper bounds on alpha and/or DOB cutoff frequency, degrading stability and performance.

B. Reaction Torque Observer

An RTOB is a DOB application for estimating environmental impedance, with a control structure similar to a DOB but a distinct model-based role. Its cutoff frequency and estimated parameter variations are explicit design elements.

  • RTOB structure: An RTOB estimates environmental impedance as an application of a disturbance observer.It is designed by subtracting system uncertainties from the input of a DOB.
  • RTOB structure: The RTOB model includes estimated friction, interactive torque, inertia variation, and torque-coefficient variation.Its cutoff frequency is denoted by g_RTOB.
  • RTOB structure: DOB and RTOB control structures are quite similar, but the RTOB is the model-based control method.This model-based structure is the main design challenge identified for the RTOB.

III. ROBUST POSITION AND FORCE CONTROL SYSTEMS

The section introduces stability analyses for the robust position and force control systems.

  • Scope: Stability analyses are presented for the robust position and force control systems.

A. Position Control

The position-control analysis derives transfer functions and stability criteria for a DOB-based robust position controller with finite velocity-measurement bandwidth. It identifies a trade-off between robustness and stability and shows that outer-loop gains also affect robustness.

  • System model: The acceleration-based position-control system uses a DOB inner loop and an outer-loop performance controller based on the nominal plant model.The transfer functions are derived from the block diagram for infinite and finite velocity-measurement bandwidth.
  • Stability analysis: Finite velocity-measurement bandwidth makes the characteristic functions depend on the DOB parameters and the velocity-measurement bandwidth.The stability analysis applies the Routh-Hurwitz theorem to obtain a stability criterion.
  • Stability analysis: Increasing or decreasing nominal inertia or torque coefficient improves stability, but nominal inertia cannot be increased freely because of the DOB robustness constraint.This establishes a trade-off between DOB robustness and position-system stability.
  • Robustness analysis: The position-system robustness depends on the outer-loop performance controller as well as the DOB.When 0.5 DOB v g g α >, increasing the outer-loop control gain can improve robustness, while high-frequency inner-loop noise and disturbance sensitivity remains.
  • Robustness analysis: The sensitivity and co-sensitivity transfer functions are derived for the robust position-control system under finite and infinite velocity-measurement bandwidth.These functions are used to evaluate how controller and DOB parameters affect robustness.

B. Force Control

The force-control section models an RTOB-based robust force-control system and analyzes how environmental impedance, observer bandwidths, and identification accuracy affect stability and performance. It proposes bandwidth and identification constraints for improving the system’s behavior.

  • System model: An RTOB estimates environmental impedance within a robust force-control architecture, while the DOB estimates external disturbances and system uncertainties in the inner loop.Imperfect identification can degrade both force-control performance and stability.
  • Identification effects: Imperfect inertia or torque-coefficient identification changes the open-loop relative degree and can introduce a right-half-plane zero when α > β.The proposed minimum-phase constraint is β ≥ α; increasing α − β deteriorates stability and lowers force-control bandwidth.
  • Open-loop analysis: The open-loop transfer functions contain a pole at the origin, so DOB-based force control removes steady-state force-control error.This result is stated for the analyzed open-loop formulations.
  • Stability analysis: Stability deteriorates as environmental stiffness increases or damping decreases because the open-loop zero moves away from the origin and phase lag increases.The analyzed open-loop transfer function has relative degree two with root-locus asymptotes at ±90º.
  • Design criteria: Using different DOB and RTOB bandwidths preserves the root-locus relative degree while introducing a phase lead-lag compensator that can improve stability and performance.The proposed phase-lead configuration is obtained when RTOB DOB g g >.
  • Identification effects: Increasing β − α improves stability but deteriorates performance because of environmental-impedance estimation error.The paper recommends precise torque-coefficient identification, while inertia identification may be neglected in many low-acceleration force-control cases.

IV. SIMULATION AND EXPERIMENT

This section states that simulation and experimental results are presented to evaluate the robust motion-control analyses and design proposals.

  • Simulation and experimental results are presented in this section.
  • The results section follows the preceding stability and design-criterion analyses.
  • The section serves as the paper’s evaluation stage before the conclusion.

A. Simulation

The simulations show that practical velocity measurement creates a robustness constraint for DOB tuning, producing a trade-off between robustness and stability. For RTOB force control, stability depends on observer parameters and identification accuracy.

  • DOB co-sensitivity changes significantly at high frequencies as α and/or g_DOB increase when velocity measurement is finite.
  • Practical velocity measurement prevents α and g_DOB from being increased freely because of the robustness constraint.
  • The outer-loop position controller improves position-control robustness, while increased inner-loop DOB parameters increase high-frequency noise sensitivity.
  • The stability of the DOB-based robust position-control system trades off against DOB robustness.
  • Increasing g_RTOB and/or α improves robust force-control stability when inertia and torque coefficients are identified precisely.
  • Imperfect identification changes force-control stability significantly: α > β causes deterioration through an RHP zero, whereas α < β improves stability.

B. Experiment

Experiments on a two-link planar arm evaluate the proposed position, torque, and hybrid motion-control systems. The reported responses achieve the position and torque-control goals, with uncertainty identification improving robust force-control performance.

  • Experiments use joint-space control of a two-link planar robot arm with the setup specified in Table II.
  • As α increases, the DOB becomes more sensitive to noise and its robustness deteriorates when g_DOB = 200 rad s^-1.
  • The DOB parameters α and g_DOB should be tuned using the stated robustness constraint.
  • The robust force-control system’s stability changes significantly with DOB and RTOB design parameters.
  • Torque control runs during 0–5 and 10–15 seconds, while position control runs during 5–10 seconds in the hybrid implementation.
  • Position and torque-control goals are achieved, and identifying uncertainties such as friction during position control improves RTOB force-control performance.

V. CONCLUSION

The conclusion presents design tools and analyses for DOB- and RTOB-based robust motion control. It emphasizes the robustness–stability trade-off, the importance of velocity measurement, and the effects of parameter identification errors.

  • Increasing nominal inertia or decreasing nominal torque coefficient improves stability but deteriorates DOB robustness, and vice versa.
  • A new design method is proposed to improve both stability and robustness in DOB-based robust motion-control systems.
  • Velocity measurement is important for DOB-based system stability, robustness, and performance.
  • The proposed RTOB stability analysis models DOB and RTOB as phase lead-lag compensators and finds that increasing RTOB bandwidth improves force-control stability.
  • Identification errors affect force-control stability: a higher identified inertia or lower identified torque coefficient introduces an RHP zero and worsens stability as force-control gain increases.
  • Lower identified inertia can improve robust force-control stability without degrading performance, while torque-coefficient identification remains crucial.
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