Modular Design of Nonlinear Observers for State and Disturbance Estimation

Dynamic uncertainties and unknown disturbances will degrade the tracking performance of robots. When using a disturber observer-based controller, the key to effectively compensate for these uncertainties is to measure or estimate as accurately as possible any disturbance. To relax restrictions on the design of the current nonlinear disturbance observer for the robot, a universal nonlinear disturbance observer is proposed for higher estimation performance. The stability of the proposed universal nonlinear disturbance observer is theoretically analyzed and the boundaries of estimation error are proven according to the vector differential equation. Finally, the proposed universal nonlinear disturbance observer is evaluated via simulation by comparison to the nonlinear disturbance observer. The result shows a faster estimation speed and a higher estimation accuracy of the universal nonlinear disturbance observer.

This paper proposes a passivity-based nonlinear disturbance observer (DOB) design for a powered upper-limb robot control. The proposed DOB allows for the nonlinearities of the robot dynamics, whereas the typical DOB designs cannot. Moreover, by virtue of the passivity property, human operator and environmental interactions can be embedded in the control loop. As a DOB, the proposed approach has a disturbance observation property that makes the actual robot behave like a nominal model selected by the user. Performance analysis proposes a gain tuning rule. In experimental validation, actual powered upper-limb robot is used to perform unknown payload carrying applications.

Static offset and synchronous vibration are obstacles to precision tracking of a rotating shaft supported by active magnetic bearings (AMBs). A constant and harmonic disturbance observer is an effective approach to estimate and suppress these undesired effects. A disturbance observer is particularly well-suited for tracking applications since it can directly compensate for AMB force nonlinearity. In this paper, we propose a nonlinear reduced-order disturbance observer which is incorporated into a flatness-based tracking control. Since a reduced-order approach requires knowledge of velocity, we design an inner-loop velocity observer which can achieve convergence at a faster rate than the disturbance observer. This hierarchical observer simplifies the control because disturbance estimates are decoupled for each degree of freedom (DOF) and disturbance compensation is modularized. Experimental results on a commercially available 5-DOF system demonstrate accurate position tracking over the bearing air gap for a wide range of shaft velocities.

Unknown-input observation techniques for infiltration and water flow estimation in open-channel hydraulic systems

Continuous high order sliding mode controller design for a flexible air-breathing hypersonic vehicle

A backstepping-like design approach for reduced-order nonlinear observers is proposed. The basic idea of this approach is as follows. First, an appropriate function of the state variables to be estimated is constructed. The next function of the state variables to be estimated is then derived by designing the previous nonlinear function observer. Finally the procedure terminates, resulting in a partial differential equation to be solved. If the resultant differential equation is solvable, then the observer can be calculated. The connection between observers with linear error dynamics and this approach is discussed. © 1998 Scripta Technica, Inc. Electr Eng Jpn, 121(3): 53–59, 1997

Improved sliding-mode control for a class of disturbed systems based on a disturbance observer

The control of unmanned aerial vehicles (UAVs) has been an active area of research over the past decade, particularly for operations in complex environments. This paper addresses the finite-time fault-tolerant control problem for UAV subjected to simultaneous actuator faults and wind disturbances. A novel adaptive finite-time disturbance observer-based fault-tolerant control (AFTDO-FTC) scheme is proposed. This scheme integrates a finite-time sliding surface, a nonlinear disturbance observer, and an adaptive controller to achieve accurate tracking of position and attitude. First, a nonlinear disturbance observer is designed to estimate the lumped uncertainty arising from combined faults and wind disturbances. Then, a finite-time sliding surface, formulated using weighted error vectors, is introduced to effectively mitigate the adverse effects of estimation errors from the disturbance observer. Furthermore, adaptive finite-time position and attitude controllers are developed based on the estimates provided by the adaptive disturbance observer. Finally, the effectiveness of the proposed method is verified through comparative simulations and Lyapunov stability analysis.

The disturbance rejection problem of aerial vehicles is a widely concerned issue. For attitude dynamics, we propose a method for directly designing a geometric observer (GOB) based on the special orthogonal group SO(3), thus reducing the impact of model mismatch and being unrestricted by the aircraft attitude. Considering the type of measurement available, we have developed two GOBs: GOB-I, which uses both attitude and angular velocity measurements, and GOB-II, which uses only attitude measurement. The stability of GOB is theoretically proved, with the GOB-I exhibiting almost global asymptotic stability and the GOB-II demonstrating local asymptotic stability. We have compared the estimation performance of our proposed GOB with four other disturbance observers (DOBs) for five types of disturbances. The simulation results show that, in the small attitude scenarios, our proposed GOB-I observer performs comparably with the compensation function observer (CFO) and the nonlinear disturbance observer (NDOB) that use both attitude and angular velocity measurements, while the GOB-II performs comparably with the extended state observer (ESO) that uses only attitude measurements. In the agile attitude scenarios, our proposed GOB-I observer significantly outperforms CFO and NDOB, and GOB-II also performs much better than ESO. Compared with the reduced-order observer, which uses only angular velocity measurement, the GOB-I can handle more complex disturbances and provides compensation for sensor errors. Flight experiments conducted with a lifting-wing quadcopter demonstrate the efficiency of our method in resisting unknown payload in hover flight and model uncertainty in agile maneuver.

DOB (Disturbance Observer) is an useful control method for estimating the disturbance applied to dynamic systems. Disturbance observer can be used to implement a robust control system to generate a control input for rejecting the disturbance, and it can be also used to estimate the disturbance to obtain information. The system that uses disturbance estimation is investigated for high performance control such as automatic door systems, walking robot and electric power steering system in vehicles. In this paper, a novel disturbance observer which is called disturbance and current observer for estimating load torque in the motor system is proposed. The difference between the DOB for disturbance rejection and DCOB is mathematically verified. Current and angular velocity are required for estimating the load torque of the motor in DOB. However, the DCOB can estimate load torque and current without current sensor. DCOB is designed based on modeling of the motor system. Appropriate Q-filter is selected and the applicability of DCOB is verified by simulation. The estimated disturbance and current of the electric motor can be verified without current sensor, as experiments of the actual motor system.

In this study, the fault-tolerant control problem is investigated for a class of non-affine output-constrained multi-input multiple-output non-linear systems with actuator faults. The controlled systems contain unknown non-linear functions, unknown external disturbance and immeasurable states. The fuzzy logic systems and a robust compensation function are employed to deal with the unknown non-linear functions and non-affine non-linear actuator fault problems. Then, the state observer and the non-linear disturbance observer are developed for estimating the immeasurable states and unknown compounded disturbance, respectively. By using the barrier Lyapunov function method and in the unified framework of adaptive backstepping output feedback control design, a novel adaptive fuzzy fault-tolerant controller design scheme is developed. It is shown that all the variables of the closed-loop system are semi-globally uniformly bounded. Moreover, the system outputs cannot violate their predefined bounds in the presence of the non-affine non-linear faults. A simulation is given to validate the effectiveness of the proposed approach.

In this paper a new bilinear and nonlinear second-order state observer which is globally asymptotically stable is constructed to estimate the unmeasurable state variables. Then an unstable controlled current induction motor drive system which cannot be stabilized by a linear state observer is successfully stabilized by feeding the reconstructed state variables from the nonlinear observer to the frequency control channel. This scheme is easily implementable, resulting in an asymptotically stable overall closed-loop system. These results are numerically verified by simulation.

Quadrotor unmanned aerial vehicles (UAVs) operating in agricultural fields for aerial photography are susceptible to external disturbances. The disturbances result in trajectory deviation and irregular image overlapping that considerably degrade image quality. Disturbance observers (DOs) are commonly researched for counteracting these effects but may have delays and limitations in handling diverse and high-frequency disturbances. To this end, this work proposes a continuous high-order sliding mode-assisted DO (HSMDO) with limited time convergence characteristics for the estimation of disturbances in systems. The observer consists of a classical nonlinear DO (NDO) and a sliding mode-assisted system (SMAS). The NDO is used to estimate disturbances preliminarily. The SMAS is utilised to assist the NDO in estimating the high-frequency component of disturbances and ensure that the entire DO is finite-time convergent. Finally, the tracking controller is designed on the basis of the HSMDO, which enables UAVs to track the prescribed trajectories under disturbances stably. Simulation results show that the proposed HSMDO can accurately estimate various types of disturbances. Moreover, the tracking controller based on the HSMDO can improve the antidisturbance performance of systems and ensure the trajectory tracking accuracy of UAVs.

A nonlinear state observer can be used as a resolver-to-digital converter (RDC); however, when the speed is not constant, its performance deteriorates. In this paper, a composite state observer is presented. The estimation speed from the nonlinear state observer is compensated by the estimation speed from the arctangent method in the feed-forward form. Compared with the arctangent method, this method has a strong ability to suppress random disturbances. Compared with an RDC based on a nonlinear state observer, the accuracy of the angle and speed is improved as the appearance of phase delay is weakened. Experiments demonstrate the effectiveness of the observers.

An event-triggered based robust control for electro-hydraulic servo machines with active disturbances rejection