An Enhanced Nonlinear ADRC Speed Control Method for Electric Propulsion System: Modeling, Analysis, and Validation

This paper proposes a novel class of adaptive extended state observers (AESOs) that significantly expand the applications of extended state observers (ESOs) to nonlinear disturbed systems. An AESO is designed as a linear time-varying form that, as a result, combines both the advantages of theoretical completeness in a conventional linear ESO (LESO) and good practical performance in a conventional nonlinear ESO (NESO). To tune the time-varying observer gains, AESO error dynamics is first transformed into a canonical (phase-variable) form. Then, time-varying PD-eigenvalues are assigned for the canonical system based on differential algebraic spectral theory. Theorems for stability and estimate error bounds of the AESO are given in the presence of unknown disturbances. These theorems also offer some important guidelines for assigning the PD-eigenvalues. To demonstrate the effectiveness of this new observer, two representative applications, including a numerical single-input–single-output example and a practical multiple-input–multiple-output hypersonic vehicle application, are exemplified, and comparison simulations are conducted among AESO, LESO, and NESO. Future work is pointed out in the end.

In this paper, an improved nonlinear active disturbance rejection control (INLADRC) approach is proposed for load frequency control of hybrid microgrid with communication delay. The INLADRC technique includes a nonlinear extended state observer (NESO) to estimate the system states and a nonlinear controller for the cancellation of the generalized disturbance acting on system. The effect of communication delay in the hybrid microgrid system is alleviated via the incorporation of an auxiliary structure that also restores the synchronization between the inputs of NESO. The efficacy of the proposed approach is validated via a comprehensive analysis, wherein step variations as well as random perturbations are considered in solar power, wind power and load demand. Further, the performance of proposed technique is also corroborated via consideration of real time solar and wind data. Moreover, the robustness of INLADRC technique is investigated in presence of parametric uncertainty, model-plant mismatch, delay time mismatch as well as varying communication delay. An extensive comparative analysis is a testimony to the effectiveness of INLADRC approach.

The active disturbance rejection control is used to design the control scheme for the vertical inverted pendulum system. Based on the original active disturbance rejection control algorithm, a linear/nonlinear switched extended state observer is proposed for such an unstable system with single input and double output, strong nonlinear and strong coupling. Firstly, the reason of the limited ability of nonlinear extended state observer to estimate large perturbations is analyzed, then a linear extended state observer is proposed to make up for the defects of NLESO, and the feasibility of the proposed linear/nonlinear auto disturbance rejection switching control is verified by numerical simulation.

For the purpose of realizing permanent magnet synchronous motor (PMSM) systems with strong robustness and smooth speed, the quasi-proportional-resonant (QPR) controller is combined with super-twisting extended state observer (STESO) in this paper. Although traditional active disturbance rejection control scheme generally selects a sufficiently large bandwidth of linear extended state observer (LESO) to enhance the time-varying disturbance rejection capacity, the bandwidth of LESO is limited by system stiffness. To solve this tough issue, the STESO using generalized super-twisting technique is developed to optimize the stability and anti-disturbance capacity of motor drive system. In addition, the QPR controller is combined with the proposed STESO to suppress the motor speed fluctuation. Experimental results show that the proposed STESO-based QPR control algorithm has satisfactory characteristics.

Nonlinear active disturbance rejection control is much more effective than linear active disturbance rejection control in tolerance to uncertainties and disturbances. However, it brings a great challenge for theoretical analysis, especially the stability analysis. This article proposes a linear matrix inequality method to analyze the absolute stability of generalized nonlinear active disturbance rejection control form which contains multiple nonlinearities with different parameters in both extended state observer and control law for single-input single-output systems. The generalized nonlinear active disturbance rejection control algorithm and the single-input single-output system are transformed into a direct multiple-input multiple-output Lurie system. A sufficient condition to determine its absolute stability based on linear matrix inequality method is given. The Lyapunov function of the Lurie system exists when the group of linear matrix inequalities is feasible. The free parameters and coefficients in Lyapunov function are given by the solution of these linear matrix inequalities. The electromagnetic valve actuator system in camless engine is presented as an application to illustrate how to perform the proposed method for absolute stability analysis and the stable region of parameter perturbations is obtained via the method. Simulation results show that the linear matrix inequality–based method is convenient and effective to determine whether the closed-loop system is absolutely stable.

Time-varying disturbance of drum water level is difficult to estimate and compensate, which leads to time-varying periodic error of the whole system. System model is reconstructed by using prior information of equivalent disturbance, and the components of known modes in equivalent disturbance are estimated and compensated by the generalized extended state observer. Thus, the error can be eliminated and the control accuracy of the system can be improved. Compared with the traditional active disturbance rejection control (ADRC) system based on linear extended state observer, the control performance under different types of external disturbances is studied. Simulation results show that the proposed generalized extended state observer can completely estimate and compensate the components of the known modes in the equivalent disturbance with small overshoot, short adjustment time, strong anti-interference ability and high control precision.KeywordsADRCState observerDrum water level

A nonlinear Third-Order Extended State Observer (TESO) is proposed for the estimation of the rotor position and speed for sensorless Interior Permanent Magnet (IPM) synchronous motor drives. An optimized parameter tuning method is deployed to reconcile the needs of expanding the disturbance observation bandwidth and suppressing the measurement noise effectively. Both the steady state and transient performance of the TESO are verified through the experimental tests. In comparison with the performance of a conventional Linear Extended State Observer (LESO), the proposed observer is proved to have better noise suppression ability and disturbance observation performance in wide operating range.

In this paper, a novel nonlinear active disturbance rejection (ADR) controller is proposed for the speed control of electric drives so that a better robustness to parameter variations can be achieved. The nonlinear observer is designed by using the sliding mode techniques. When the nonlinear observer is simplified as a linear one, it is equivalent to a phase-locked loop observer (PLLO). However, compared with the existing PLLO, the proposed observer has two gains with specific physical interpretation, which simplifies the gain tuning process, especially for the nonlinear observer. To alleviate the chattering problem, the fraction power function is employed in the observer and the guideline for parameter setting is present. An experimental comparative study of the linear PLLO and the proposed nonlinear PLLO is provided to show the effectiveness.

The dual observation of periodic and aperiodic interferences cannot be balanced by traditional linear extended state observer (T-LESO). Therefore, the speed fluctuations caused by uncertain periodic and aperiodic interferences in the interior permanent magnet synchronous motor control system cannot be suppressed by the traditional linear active disturbance rejection controller. To resolve the aforementioned problem, an improved linear active disturbance rejection controller (I-LADRC) in which multifrequency quasi-resonant filtering decoupling linear extended state observer and generalized linear extended state observer (G-LESO) are cascaded is proposed. In this controller, the interference feedforward control method of T-LESO is first changed, the observer bandwidth <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ω_o</i> and controller bandwidth <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ω_c</i> in the transfer function based on the interference term are decoupled from each other, reducing the difficulty of parameter tuning. On this basis, a multifrequency quasi-resonant filter is embedded in the decoupled linear extended state observer (LESO), so that periodic interferences can be accurately observed. For G-LESO, a fourth-order LESO is adopted to enable more accurate observation of aperiodic high-order interferences. The outer loop controller based on I-LADRC is designed, and the correctness and effectiveness of this method are verified through experiments.

Considering the strong nonlinearity, fast time-varying and strong coupling dynamic characteristics of the high-speed vehicles (HSV), combining with the fact that the extended state observer (ESO) can effectively observe the total disturbance of the system and the predictive sliding mode controller (PSMC) has strong robustness and the ability to reduce chattering, a predictive sliding mode control method with extended state observer is proposed in this paper. Firstly, the HSV model is simplified for the attack angle control; Secondly, the tracking sliding mode surface is predicted and the sliding mode control law is derived by using the optimized performance index, which will avoid the switching function and reduce chattering effectively; Thirdly, a linear extended state observer (LESO) is designed to observe the parameters perturbation and the total disturbances of the system, the estimated value is compensated into the PSMC. Fourthly, the numerical simulation shows that the PSMC with LESO can track the step instruction of angle of attack stably even if there are parameters deviations and external composite disturbances. In addition, the control amount does not exceed the rudder deflection angle of the actuator, and the chatter phenomenon is effectively alleviated.

ABSTRACTIn order to reduce the error and phase delay of the classical extended state observer (ESO) in estimating the system state and disturbance, in this paper, we combine ESO and tracking differentiator (TD) to construct a tracking differential extended state observer (TDESO). The observation error and observation speed of TDESO are also discussed. Then a nonlinear active disturbance rejection control system improved by TDESO for a linear plant is transformed into a Lurie system. Moreover, the circular criterion is used to analyse the absolute stability of the transformed Lurie system. Finally, TDESO is optimised and an improved linear state error feedback (PLSEF) is proposed to improve the rapidity of the system by using simulation and time domain analysis. And a second-order system is used to illustrate the performance of the proposed scheme. The simulation results show that our algorithm is effective.

In this paper, a systematic procedure for controller design is proposed for a class of nonlinear underactuated systems (UAS), which are non-feedback linearizable but exhibit a controllable (flat) tangent linearization around an equilibrium point. Linear extended state observer (LESO)-based active disturbance rejection control (ADRC) is shown to allow for trajectory tracking tasks involving significantly far excursions from the equilibrium point. This is due to local approximate estimation and compensation of the nonlinearities neglected by the linearization process. The approach is typically robust with respect to other endogenous and exogenous uncertainties and disturbances. The flatness of the tangent model provides a unique structural property that results in an advantageous low-order cascade decomposition of the LESO design, vastly improving the attenuation of noisy and peaking components found in the traditional full order, high gain, observer design. The popular ball and beam system (BBS) is taken as an application example. Experimental results show the effectiveness of the proposed approach in stabilization, as well as in perturbed trajectory tracking tasks.

At present, the classical control strategy of PID is widely adopted in the bearingless levitation system. However, it is hard to realize high performance of levitation control, due to the influence of disturbance, parameters perturbation etc. Aiming at the problem above, the novel bearingless levitation system based on Extended State Observer (ESO) is suggested in this paper. According to the basic principle that ESO can obverse the total disturbance, the mathematical model of the system is built. The stability of the system is analyzed, and the parameters adjustment is demonstrated theoretically, which provides a new method for the levitation control system. Meanwhile, the range of the parameters is specified in the stable region. Moreover, combining with the physical significance of the main parameters, the principle of the parameters adjusting in the nonlinear Extended State Observer is improved. Finally, by simulation, it is verified that ESO makes a significant contribution to the disturbance rejection of the bearingless levitation system, and the validity of the scheme above is proved.

Background: In recent years, patents have shown that upper-limb rehabilitation robots play a significant role in home-based rehabilitation training for stroke hemiplegia patients. Changes in muscle tension during the flaccid paralysis phase cause the rehabilitation robot to deviate from the predetermined motion trajectory. This poses a challenge to the mathematical modeling of the rehabilitation robot and the design of the nonlinear extended state observer (NESO). Objective: To address the problem of trajectory tracking errors caused by the rehabilitation robot when the patient's muscle tension changes, a method based on optimizing the nonlinear function within the NESO is proposed. Methods: First, a mathematical model of the upper-limb rehabilitation robot is established to obtain the dynamic relationship between the robot's velocity and the input voltage. Second, the nonlinear function of NESO is optimized by adjusting the gain values of the sine and tangent functions to effectively estimate the muscle tension and reduce the problem of accumulative error due to changes in muscle tension. Finally, comparative simulations of trajectory tracking including the optimized nonlinear function as well as the sine, tangent and power functions are performed on the MATLAB platform. Results: NESO is constructed to estimate changes in muscle tension based on sine, tangent, and power functions, as well as optimized nonlinear functions. The equivalent gain values of each function and the muscle tension estimation curves of NESO are compared. The simulation results show that the equivalent gain value of the optimized nonlinear function acting in NESO is increased to more than 8 and the convergence time is reduced by 11.9% accordingly. This conclusion is validated by simulations and practical tests. Conclusion: The optimized nonlinear function shortens the estimation time of the NESO for changes in muscle tension, which can provide a reference value for the design of observers for upper-limb rehabilitation robots of patients in the flaccid paralysis stage.

Disturbances and uncertainties are the main concerns in control systems. To obtain this information in real time, the extended state observer is proposed as the core of the active disturbance rejection control. However, the estimation errors of extended state observer cannot converge to zero in the presents of unknown but bounded disturbances, which will bring unexpected tracking errors to the closed-loop system. By taking advantage of the linear extended state observer and the super-twisting algorithm, the super-twisting extended state observer is proposed to deal with the non-diminishing second-order derivable disturbances in this paper. The asymptotic convergence of the super-twisting extended state observer and the controller are proved by the Lyapunov method. Moreover, the effectiveness and robustness of the super-twisting extended state observer are verified by simulation analysis. Simulation results show that the proposed super-twisting extended state observer maintains the minimized estimation error with less settling time compared the with linear extended state observer. The tracking performance of the controller with the proposed observer is greatly improved.