Decoupling Control for Module Suspension System of Maglev Train Based on Feedback Linearization and Extended State Observer

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.

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

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.

In this paper, a novel speed-sensorless suspension decoupling control strategy for bearingless motor was proposed based on linear Extended State Observer (ESO). In the proposed control strategy, a second-order and a third-order linear-ESO algorithm were added respectively into torque d-q axis current-loop and suspension system x-y direction displacement-loop. A product of electrical angular speed and torque system d-q axis current and a product of torque q axis flux and suspension system d-q axis current were defined as disturbances in order to use the linear-ESO algorithm to estimate the defined disturbances. By obtaining speed information and compensation for disturbance force, the motor can work on speed-sensorless condition and traditional decoupling algorithm can be simplified. The simulation results show that the proposed control strategy can realize accurate speed estimation and guarantee stable suspension under the rated speed.

Active disturbance rejection based trajectory linearization control for hypersonic reentry vehicle with bounded uncertainties

This paper presents a sliding mode synchronization controller (SMSC) based on extended state observer (ESO) for the dual-drive system in gantry-type machine tools (GTMT). This controller achieves not only excellent tracking accuracy but also high synchronization performance. Firstly, a sliding mode synchronization controller is designed for the dual-drive system based on a simplified mode. Then, in order to handle the difficulties associated with the parameter uncertainties, external disturbances and coupling effects of the dual-drive system, a linear extended state observer (LESO) is designed. In this active disturbance rejection control (ADRC) technology, the total disturbances are treated as an extended state of the system and compensated with the disturbance observed value. Moreover, Rigorous theoretical analysis is performed to show that the proposed control method is able to achieve asymptotical tracking and synchronization performance for the dual-drive system in GTMT. Finally, Simulation studies are carried out and the results show that the proposed control strategy performs an improved tracking and synchronization motion control in comparison to the independent axis P-PI control approach.

In this paper, a trajectory linearization control based control law using a linear extended state observer (LESO) is proposed for the output tracking problem of a nonlinear system with uncertainties. First, based on the tracking error dynamics derived by Taylor expansion for the original nonlinear system along the desired trajectory, a feedback linearization (FL) based control law is designed to stabilize a linear time‐varying (LTV) system. To reduce the controller performance sensitive to uncertainties, with partial model information, LESO is constructed to estimate the tracking error vector, as well as the uncertainties in an integrated manner. The closed‐loop stability of the system under the proposed compound scheme is established. Also, simulation results on affine and non‐affine nonlinear uncertain systems are provided to demonstrate the effectiveness of the control strategy. Finally, the issues of sensitivity to sensor noise and the guidelines of tuning parameters are discussed.

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.

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.

Levitation control is a core technique of magnetic levitation (Maglev) trains, whose performance has a significant impact on the driving safety and ride comfort during the operation of Maglev trains. With the rapid development of high temperature superconducting (HTS) materials, a novel hybrid levitation system for Maglev trains, composed of HTS and normal conducting electromagnets, is becoming a more promising alternative to the conventional levitation system, due to a lager levitation air gap and lower energy consumption. The controller of the hybrid levitation system is hard to design due to strong nonlinearity, open-loop instability and fast-response requirements. In this study, we propose a robust model predictive control (MPC) strategy for the novel hybrid levitation system in which state constraints are taken into account, including the air gap, and the velocity and acceleration of the hybrid magnet. In the MPC strategy, the prediction model employs a stabilized model through nonlinear and linear state feedback. With regard to the online computational load, the primal-dual interior-point (PDI) algorithm is adopted to solve the optimization problem with high efficiency to deal with constraints in a real-time manner. Finally, simulation results are demonstrated to verify the effectiveness of the proposed MPC-PDI control strategy for the hybrid levitation system, and the significances considering state constraints are revealed. This study provides an engineering realization solution to the novel hybrid levitation system of a Maglev train.

In this paper, time-scale separation, feedback linearization (FL), and extended state observer (ESO) based new design for an acceleration tracking pitch autopilot of a tail controlled, skid-to-turn tactical missile is presented. The pitch plane dynamics has been split into pitch rate dynamics as fast, and the acceleration dynamics as a slow subsystem by exploiting the naturally existing time-scale separation between them. FL-based controllers are then designed for the subsystems separately. To achieve robustness in the presence of uncertainties and disturbances, an ESO is designed for each of the subsystem separately. The ESOs estimate the effect of uncertainties in the respective subsystem and the estimate is used to robustify the feedback linearizing controller designed for the respective nominal subsystem. The design neither requires accurate plant model nor any information about the uncertainty. Closed-loop stability for the overall system is established. The effectiveness of the design in meeting specified tracking performance in the presence of significant uncertainties, unmodeled dynamics, measurement noise, control input, and rate saturation, and in varying missile velocity and altitude scenario is illustrated by simulation. Furthermore, to analyze the performance for different initial conditions and parameter perturbations, Monte Carlo simulation study is carried out and the results are presented. Finally, performance comparison of the proposed design with some existing controllers is presented to showcase the efficacy of the proposed design.

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.

The pitching axis is the main axis of a satellite camera and is used to control the pitch posture of satellite cameras. A control strategy based on extended state observer (ESO) is designed to obtain a fast response speed and highly accurate pitching axis control system and eliminate disturbances during the adjustment of pitch posture. First, a sufficient condition of stabilization for ESO is obtained by analyzing the steady-state error of the system under step input. Parameter tuning and disturbance compensation are performed by ESO. Second, the ESO of speed loop is designed by the speed equation of the pitching axis of satellite cameras. The ESO parameters are obtained by pole assignment. By ESO, the original state variable observes the motor angular speed and the extended state variable observes the load torque. Therefore, the external load disturbances of the control system are estimated in real time. Finally, simulation experiments are performed for the system on the cases of nonload starting, adding external disturbances on the system suddenly, and the load of system changing suddenly. Simulation results show that the control strategy based on ESO has better stability, adaptability, and robustness than the PI control strategy.

In sensorless control of interior permanent magnet synchronous motor (IPMSM) drives, extended state observers (ESOs) are preferred due to their advantages, e.g., flexible application, and simple implementation. However, the conventional ESOs may experience the degraded performance with the challenging issues of rapidly changing back electromotive force (BEMF) in a sinusoidal form and ramp disturbances in position estimation. To enhance the position estimation accuracy, this article proposes an estimation scheme based on a novel generalized integrator ESO (NGI-ESO) and an integrally compensated (IC)-third-order (3rd)-linear ESO (IC-3rd-LESO). In the proposed estimation scheme, with the modified mathematical model of the BEMF, the NGI-ESO is designed to achieve accurate estimations of the BEMF. Moreover, the IC-3rd-LESO with a compensation loop is used to mitigate position estimation errors caused by the ramp disturbances. Consequently, the overall performance of sensorless-controlled-IPMSM drives is enhanced. The performance of the proposed estimation scheme under different conditions is verified and compared to that of the conventional ESO schemes by using extensive experimental tests.

The DC distribution network has more advantages in power transmission, grid connection of distributed energy, and reliability of power supply when compared with AC distribution network, but there are still many problems in the development of DC distribution network. DC bus voltage control is one of the hot issues in the research of DC distribution network. To solve this problem, in this paper, a new type of sliding mode active disturbance rejection control (SMADRC) controller for AC/DC converters is designed and applied to the voltage outer loop. The linear extended state observer (LESO) can observe the state variables and the total disturbance of the system. The SMADRC is composed of a sliding mode controller, LESO, and disturbance compensator, which can compensate the total disturbance observed by LESO properly. Therefore, it improves the dynamic. At the same time, it can also reduce the system jitter that is caused by sliding mode controller. The state variables that are observed by the LESO are used in the design of sliding mode controller, which greatly simplifies the design of sliding mode controller. Finally, the simulation results of Matlab/Simulink show that the controller has good start-up performance and strong robustness.