Active disturbance rejection trajectory tracking control for pneumatic servo system based on backstepping approach

Active disturbance rejection control is proposed to study the problems on trajectory tracking and decoupling for a two-joint system driven by pneumatic artificial muscles. Because of coupling and nonlinearity, it is very hard to obtain good performance in trajectory tracking for the two-joint system. The active disturbance rejection nonlinear controller includes a tracking differentiator, an extended state observer and a nonlinear error feedback controller. The tracking differentiator is introduced to arrange a transitional process to track input signal and get differential signal. The extended state observer is designed to estimate the non-linearity of system. The nonlinear error feedback controller is designed to improve the performance of system. Simulation results are given to show the effectiveness of proposed controller in this paper.

In engineering practice, there are many nonlinear problems in pneumatic servo systems, such as parameter uncertainty, dead zone, saturation, and so on. Therefore, the pneumatic servo system should be regarded as a nonlinear system rather than a simple linear system. Obviously, dealing with nonlinear problems based on a nonlinear system is a challenging problem, which is the key point to improve the accuracy, rapidity, and stability of position control in the pneumatic servo systems. At present, researchers have applied various nonlinear control methods to deal with the nonlinear problems in the pneumatic servo systems, such as active disturbance rejection control(ADRC), backstepping method, sliding mode control(SMC), and finite-time control method. Overview of the recent research on the above methods is given in this chapter.

The active disturbance rejection control technology was designed to solve the problem of formation maintenance in UAV cooperative formation flight, so that the response process had good dynamic quality and small static error. This paper first established a UAV formation flying model based on relative error in a two-dimensional plane. On this basis, the tracking differentiator, the extended state observer and the nonlinear state feedback controller were designed. The simulation results showed that the active disturbance rejection controller designed has good control performance and could realize the mission of maintaining the UAV with high precision.

Two new active disturbance rejection control (ADRC) structures for nonlinear systems are introduced: a locally linearized variant and a fully nonlinear formulation. Both approaches incorporate model knowledge to enhance performance but differ in how nonlinear dynamics are integrated into the control and observer design. The first proposed structure employs a state-dependent local approximation of the nonlinear model to generate dynamic controller and observer gains, aiming to balance robustness and accuracy. In contrast, the second one directly embeds the full nonlinear dynamics into both the control law and extended state observer, tightly coupling performance to model fidelity. The proposed methods were experimentally validated on a magnetic levitation system, known for its strong nonlinearity, and compared with a classical linear ADRC (LADRC). Furthermore, stability analysis of the methods was conducted using Lyapunov theory. Results show that the linearized structure consistently improves regulation performance over LADRC and, in most cases, achieves similar results to nonlinear ADRC with lower computational effort. However, the performance of the nonlinear approach may degrade under modeling inaccuracies and limited observer bandwidth. This study highlights that the way model information is integrated–rather than its level of detail–has a decisive impact on control quality. Finally, practical design guidelines are provided to assist in selecting an appropriate ADRC structure for nonlinear applications where robustness, computational efficiency, and limited model knowledge must be balanced.

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.

This paper proposes a control approach that can provide significant energy savings for the control of pneumatic servo systems. The control methodology is formulated by decoupling the standard four-way spool valve used for pneumatic servo control into two three-way valves, then using the resulting two control degrees of freedom to simultaneously satisfy a performance constraint (which for this paper is based on the sliding mode sliding condition), and an energy-saving dynamic constraint that minimizes cylinder pressures. The control formulation is presented, followed by experimental results that indicate significant energy savings with essentially no compromise in tracking performance relative to control with a standard four-way spool valve.

Although the structure of PI controller is simple, there are some flaws. In order to overcome the contradictions between the rapid response and overshoot for speed, the model of active disturbance rejection control (ADRC) was established in the paper. The transition process for a given speed was got by tracking - differentiator (TD). The sum of internal and external disturbance is estimated by the extended state observer (ESO). The capability of resisting disturbance is improved for the disturbance compensated timely. Permanent magnet synchronous motor (PMSM) direct torque control based on ADRC scheme is realized. The simulation results have shown its availability.

To improve the robustness and the anti-disturbance of control system, regulate its stiffness, a scheme concluding linear active disturbance rejection controllers for pneumatic servo system is proposed. Two linear active disturbance rejection controllers are designed respectively to track the motion and pressure reference. The design of a linear active disturbance rejection controller is independent of precisely mathematical model of the system. The extended state observer can track successfully the states and extended state of the system, and it is possible to realize the states feedback and handle the model uncertainty and compensate external disturbance. The simulation results show that pneumatic servo system based on linear active disturbance rejection controllers is robust against modeling uncertainty and external disturbances. The dynamic performance of the system using linear active disturbance rejection controllers also can be improved as well.

Vibration is a common problem in rotating machine. Active Magnetic Bearing (AMB) produces controllable magnetic force to levitate rotor and the control algorithm contributes to reduce vibration. This paper proposes a vibration suppression strategy based on active disturbance rejection control (ADRC). ADRC applies extend state observer (ESO) to estimate generalized disturbance. However, in AMB system, disturbance is mainly caused by centrifugal force, whose frequency is rotating frequency. For sinusoidal disturbance, ESO cannot estimate it absolutely. To estimate sinusoidal disturbance in AMB system, generalized integrator ESO (GI-ESO) is applied in ADRC. The resonant frequency of GI is set as rotating frequency. Transfer function of error of GI-ESO is analyzed and notch feature at resonant frequency is displayed. The transfer function of third-order of ADRC applied GI-ESO is obtained. Stability of proposed vibration suppressing strategy is analyzed by root locus. Results of simulations show better effect for sinusoidal disturbance estimation of GI-ESO. After applying ADRC based on GI-ESO, vibration of displacement in AMB system is reduced effectively, which shows the effectiveness of proposed vibration suppressing strategy.

In the permanent magnetic synchronous motor (PMSM) system with active disturbance rejection controller (ADRC), the estimation accuracy of extended state observer (ESO) will decrease when the ADRC does not depend on the system model completely. In order to improve the estimation accuracy, this paper proposes an improved ADRC approach by adding a model compensation term. Furthermore, the rotor inertia and viscous friction coefficient in the model compensation term is identified by the model reference adaptive identification (MRAI) algorithm. The load torque is estimated according to the mechanical equation of PMSM system. Then the identification values of rotor inertia, viscous friction coefficient, and load torque make up the compensation term of the ESO. Simulation results indicate that this improved ADRC approach has the better parameter robustness and anti-load-disturbance performance.

PurposeThis paper aims to study a disturbance rejection controller to improve the anti-interference capability and the position tracking performance of airborne radar stabilized platform that ensures the stability and clarity of synthetic aperture radar imaging.Design/methodology/approachThis study proposes a disturbance rejection control scheme for an airborne radar stabilized platform based on the active disturbance rejection control (ADRC) inverse estimation algorithm. Exploiting the extended state observer (ESO) characteristic, an inversely ESO is developed to inverse estimate the unmodeled state and extended state of the platform system known as total disturbances, which greatly improves the estimation performance of the disturbance. Then, based on the inverse ESO result, feedback the difference between the output of the tracking differentiator and the inverse ESO result to the nonlinear state error feedback controller (NLSEF) to eliminate the effects of total disturbance and ensure the stability of the airborne radar stabilized platform.FindingsSimulation experiments are adopted to compare the performance of the ADRC inverse estimation algorithm with that of the proportional integral derivative controller which is one of the mostly applied control schemes in platform systems. In addition, classical ADRC is compared as well. The results have shown that the ADRC inverse estimation algorithm has a better disturbance rejection performance when disturbance acts in airborne radar stabilized platform, especially disturbed by continuous airflow under some harsh air conditions.Originality/valueThe originality of this paper is exploiting the ESO characteristic to develop an inverse ESO, which greatly improves the estimation performance of the disturbance. And the ADRC inverse estimation algorithm is applied to ameliorate the anti-interference ability of the airborne radar stabilization platform, especially the ability to suppress continuous interference under complex air conditions.

In order to meet the precision requirements and tracking performance of the continuous rotary motor electro-hydraulic servo system under unknown strong non-linear and uncertain strong disturbance factors, such as dynamic uncertainty and parameter perturbation, an improved active disturbance rejection control (ADRC) strategy was proposed. The state space model of the fifth order closed-loop system was established based on the principle of valve-controlled hydraulic motor. Then the three parts of ADRC were improved by parameter perturbation and external disturbance; the fast tracking differentiator was introduced into linear and non-linear combinations; the nonlinear state error feedback was proposed using synovial control; the extended state observer was determined by nonlinear compensation. In addition, the grey wolf algorithm was used to set the parameters of the three parts. The simulation and experimental results show that the improved ADRC can realize the system frequency 12 Hz when the tracking accuracy and response speed meet the requirements of double ten indexes, which lay foundation for the motor application.

Based on active disturbance rejection control technique and characteristics of electric power steering, a steering angle tracking controller is designed, which consists of an aligning moment estimator to deal with modeling error and nonlinearity of electric power steering. The aligning moment estimator is based on an extended state observer and takes steering system friction and differential drive steering torque, which is a unique phenomenon in a distributed drive electric vehicle, into consideration. According to the estimated aligning moment and tracking differentiator, the steering angle tracking controller is designed based on a nonlinear state feedback control and feedforward compensation control laws. Results of various simulations and experiments, including pivot steering, step input steering, and sinusoidal input steering, show that the proposed controller has good performance in tracking reference steering angle and is convenient to implement. With the aligning moment estimator, the proposed controller shows better results in comparative experiments than a conditional integral-based steering angle tracking controller.

In this paper, the problem of attitude tracking control for a class of vertical take-off landing (VTOL) aircraft in the presence of uncertain disturbances is addressed. The active disturbance rejection control (ADRC) method is utilized to address uncertain disturbances, while the radial basis function (RBF) neural network is considered for handling unknown nonlinear dynamics. By incorporating a modified tracking differentiator, a nonlinear state error feedback controller, and an extended state observer, the disturbance observation problem in the aircraft system is solved. These disturbances, seen as a combined disturbance in the aircraft system, are counteracted through the extended state observer. Furthermore, the unknown nonlinear dynamics within the aircraft system are approximated using the RBF neural network. Subsequently, the paper suggests adaptive ADRC strategies based on neural network and formulates adaptive control laws to estimate unknown parameters. The Lyapunov stability theory proves the effectiveness of the proposed control strategies. The simulation results show that the attitude tracking control problem of VTOL aircraft can be achieved under the proposed control strategies and adaptive control laws.

In a surface vehicle ride, the passenger’s comfort is desirable, ensuring safety under various tight constraints. To consider this requirement, this article has proposed a lateral control for autonomous vehicle considering the lateral offset error constraints. A reduced-order dynamics of the vehicle has been considered for improving and easy implementation of backstepping. A nonlinear control has been developed by utilizing the Time-varying Asymmetric Barrier Lyapunov Function via the Active Disturbance Rejection Control (ADRC) approach. The Extended State Observer, a component of applied ADRC, estimates all unknown system states as well as the unknown disturbance. The desired trajectories (smooth and non-smooth) based on the yaw rate profile have been synthesized to test the performance of the vehicle. Simulation results are presented to show the effectiveness of the proposed closed-loop control strategy. The vehicle performance has been compared using the proposed method, the conventional Quadratic Lyapunov Function and Symmetric Barrier Lyapunov Function based control. The proposed control provides a smoother control signal, small tracking error and robustness in presence of hard road constraints for smooth/non-smooth vehicle motion.