Extended-State-Observer-Based Control of Flexible-Joint System With Experimental Validation

The magnetic levitation (MagLev) system control is one of the most complex problems due to open-loop instability, nonlinear dynamics and uncertain parameters. The 3 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rd</sup> order differential model of MagLev is linearized by using input-output linearization. The control law is designed using feedback linearization (FL) augmented by uncertainty estimates. The states and uncertainties are estimated using extended state observer (ESO). This paper addresses the issue of robustification of FL control law against the uncertainty and nonlinear perturbation by using ESO. The stability of overall system is assured and is dependent on the pole placement. The results demonstrate the efficacy of extended state observer for estimating wide range of uncertainty in a highly nonlinear plant, when maximum information of MagLev system is unknown.

This article describes the design of a linear observer–linear controller-based robust output feedback scheme for output reference trajectory tracking tasks in the case of nonlinear, multivariable, nonholonomic underactuated mobile manipulators. The proposed linear feedback scheme is based on the use of a classical linear feedback controller and suitably extended, high-gain, linear Generalized Proportional Integral (GPI) observers, thus aiding the linear feedback controllers to provide an accurate simultaneous estimation of each flat output associated phase variables and of the exogenous and perturbation inputs. This information is used in the proposed feedback controller in (a) approximate, yet close, cancelations, as lumped unstructured time-varying terms, of the influence of the highly coupled nonlinearities, and (b) the devising of proper linear output feedback control laws based on the approximate estimates of the string of phase variables associated with the flat outputs simultaneously provided by the disturbance observers. Simulations reveal the effectiveness of the proposed approach.

Examines the application of linear optimal control theory to a low-order nonlinear chaotic convection problem. Linear control feedback is found to be fully effective only when it is switched off while the state is far from the desired equilibrium point, relying on the attractor of the system to bring the state into a neighborhood of the equilibrium point before control is applied. Linear estimator feedback is found to be fully effective only when (a) the Lyapunov exponent of the state estimation error is negative, indicating that the state estimate converges to the uncontrolled state, and (b) the estimator is stable in the vicinity of the desired equilibrium point. The aim in studying the present problem is to understand better some possible pitfalls of applying linear feedback to nonlinear systems in a low-dimensional framework. Such an exercise foreshadows problems likely to be encountered when applying linear feedback to infinite-dimensional nonlinear systems such as turbulence. It is important to understand these problems and the remedies available in a low-dimensional framework before moving to more complex systems such as turbulence.

This paper proposes a new type of extended state observer (ESO) for state observation of nonlinear system with measurement noise. ESO can observe the inner and outer disturbance of uncertain system and it is the foundation of active disturbance-rejection controller, while the measurement noise degrades the performance of the normal ESO. In this paper, fal function feedback structure is used to deal with measurement noise, then ESO is applied, thus their combination can eliminate the effect of measure noise on ESO. Comparing with the method of extending a rank state to ESO and the method of extending the filter equation to ESO, this new method does not need to extend the rank of ESO. So the tracking error increasing problem and the parameter tuning problem which are brought by the rank increase of ESO can be avoided. The simulation results shows that this method can satisfactorily track states for system with measurement noise.

The suspension gap of the electromagnetic suspension maglev train is around 8 mm. In practice, it is found that the system gap fluctuations are amplified due to the inner coupling of the suspension module system in the maglev train. In addition, maglev trains are affected by load disturbances and parameter perturbations during operation. These uncertainties reduce the ride comfort. Therefore, it is necessary to propose a novel control strategy to suppress inner coupling while reducing the influence of uncertainties on the system. In this paper, a control strategy based on feedback linearization and extended state observer (ESO) is proposed to address this challenge. Firstly, the suspension module system model is established with parameter uncertainties and external disturbances. Additionally, the inner coupling of the suspension module is represented in this model. Subsequently, the feedback linearization method based on differential geometry theory is applied to reduce the effect of inner coupling. Meanwhile, the system uncertainties are transformed into equivalent disturbances by this method. Afterward, a linear ESO is designed to estimate the equivalent disturbances. Finally, a state feedback controller is used to achieve stable suspension and compensate for the disturbances. Simulation and experimental results show that the proposed decoupled control strategy significantly suppresses the influence of inner coupling and uncertainties on the system compared with the traditional PID control strategy.

In this paper, an adaptive iterative learning control algorithm is designed based on extended state observer. Traditional robotic path tracking control has low control precision and poor control performance. A basic structure of the double joint manipulator is used for study. The system model is established, and a manipulator trajectory tracking control scheme is proposed. The specific algorithm principle and implementation method are given. The proposed algorithm consists of variable gain PD control, adaptive control, and extended state observer. The PD control can change the control gain adaptively because of the adaptive feedback loop to ensure the system stability. The extended state observer regards both the internal interference and the external random disturbance of the system. The state is used to compensate for the uncertainty of both. Experiment results show that the proposed algorithm improves the range and performance of the trajectory tracking error while improving the system convergence, and improves the control performance of the system.

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.

Recently, magnetic telemanipulation devices have shown a great deal of promise in such areas as semi-conductor manufacturing, wind tunnels, drug delivery, and many more. However, these devices are generally associated with problems caused by payload variation and uncertainties in the parameters of the system which in turn, have limited the development and application of magnetic telemanipulation technology to its full capacity. This paper addresses and deals with these issues by implementation of a precise position control method for a magnetic telemanipulation system with high level of uncertainties in its parameters. The levitation system used in this study is primarily designed for performing remote pick and place operations. The levitated object is a 28 gr microrobot capable of grasping and releasing payloads as heavy as 8 gr. To cope with the uncertainties in the modeling and payload variation, a model reference adaptive feedback linearization (MRAFL) controller is designed and its performance compared with an ordinary feedback linearization (FL) controller. Through experimental results it is shown that the MRAFL controller enables the microrobot to grasp and transport a payload as heavy as 30% of its own weight without a considerable effect on its positioning accuracy. In the presence of the payload, the MRAFL controller resulted in a RMS positioning error of 8 μm} compared with 27.9 μm} of the FL controller. The approach presented in this work is versatile as it leads to the modeling and control of a highly nonlinear system through a modular approach that can be applied to a variety of magnetic levitation and telemanipulation systems.

Guidance law of the autonomous underwater vehicle (AUV) against maneuvering target with a predefined impact angle is proposed in this paper. According to the geometric relationship, the desired impact angle is converted to in terms of the desired line of sight (LOS) angle for the maneuvering target. In order to make the LOS angle and its rate converging to the desired values respectively, the nosingularity sliding mode control (NSMC) and feedback linearization control (FLC) are utilized to design the guidance law which can converge within finite time. Firstly, FLC is utilized to convert the guidance system to be linearizable, and using NSMC to design the controller to make the system to converge within finite time. Then, to deal with the unknown disturbance, the extended state observer (ESO) is utilized to estimate it. Due to the switch gain of the NSMC is difficult to choose, an RBF neural network is utilized to adaptive adjust it. The proof of system stability is given and numerical simulations are illustrated to test and verity the proposed guidance law's performance.

In this paper, a robust adaptive control scheme using feedback linearization control (FLC) technique and active disturbance rejection control (ADRC) to achieve strong anti- disturbance performance for induction motor (IM) drive. Firstly, a FLC is developed to ensure the IM drive stability. As a result of model uncertainties, unmodeled dynamics and exogenous disorder, the control system performance can be affected. Aiming to improve the anti-disturbance performance, an extended state observer (ESO) is developed for estimating the total disturbances and states of the IM drive. To optimize the behavior of the ADRC, an action dependent heuristic dynamic programming (ADHDP) online strategy is employed for self- tuning of ESO parameters optimally and iteratively improving the estimation accuracy. Thus, critic and actor neural networks are adopted to solve the Hamilton-Jacobi-Bellman (HJB) equation online. At the same time, actor neural network provides the optimal control performance. The validity of the proposed FLC-ADRC scheme based on the optimal adaptive ESO via ADHDP approach is verified experimentally. The test results verify that the FLC-ADRC can make the IM drive follow the reference trajectory quickly and accurately and grants robust control performance regardless of uncertain dynamics as well as interior and exterior disorders.

This paper proposes the theoretical framework and the consequent application of the input-output Feedback Linearization (FL) control technique to Linear Induction Motors (LIM). LIM, additionally to Rotating Induction Motor (RIM), presents other strong non-linearities caused by the dynamic end effects, leading to a space-vector dynamic model with time-varying inductance and resistance terms and a braking force term. This paper, starting from a recently developed dynamic model of the LIM taking into consideration its end effects, defines a FL technique suited for LIMs, since it inherently considers its dynamic end effects. Additionally, it proposes a technique for the on-line estimation of the inductor resistance, based on Model Reference Adaptive System (MRAS) on-line estimator, exploited for adapting on-line the FL control action versus inductor resistance variations leading to undesirable steady-state tracking errors. The stability of the proposed MRAS on-line estimator has been proven theoretically, adopting the Popov’s criterion for hyperstability. The proposed approach has been validated experimentally on a suitably developed test set-up, under both no load and loaded conditions. It has been compared firstly with the simplest control structure, which is the scalar V/f control, secondly, under the same closed-loop bandwidths of the flux and speed systems, with the industrial standard in terms of high performance control technique: Field Oriented Control (FOC).

A position-disturbing force servo loading system consisting of two opposing hydraulic cylinders, a hydraulic loading cylinder and a bearing hydraulic cylinder, is the most common loading form. Aiming at the problem that the bearing hydraulic cylinder would bring superfluous force to the loading system, a solution to the ADRC controller is proposed. Based on the analysis of the mathematical model of the position disturbance type electro-hydraulic servo force loading mechanism, a first-order linear active disturbance rejection controller is designed according to the relative order of the system. The total disturbance of the system, including the superfluous force, is estimated by the extended state observer, and the linear error feedback control law is used for real-time compensation. The simulation results show that compared with the PID controller, the ADRC controller has better tracking accuracy, higher response speed and stronger robustness, and has the stronger anti-interference ability when the bearing system moves.

The accuracy of the line-of-sight of aviation photoelectric optoelectronic stabilization platforms is limited by two factors: external disturbance and sensor noise. An extended state observer (ESO) can effectively improve their anti-interference ability. However, due to the serious problem of gyroscope noise, further improvement of an ESO's disturbance suppression effect is limited. This article proposes a control structure that combines a Kalman filter (KF) and ESO, effectively improving upon the interference suppression ability of a traditional ESO under the influence of noise. Firstly, an ESO was used to observe the lumped disturbance of the system, and then, the observed disturbance was compensated for in the control loop. Secondly, based on the compensation servo control system, the state equation of the system was reconstructed using a Kalman filter. Finally, the reconstructed filtered state variables were iterated onto the universal state observer, achieving the observation of disturbances while filtering out sensor noise. Under the conditions of a laboratory flight simulation turntable, the line-of-sight stability accuracy level was improved under disturbance excitation. It can be seen that the combination of a Kalman filter and extended disturbance observer proposed in this project improves the ESO's anti-interference ability under the influence of noise.

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.

To regulate uncertainties in system dynamics and external disturbances, a robust controller is proposed for a plant with time-varying uncertainty. The design is based on the concept of extended state observer (ESO) with repetitive controller (RC). In real time estimation and mitigation of the total effect of various uncertainties, ESO based RC is particularly effective against a wide range of parameter variations, model uncertainties, and large disturbances. With only two tuning parameters, the controller provides a simple and user friendly solution to complex engineering problems in practice. The comparison results verified the effectiveness of the ESO based RC over state observer (SO) based RC.