Big torque inputs in controls could increase energy consumption, and big estimated perturbations in observers could produce device damages. Therefore, it would be interesting to propose a constrained control for safe reference tracking and a constrained observer for safe perturbation estimation in robots. Furthermore, the best gains in controls produce a balance between safe reference tracking and save energy consumption. Therefore, it would be interesting to propose a method to find the best gains. In this paper, an observer-based differential evolution constrained control is proposed for safe reference tracking in robots. The contributions are described as follows: (1) a constrained observer is proposed for safe perturbation estimation in robots, (2) a constrained control is proposed for safe reference tracking in robots, (3) a differential evolution optimizer is used to find the best gains in an observer-based constrained control, (4) the robust stability in an observer-based constrained control is assured, (5) the pseudo-code of an observer-based differential evolution constrained control is detailed. The proposed observer-based differential evolution constrained control is applied for safe reference tracking in two robots. 

Observer-based differential evolution constrained control for safe reference tracking in robots.

This article develops a novel separation identification approach for the Hammerstein-Wiener nonlinear systems with process noise using correlation analysis technique. The Hammerstein-Wiener nonlinear systems have three parts, namely, an input nonlinear block, a linear block, and an output nonlinear block. The designed hybrid signals that consist of separable signal and random signal are devoted to achieving parameters separation identification of the Hammerstein-Wiener nonlinear system, that is, the three blocks are identified independently. First, the characteristics of separable signals under the action of static nonlinear block are analyzed, and two groups of separable signals with amplitude relation are utilized to estimate parameters of output nonlinear block. Moreover, the linear block parameters are identified by using correlation analysis approach, which deals with effectively immeasurable problem of internal variable information. Finally, the data filtering technique is implemented to weaken the influence of noises, and filtering-based recursive extended least squares algorithm is developed for figuring out the parameters of nonlinear block and colored noise model. The validity and accuracy of the proposed scheme are verified by two simulations, and simulation results exhibit that the proposed method can obtain higher identification precision and better robustness than the existing identification algorithms. 

Separation identification approach for the
 Hammerstein‐Wiener
 nonlinear systems with process noise using correlation analysis

Disturbances of the permanent magnet synchronous motor (PMSM) drive system are usually observed and fully compensated to improve the robustness in existing two-degrees-of-freedom control schemes. However, these schemes neglect the potential advantages of the disturbances that have not been well investigated yet. To this end, this article proposes a new adaptive conditional disturbance negation (ACDN)-based control scheme for the PMSM drive system to enhance the performance by exploiting the potential advantages of the disturbances. The proposed scheme can utilize advantageous disturbances and negate detrimental disturbances, achieving better dynamic performance and robustness. First, a generalized supertwisting extended state observer with continuous right-hand sides is designed for disturbance estimation, which realizes precise estimation within a finite time. On this basis, a unique ACDN governor is constructed by developing a disturbance characterization indicator that indicates whether the estimated disturbance is advantageous or detrimental. Besides, an efficient and straightforward nonsmooth-integral controller is designed to collaborate with the ACDN governor via two complementary nonsmooth terms and integral. Finally, rigorous stability analysis and experimental results demonstrate the feasibility and superiority of the proposed control scheme. 

Adaptive Conditional Disturbance Negation-Based Nonsmooth-Integral Control for PMSM Drive System

The generator rotor is crucial for the high-rate and reliable continuous-wave mud pulse transmission system. However, its dynamic responses are constrained by resistant load shocks and harsh operating environments. This study proposes an enhanced nonlinear active disturbance rejection control (EADRC) that integrates cascaded extended state observer (CESO) and enhanced nonlinear state error feedback (NLSEF) to address the abovementioned issues. The rotor motion model considering hydraulic torque is analyzed to characterize external load shocks, and an optimized nonlinear function, fal(·), is designed to improve slow convergence speed in high-error states. CESO is constructed to achieve timely and accurate disturbance estimations, while enhanced NLSEF is established to combine current and future system information for efficient feedback. Moreover, estimation capability and stability are theoretically proven based on the Lyapunov function. Simulations and experiments show that the proposed EADRC exhibits rapid response, high accuracy, and strong robustness in rotor speed control. 

Improved nonlinear active disturbance rejection control for a continuous-wave pulse generator with cascaded extended state observer

As for the torque control system of induction motors, there are generally two technical problems. One is the torque feedback error caused by the low accuracy of the flux observer, and the other is the torque ripple caused by insufficient harmonic current suppression. In order to provide accurate electromagnetic torque feedback information, an improved voltage and current hybrid model-based flux observer is designed, which improves the effectiveness of flux observation and the accuracy of electromagnetic torque feedback. Furthermore, an improved quasi-resonant linear active disturbance rejection-based current loop control method is proposed to suppress the harmonic current and reduce the torque ripple. And the disturbance observation characteristics, parameter influence, and self-stability of the control system are analyzed based on the frequency domain method. Finally, to verify the effectiveness of the proposed method, simulation, and physical experiments are designed in this paper. The experimental results show that the proposed method can effectively reduce the flux observation error and the current harmonic component, and thus greatly improve the torque tracking control performance. 

Induction motor torque closed-loop vector control system based on flux observation and harmonic current suppression

Extended state observer based current-constrained controller for a PMSM system in presence of disturbances: Design, analysis and experiments

Aiming at the speed fluctuation caused by the unbalanced load fault of the permanent magnet synchronous motor system, a composite active disturbance rejection fault tolerant control method is proposed in this paper. Firstly, the mathematical model of load torque is deduced based on the kinematic analysis of the fault. A model of electromechanical coupling is established with the torque coupling relationship between the motor and load. Secondly, the estimation of the fault model information from a load observer is used to improve the design of extended state observer so the influence of the fault on the performance of the whole control system can be attenuated via the feedforward compensation channel. Finally, a real-time hard-in-the-loop based NI CompactRIO 9045 and LabVIEW for PMSM system is designed to verify and compare the performance of the proposed controller against conventional active disturbance rejection controller. The experiment results demonstrate the effectiveness and superiority of the proposed controller.

A Composite Linear Active Disturbance Rejection Fault Tolerant Controller for a PMSM System in Unbalanced Load Fault: Design and Hardware Implementation

Model uncertainties, external excitations and complex boundary conditions, etc. present in the control system lead to poor robustness of the controller. Therefore, an extended state observer (ESO) is utilized to compensate for these disturbances. However, a conventional ESO is not sufficiently capable to deal with rapid periodic disturbances. A frequency-shaped linear quadratic regulator (FSLQR) is, hence, developed by employing a frequency independent cost function according to the disturbance spectrum. In addition, knowing that periodic disturbances may have unknown or varying frequencies, a frequency-adaptive mechanism is introduced to address such issues, which enables the proposed method to mitigate the influences of frequency deviations. This is the first attempt to introduce frequency shaping technology into the control framework based on extended state observer. The control scheme of the introduced approach is general, but is conveyed here using solely an all-clamped plate structure with an inertial actuator, which is considered a typically benchmark for vibration phenomenon. The effectiveness and advantage of the proposed strategy are validated with comparative experimental studies on a hardware-in-the-loop laboratory testbed and a theoretical analysis based on Lyapunov theorem. Compared with the classical method based on ESO, the vibration experimental results demonstrate that the control performance of the first mode and the second mode are improved, both having upgraded approximately 6 dB. 

Multi-modal vibration control for all-clamped plate subjected to periodic disturbances by ESO-based frequency-shaped LQR

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Extended state observer based current-constrained controller for a PMSM system in presence of disturbances: Design, analysis and experiments

A Composite Linear Active Disturbance Rejection Fault Tolerant Controller for a PMSM System in Unbalanced Load Fault: Design and Hardware Implementation

Multi-modal vibration control for all-clamped plate subjected to periodic disturbances by ESO-based frequency-shaped LQR