Search Results (18)

While the Internal Model Principle (IMP) and Disturbance Observer (DOB) are fundamental to robust control, their systematic equivalence within a unified framework has received limited attention. IMP-based control achieves robustness through the structural inclusion of signal generators, whereas DOB-based methods rely on extended state representations for disturbance estimation. This paper bridges this gap by designing a state-space Reduced-Order Disturbance Observer (RODOB)-based controller that achieves systematic equivalence with an IMP-based transfer function controller. As a design example, an IMP-based controller is synthesized using a Linear Quadratic Regulator (LQR) for an augmented system in error space, with reference inputs directly integrated into the RODOB structure to eliminate the need for additional filters. Simulations and hardware experiments on a Brushless DC (BLDC) motor verify that both structures exhibit consistent control input and output characteristics, significantly outperforming conventional cascade and PID strategies. Numerical stability during digital implementation is ensured via partial fraction expansion. Furthermore, a method for estimating equivalent disturbances—encompassing both external loads and model uncertainties—is proposed by leveraging RODOB states. These findings suggest significant potential for future applications in fault diagnosis and real-time condition monitoring. Full article

Coaxial contra-rotor unmanned aerial vehicles (UAVs) are attractive for their compact structure and aerodynamic efficiency, making them suitable for long-endurance and heavy-payload operations. However, the coaxial configuration introduces strong rotor coupling, phase lag, and additional disturbances, which pose significant challenges for stable control. To overcome these issues, we propose a cascaded Active Disturbance Rejection Control (ADRC-C) framework, in which a two-level control structure is adopted. The outer loop employs a classical ADRC controller to estimate and compensate for the lumped external forces, providing the compensated attitude command to the inner loop. The inner loop, in turn, adopts an $SO\left(3\right)$-based Extended State Observer (ESO) to handle high-frequency torque disturbances through real-time estimation and compensation. The proposed approach is validated through numerical simulations. Results confirm that the cascaded ADRC consistently outperforms conventional PID control in tracking accuracy, transient response, and disturbance rejection, demonstrating strong robustness for demanding coaxial UAV missions. Full article

In order to reduce the impact of various disturbances on the permanent magnet synchronous motor (PMSM) system especially during low-speed (0–300 rpm), this paper proposes a novel repetitive fractional-order active disturbance rejection control (RFO-ADRC) method. It combines repetitive control and fractional-order active disturbance rejection control (FO-ADRC) innovatively in an cascaded structure. Repetitive compensation is employed to handle the periodic disturbances arising from the structural characteristics of PMSM. FO-ADRC is employed to compensate for the residual aggregated disturbances. It novely replaces the nonlinear error feedback control (NLSEF) link in active disturbance rejection control (ADRC) with fractional-order control, and then incoportes an improved smooth function into the extended state observer (ESO), effectively reducing parameter adjustment complexity and mitigating inherent chattering. Finally, the proposed RFO-ADRC is validated on a 1.5 kW PMSM experimental platform and compared with PI, ADRC, and FO-ADRC. Experimental results show that RFO-ADRC achieves a start-up time of 0.36 s fastest, zero overshoot, a steady-state speed error within ±2.27 r/min lowest, a total harmonic distortion (THD) of 6.47% lowest, and a recovery time of 0.22 s under sudden load changes fastest, demonstrating superior performance. Full article

Positioning servo systems utilizing permanent magnet synchronous linear motors (PMSLMs) are conventionally governed by cascaded P-PI controllers, which, despite their simplicity and robustness, suffer from limited tracking and anti-disturbance performance due to their single-degree-of-freedom (1-DOF) structure. This paper introduces a novel two-degree-of-freedom (2-DOF) control algorithm that integrates explicit model predictive control (EMPC) with a differential-compensated extended state observer (DCESO). The EMPC framework leverages position and velocity as state variables, eliminating the need for integral terms and thereby enhancing dynamic response. By employing an offline optimization approach, a control law is explicitly formulated to handle system constraints while minimizing online computational overhead. Additionally, a velocity feedforward term derived from the MPC framework is incorporated to further reduce tracking errors. To bolster disturbance rejection, the proposed DCESO introduces a differential compensator that mitigates the low-pass effects inherent in traditional ESOs, thereby improving estimation dynamics. Experimental results demonstrate that the proposed method significantly outperforms the conventional P-PI controller, increasing the position loop bandwidth from 147 Hz to 208 Hz and markedly enhancing anti-disturbance performance. The algorithm’s low online computational demand makes it highly suitable for industrial applications. Full article

In the development trend of intelligent and high-performance construction machinery, the dual-spool electro-hydraulic valve, as a new-generation core control element, directly affects the operation accuracy and energy-efficiency level of construction machinery. The standard linear extended state observer (LESO) produces relatively serious peaks as the system order increases, which leads to the degradation of the observer’s performance and affects the controller’s accuracy. To solve this problem, this paper innovatively proposes an output feedback control strategy for a cascaded structure observer for the dual-spool electro-hydraulic valve. This paper designs an output feedback controller based on the cascaded structure observer. The uniform exponential stability (USE) criterion ensures that the tracking error of the observer for the system state is bounded. The expected load pressure is constructed based on the expected trajectory to replace the actual load pressure, avoiding the influence of the nonlinear coupling between the load pressure and the input signal on the control system. Finally, a stable output feedback controller is obtained based on the backstepping control method and Hurwitz polynomial stability analysis. This study first applies the cascaded structure observer to the field of dual-spool electro-hydraulic valve control, providing a new theoretical framework and technical path for the high-precision control of the hydraulic system of construction machinery. Theoretical analysis shows that compared with the standard LESO, the cascaded structure observer can significantly reduce the online computational burden and effectively suppress the peak phenomenon, providing stronger estimation ability. Finally, a large number of simulation examples verify the effectiveness and superiority of the output feedback controller based on the cascaded structure observer. In all four test scenarios, the average tracking error of C1 (the output feedback controller designed based on the cascaded structure linear extended state observer) is about 5.1%, the average tracking error of C2 (the output feedback controller designed based on the standard structure linear extended state observer) is about 7.8%, and the average tracking error of C3 (the high-gain PID controller) is about 19.2%. The average control accuracy of the designed C1 controller is improved by 2.7% and 14.1% compared with C2 and C3, respectively. In terms of the estimation of external disturbances, the average error of C1 is 14% and the average error of C2 is 29.6%. The estimation accuracy of the former is improved by 15.6% compared with the latter. Full article

With the growing demand for advanced control algorithms in permanent magnet synchronous motor (PMSM) speed regulation, active disturbance rejection control (ADRC) has garnered significant attention for its simplicity and effectiveness as an alternative to traditional proportional-integral (PI) controllers. However, two key challenges limit its broader application: the lack of an intuitive equivalence analysis that highlights the advantages of ADRC over PI control and the complexity in selecting appropriate extended state observer (ESO) structures within ADRC. To address these issues, this paper develops an equivalent model of ADRC based on the structure of a generalized PI controller, offering a clearer understanding of its operational principles. The results demonstrate the relationship between ADRC and generalized PI control while highlighting ADRC’s superior capabilities. Additionally, this paper constructs a generalized model that incorporates all ADRC observer configurations, including both high-order ESO (HESO) and cascaded ESO (CESO), enabling a comprehensive analysis of ADRC with various observer structures and establishing equivalence relationships between them. The findings provide valuable insights into the efficacy and versatility of ADRC in PMSM speed regulation, supported by experimental validation on a test bench using the dSPACE DS1202 MicroLabBox. Full article

To enhance the speed-control performance of a permanent magnet synchronous motor (PMSM) drive system, an improved sliding-mode anti-interference control strategy is presented. Firstly, to tackle the speed fluctuation issue caused by cogging torque (a periodic disturbance) and time-varying disturbances at low set speeds in PMSM, an improved sliding-mode control (ISMC) is proposed. It consists of a continuous adaptive fast terminal sliding-mode surface (CAFTSMS) and a new reaching law (NRL). The CAFTSMS boosts the system’s immunity to interference, while the NRL, improved via an adaptive function, enhances the fast transient response and notably reduces speed fluctuations. Secondly, a quasi-proportional resonant (QPR) controller is introduced. It suppresses specific-order system harmonics, significantly reducing the harmonic amplitude and strengthening the system’s ability to handle periodic disturbances. Finally, a cascaded extended state observer (CESO) with a special cascade structure is proposed to solve the observation-delay problem in the traditional cascade structure. Experimental results show that the proposed sliding-mode anti-disturbance control strategy performs excellently in overcoming disturbances. Full article

In complex indoor environments, target tracking performance is impacted by non-line-of sight (NLOS) noises and other measurement errors. In order to fix NLOS errors, a double extended Kalman filter (DEKF) algorithm is proposed, which refers to a kind of cascaded structure composed of two Kalman filters. In the proposed algorithm, the first filter is a classic Kalman filter (KF) and the second is an extended Kalman filter (EKF). Time of arrival (TOA) measurements collected by multiple stationary ultra-wideband (UWB) sensors are used. The residual errors between the measured TOA and that of the first KF are predicted, and the covariance of the first KF is adjusted correspondingly. Then, we use the estimated distance state of the first KF as a measurement vector for the second EKF in order to obtain a smoother observation. One of the advantages of the proposed algorithm is that it is able to perform target tracking with good accuracy even without or with only one LOS TOA measurement for a period of time without prior information about the NLOS noise, which may be difficult to obtain in practical applications. Another advantage is that the accuracy does not greatly decrease when NLOS noises exist for a long period of time. Finally, the proposed DEKF can maintain the high-precision positioning characteristics in both the constant velocity (CV) model and the constant acceleration (CA) model in the LOS/NLOS environment. Our simulation and experimental results show that the proposed algorithm performs much better than other algorithms in SOTA, particularly in severe mixed LOS/NLOS environments. Full article

In complex indoor environments, target tracking performance is impacted by non-line-of-sight (NLOS) noises and other measurement errors. In order to fix NLOS errors, a Double Extended Kalman filter (DEKF) algorithm is proposed, which refers to a kind of cascaded structure composed of two Kalman filters. In the proposed algorithm, the first filter is a classic Kalman filter (KF) and the second is an Extended Kalman filter (EKF). The time of arrival (TOA) measurements collected by multiple stationary ultra-wide band (UWB) sensors are used. Residual errors between the measured TOA and the prediction from the first KF are used to adjust the covariance of the first KF accordingly. Then, we use the estimated distance state of the first KF as a measurement vector of the second EKF in order to obtain a smoother observation. One of the advantages of the proposed algorithm is that it is able to perform target tracking with a good accuracy even without or with only one line-of-sight(LOS) TOA measurement for a period of time without prior information of the NLOS noise, which may be difficult to obtain in practical applications. Another advantage is that the accuracy does not significantly decrease when NLOS noises persist for a long period of time. Finally, the proposed DEKF can maintain high-precision positioning characteristics in both the constant velocity (CV) model and the constant acceleration (CA) model for LOS/NLOS environments. In the case of mixed LOS/NLOS environments, the RMSE of the proposed algorithm can be kept within 5 cm, while the RMSEs of other compared algorithms are easily beyond tens of centimeters. At the same time, when the confidence of RMSE is set to 95% for 1000 MC simulations, the confidence interval of the proposed algorithm is the smallest, and the mean value is 3–5 times closer to the true value compared to other algorithms. Simulation and experimental results show that the proposed algorithm performs much better than other state-of-the-art algorithms, particularly in severe mixed LOS/NLOS environments. Full article

Although the smart grid, equipped with situational awareness and contextual understanding, represents the future of energy management and offers flexible, extensible, and adaptable intelligent grid services, it still shares similarities with traditional systems. For instance, the control performance of the DC (Direct Current) bus voltage will continue to be adversely affected by various uncertain interference factors in the future smart grid. In practice, this often leads to challenges, as inverters typically operate at high frequencies when connected to the grid. Therefore, the ability to effectively suppress fluctuations in DC bus voltage and mitigate their impact, as well as enhance the dynamic performance of the system, will be one of the key indicators for evaluating the upcoming smart grid. Consequently, this paper proposes DC-link Voltage Control using a two-stage Extended State Observer (ESO)-Cascaded Topology Structure in an LCL (Inductive-Capacitive-Inductive) Filtered Photovoltaic Grid-Connected Inverter based on Padé Approximation and Improved Active Disturbance Rejection Control. Results from both simulations and experiments demonstrate that the proposed algorithm performs effectively and is capable of suppressing fluctuations. Full article

With the increasing power of fuel cells, ultra-high-speed electric air compressors (UHSEACs) have been widely used. However, due to the ultra-high speeds involved, UHSEACs face problems such as long speed adjustment times and large speed fluctuations. Compared to other control methods, Active Disturbance Rejection Control (ADRC) is well-suited for highly nonlinear systems like UHSEACs. The Extended State Observer (ESO), a key component of the ADRC, struggles to accurately observe high-frequency excitations. To address this, the first step is to add a cascaded structure to the ESO and design a Current State Extended State Observer (CS-ESO) to better observe the electromagnetic and load excitations in the UHSEAC. The second step involves designing the ADRC based on the CS-ESO and performing speed adjustment simulations. The third step is to build a UHSEAC experimental platform and a conduct speed adjustment experiment. The findings indicate that, compared to the Proportional Integral Derivative (PID) control, the ADRC with the ESO, and the Sliding Mode Control (SMC), the use of the ADRC with the CS-ESO results in a significant reduction in overshoot—by at least 760 RPM under load-increasing conditions and 140 RPM under load-reducing conditions. Furthermore, the speed regulation time is notably decreased by at least 0.2 s and 0.1 s under these respective conditions. Full article

Linear active disturbance rejection control (LADRC) has been widely used to improve the tracking accuracy and anti-disturbance performance of telescope servo control under disturbances. However, the linear extended state observer (LESO) is sensitive to noise, and its bandwidth is limited by the resonant frequency of the telescope. To enhance the LARDC’s ability to attenuate disturbances, a novel cascade anti-disturbance structure (NCADS) with LADRC on the outer speed loop and a nonlinear disturbance observer (NDOB) on the inner current loop is proposed. The NDOB compensates for the dominant disturbance through feedforwarding the q-axis current reference, and the LESO compensates for the residual disturbance on the outer speed loop. First, the NCADS is introduced in a three-closed-loop control framework of PMSM. Then, the design method of the controller for each loop and the NDOB are presented, the parameter-tuning method based on bandwidth is demonstrated, and the convergence of the NDOB is proved. Furthermore, to improve the searching and tracking efficiency of wide-field survey telescopes, the nonlinear tracking differentiator (NTD) was modified to plan the transition process of the position loop, which only needs to set the maximum speed and acceleration of the telescope. Finally, simulations and experiments were performed on a 2.5-m-wide field survey telescope. The experimental results verify that the proposed NCADS method has a better anti-disturbance performance and higher tracking precision than the conventional method, and the improved NTD method does not need to tune parameters and achieved a fast and smooth transition process of the position loop. Full article

For an electro-hydrostatic actuator (EHA), the position, speed, and current cascade three-loop control architecture are dominant in existing active disturbance rejection control (ADRC). However, this architecture suffers from many problems, such as severe noise sensitivity of the extended state observer (ESO), excessive complexity of control structure, and too many tuned parameters, which makes the controller not easy to implement in practice. Aiming at the above drawbacks, a novel cascade double-loop ADRC strategy that is automatic current-constrained is proposed, which makes the whole ADRC architecture simplified to the position and the integrated speed–current double-loop architecture. Firstly, for the position control loop, the singular perturbation theory is used to reasonably reduce the order of the model for the position subsystem of EHA. A reduced order ADRC controller (ROADRC) is synthesized, which not only effectively reduces the noise sensitivity of ESO, but also circumvents use of the actuation acceleration information in the controller design process. Secondly, the integrated speed–current ADRC controller is designed by taking the speed and current subsystems of EHA into synthesis, which avoids the problem of excessive current loop bandwidth in conventional three-loop control architecture, and the number of tuned parameters is significantly reduced. Additionally, an uncomplicated and effective automatic current-constrained ADRC controller (CACADRC) is designed to solve the problem in the integrated speed–current ADRC that the current cannot be automatically constrained. Finally, by comparing the three-loop PI controller with the traditional three-loop ADRC, a detailed simulation analysis is carried out to verify the effectiveness and merits of the proposed controller. The simulation results show that the proposed controller not only inherits the advantages of high precision and strong disturbance rejection performance of the conventional ADRC, but can also efficiently decrease the noise sensitivity of ESO and effectively achieve the current-constrained control. Full article

This paper aims to provide a novel control framework for exactly regulating the output voltage of floating interleaved boost converters (FIBCs), which have been widely employed in fuel cell applications in recent years. Firstly, a mathematical model of the FIBC is constructed according to Kirchhoff’s current and voltage loop principles. Then a cascade control structure with a current inner loop and voltage outer loop is developed to achieve the desired voltage regulation performance. The current controller is established based on the generalized super-twisting algorithm (GSTA) to ensure that the inductor current exactly follows the current reference, which is generated by the outer loop. Meanwhile, an active disturbance rejection control (ADRC) framework is utilized for robustly regulating the output voltage despite the presence of input variation and load change in the voltage control loop based on a nonlinear continuous GSTA-based extended state observer (GSTA-based ESO). The stability of a closed loop system based on the GSTA controller and the GSTA-based ESO is conclusively proven using the Lyapunov theory. The Simscape model of the FIBC is developed, which is used to verify the feasibility and the appropriateness of the recommended control algorithm. Finally, numerical simulations are carried out to demonstrate the effectiveness of the proposed method compared to several previous works. Full article

This paper presents a systematic procedure for the control scheme design for a PVTOL aircraft system with an inverted pendular load, which is a nonlinear underactuated system. The control scheme is based on the use of angular movement as an artificial control in order to propose new auxiliary control inputs. This is achieved by a linear extended state observer-based active disturbance rejection control to reject both nonmodeled dynamics and external disturbances. The flying planar inverted pendulum is then linearized around an unstable equilibrium point, and the resulting system is subdivided into two subsystems: (1) the height system, and (2) the horizontal pendulum system. For the height system, a linear extended state observer-based active disturbance rejection control is proposed in order to accomplish a take-off and landing task in the presence of external disturbances and non-linearities neglected in the linearization process. The flatness property in the horizontal-pendulum system is exploited in order to propose another active disturbance rejection control of linear nature. The flatness of the tangentially linearized model provides a unique structural property that results in an advantageous low-order cascade decomposition of the linear extended state observer design. Numerical simulations show the effectiveness of the proposed control scheme in trajectory tracking tasks in the presence of disturbances caused by crosswinds with random amplitudes. Full article