Modern industrial control systems commonly face actuator amplitude and rate limitations like thermal systems. Overlooking actuator saturation, especially rate saturation, degrades control performance and may cause instability. This study proposes a linear matrix inequality-based active disturbance rejection control (ADRC) framework. It proves the uniformly ultimately bounded stability under disturbances and rate saturation constraints without explicit compensation. This study innovatively introduces the concept of onset frequency to analyze the impact of rate saturation. Simulation and experimental validation on a Peltier temperature control platform demonstrate the ADRC’s effectiveness in meeting actuator constraints while enhancing control performance and disturbance rejection. The results establish new theoretical foundations and practical tuning rules for actuator saturation in industrial systems.

This paper presents a hierarchical control strategy for a broad class of multi-input multi-output (MIMO) uncertain systems without a nominal identified model. The core idea is to utilize Active Disturbance Rejection Control (ADRC) to construct an equivalent desired dynamic model, which avoids the complex model identification for MIMO systems and improves the uncertainty rejection capability of the predictive controller. At the foundational layer, the extended state observer is constructed to timely estimate the uncertainties in the coupling of subsystems, enforcing these into an equivalent desired plant through dynamic compensation linearization. The modified input-output pair models depend solely on the compensation law parameter and can directly serve as the prediction model for multi-step prediction and centralized receding optimization, ensuring optimal control of the MIMO system. The strategy is validated on typical MIMO systems of various sizes (2 x 2, 3 x 3, 8 x 8), including minimum phase, unstable, higher-order, and time-delay subsystems. Monte Carlo simulations quantitatively assess the enhanced robustness. Additionally, a 2-DOF helicopter experiment system, characterized by nonlinear time-varying coupling between attitude angles, is used to evaluate the servo-regulatory performance of the proposed strategy. Results demonstrate our controller's effectiveness in nominal and mismatch model scenarios.

This study presents a transfer function matrix identification method based on gray-box modeling to address the strongly nonlinear coupling characteristics and undershoot effect in a twin rotor multiple-input multiple-output (MIMO) system. Nonlinear state-space equations are derived from first principles, with unknown parameters recursively estimated using unscented Kalman filtering (UKF). Subsequently, the transfer function matrices for the pitch and yaw channels are developed. Experimental validation confirms that the model achieves mean relative errors of 1.4% and 5.3% for theta and psi, respectively, in both time-domain overlap tests and frequency-domain power spectral density (PSD) tests, effectively capturing the system's dynamic response. The theoretical analysis identifies two primary causes of the undershoot effect: the pitch channel induces dynamic moment coupling via the cross-transfer function, resulting in the undershoot of the yaw channel, and the yaw channel itself exacerbates this phenomenon owing to its non-minimum phase zero (right half-plane zero) characteristic. The study quantitatively examines how structural parameters and operating states influence coupling strength and the distribution of non-minimum phase zeros, elucidates the dynamic evolution mechanism of the undershoot effect, identifies that the safe operating domain for suppressing this phenomenon is approximately located within theta <= 0 and - 2 rad/s <= psi(center dot) <= 2 rad/s, and additionally defines the parameter adjustment domain. Additionally, the interplay between non-minimum phase characteristics and system stability is addressed through gain margin and phase margin analysis. This study provides a theoretical foundation for the nonlinear modeling, coupled decoupling control, and undershoot effect suppression of twin rotor MIMO system.

The proven efficacy of neural network-based control schemes has spurred their application to physical systems. However, ensuring performance robustness when deploying such controllers in uncertain physical environments remains a significant challenge. This article proposes an uncertainty feedback compensation framework to guarantee the performance robustness of neural learning-based output tracking control for uncertain nonlinear systems. Active Disturbance Rejection Control (ADRC) is incorporated as an ancillary compensator, requiring only that the varying rate of uncertainty be bounded. A single critic network-based output tracking control is then developed by constructing an augmented nominal model and adaptive dynamic programming (ADP), while ADRC operates in parallel to compensate for general uncertainties in real time. Furthermore, a desired dynamic equation-based parameter tuning rule is proposed to configure ADRC for effective tracking using nominal model information. The convergence of neural network weights is established via Lyapunov analysis, and the closed-loop stability and performance robustness are further demonstrated by analyzing the boundedness of ADRC’s estimation and tracking errors under general system uncertainties. Finally, the effectiveness of the proposed method is validated through both numerical simulations and practical experiments, demonstrating substantial improvements in the safety and practical applicability of neural learning-based control.

With the advancement of intelligent regulation, controlling reheat steam temperature system has become increasingly challenging due to frequent and wide-ranging load variations, which introduce unknown disturbances along with stringent requirements for efficiency and safety. In response to these characteristics, a modified active disturbance rejection control (MADRC) method is proposed to enhance control performance. In practical industrial processes, MADRC is generally implemented in discrete form. This paper derives a stability analysis for the MADRC, establishes its precise discrete-time state-space model, and completes the discretization of both the pre-compensator and the extended state observer, respectively. Furthermore, a closed-loop augmented system is constructed based on both the system states and the observer states. On this basis, the stability of the closed-loop system is rigorously proven and analyzed using Lyapunov stability theory and the linear matrix inequality method. In simulation experiments, the control performance of four different discrete controllers is compared through the control of a reheat steam temperature system, and robustness tests are conducted, validating the superior performance of the MADRC. The results demonstrate that the designed discrete MADRC not only ensures closed-loop stability but also exhibits superior control performance.

Superheated steam temperature (SST) regulation in large coal-fired combined heat and power (CHP) units becomes increasingly challenging under deep peak-shaving. Wide-range load variations and multisource disturbances require strong disturbance rejection, whereas industrial distributed control systems typically retain PID-oriented implementations with limited computational capability. Motivated by these, this paper proposes a bilevel IMC-DDE-PID control framework for SST regulation. In the inner loop, a desired dynamic equation (DDE)-based tuning rule shapes the plant dynamics to follow a prescribed desired closed-loop model without requiring a precise process model and partially attenuates input-side disturbances. The residual disturbance is then handled by an outer internal model control (IMC) layer built upon the desired model as an embedded internal model. Comprehensive simulations are conducted on seven benchmark SISO plants and on identified SST models at multiple loads, including scenarios with large load variations and cross-load model variation, to evaluate tracking, disturbance rejection, and control variation. Finally, field tests on an in-service 660 MW CHP unit under deep peak-shaving validate the practicality of the proposed method, reducing the SST fluctuation range by 7 °C.

With the increasing prevalence of uncertainties and variability in modern energy systems, model predictive control (MPC) often faces the challenge of predictive model mismatch. This paper proposes a desired-dynamics-based predictive control (DDPC) framework, in which an inner shaping layer is introduced to transform the raw plant into a desired dynamic model for the outer MPC. A unified design methodology is developed, including equivalent-model construction, desired-dynamics selection, and two inner-layer realizations based on desired dynamic equation (DDE)-PID and active disturbance rejection control (ADRC). In this way, the prediction model used by MPC is no longer the original uncertain plant but an explicitly shaped equivalent model determined by inner-layer controller parameters. The proposed method is validated on linear and nonlinear benchmark plants, together with frequency-domain and Monte Carlo robustness analyses. Results show that DDPC improves disturbance-rejection ability and enhances robustness against model mismatch and parameter perturbations. Further evaluation on the superheated steam temperature loop of a high-fidelity 660 MW coal-fired boiler hardware-in-the-loop simulator shows that DDPC reduces the peak-to-peak temperature fluctuation from 22.88 degrees C to 11.39 degrees C in the deep peak shaving scenario, corresponding to a 50.2% reduction relative to standard MPC.

Modified active disturbance rejection control (MADRC) is commonly designed for high-order inertial processes. This paper focuses on the single parameter tuning rule of the system with MADRC based on the desired maximum sensitivity. It is observed that an asymptote exists in the Nyquist curve of the open-loop transfer function of the high-order system with MADRC. Based on this asymptote and the maximum sensitivity constraint, the mathematical relationship between the maximum sensitivity and different parameters is derived, and consequently a novel single parameter tuning rule is established. The core advantage is that parameter tuning can be completed by adjusting only one desired maximum sensitivity parameter, while allowing the actual maximum sensitivity to closely match the set value. Comparisons with other control methods verify the effectiveness of MADRC under the proposed tuning rule. Finally, the field application of MADRC to the superheated steam temperature system further validates its advantages. Compared with conventional PI-PI control, its overall performance is improved by 15%-30%. This indicates its broad application potential in other large inertial processes in industry.

Efficient and large-scale hydrogen storage and utilization are pivotal to facilitating the transition towards a renewable energy-dominated power system. A revised Graz cycle provides an efficient and promising pathway for hydrogen to electricity conversion, with the capability to support grid dispatch and peak shaving requirements. In this context, conducting dynamic analysis and control study of the revised Graz cycle holds significant value. In this study, a thermodynamic model of the revised Graz cycle is developed using the modular modeling method, which is further validated through extensive design and off-design condition tests, confirming its accuracy and suitability for further cycle investigation. Dynamic analysis reveals the distinctive underdamped oscillation characteristic inherent to the closed-cycle nature of the system. Furthermore, a novel control strategy is proposed, integrating active disturbance rejection control with a simplified decoupling network, to achieve great power tracking and temperature maintaining across a wide range of load conditions. To evaluate the effectiveness of the proposed control scheme, we simulate renewable energy-dominated system, where the revised Graz system acts as a flexible peaking regulation source. Comparative experiments under three typical load profiles are carried out, demonstrating the superiority of the proposed control scheme. This work is the first effort on dynamic modeling and control study of the revised Graz cycle, contributing a foundation for its future practice in hydrogen-based power systems.

Hydropower unit plays a more and more important role in guaranteeing the safe and stable operation of the power system and providing high-quality power supply. As a non-minimum phase system, one of the most concerned problems is the design of hydro-turbine governing system (HTGS). Internal mode control (IMC) is a good method for turbine speed control system. To solve the problem of inverse difficulty when conventional IMC is used for hydro-generator (non-minimum phase system), this paper proposes an improved IMC based on generalized inverse solver (GIS). The article verifies the superiority of this control method for different types of linear systems through simulation. At the same time, this method is applied to the hydro generator speed control system. Compared with IMC and some improved PID algorithms, IMC with GIS algorithm shows advantages in terms of tracking response and anti-disturbance performance. It achieves overshoot-free tracking with 30% less inversion and 31% shorter recovery time after failure. The response time fluctuation is reduced by 46% compared with other algorithms, which shows stronger robustness when facing the parameter ingestion problem.

In this article, we consider the stabilization of combustion oscillations in the Rijke tube, which is modeled by a linearized wave equation with heat release fluctuation ordinary differential equation (ODE) acting as a point source term. A boundary proportional-integral (PI) feedback controller is designed to suppress the combustion oscillations. The Nyquist criterion is applied to prove that eigenvalues of the operator of the close-loop system are all located on the left-hand side of the complex plane. The closed-loop system is proved to be exponentially stable by using the Riesz basis approach. Numerical simulations are presented to verify the effectiveness of the control design. Moreover, the experimental results are obtained in an experimental Rijke tube, which validates the effectiveness of the method.

The integration of proton exchange membrane water electrolyzers (PEMWEs) with renewable energy sources is pivotal for advancing sustainable hydrogen production. Digital twins (DTs) offer significant benefits by providing real-time virtual representations of physical electrolyzers without disrupting operations. However, conventional DT frameworks often rely on offline optimization to match the behavior of the DT with the physical system, which can result in mismatches during real-time operation due to data and algorithm limitations and the uncertainties of wind and solar power inputs. To address these mismatches, this study introduces a novel DT framework featuring an online behavioral matching mechanism that corrects real-time errors between the DT and physical electrolyzers. By utilizing advanced behavioral matching techniques and realtime error correction mechanisms, the proposed DT system dynamically aligns with the physical electrolyzer's performance. Experimental validation involved a personal computer running the DT, a microcomputer with the PEMWE simulator, and a wireless cloud communication router. The results indicate that the proposed mechanism reduced errors by over 65% in the majority of cases and improved accuracy by up to 3% at most compared to traditional offline methods, suggesting that the DT can maintain more accurate real-time synchronization. While these findings are promising, further research is needed to fully assess the long-term stability and scalability of the framework in industrial applications. The enhanced DT framework shows potential to significantly improve system accuracy and reliability, providing a robust solution for real-time optimization in renewable hydrogen production. This study offers a valuable step towards more resilient and efficient cyber-physical systems, with potential applications extending beyond hydrogen production.

In modern gas turbines, signal monitoring as a basis for early warning and control has proven to be an effective tool for suppressing combustion oscillations. Conventional monitoring methods include combustion databases, time series analysis, and machine learning. However, these methods have the disadvantages of high computational complexity, limited accuracy, and insufficient versatility. In order to solve these problems, this paper proposes an online monitoring method based on the extended state observer (ESO). The method first utilizes an ESO to observe the combustion system and obtains the signal envelope. Subsequently, the monitoring information is obtained based on the derivative information of the envelope. Considering the parameter tuning and noise immunity, the conventional high-order ESO is modified to a series low-order ESOs. Combined with known system information, the ESO for observation can be further optimized to improve monitoring accuracy. Finally, the effectiveness and robustness of the method are verified by Rijke tube experiments.

In this paper, for the problem of nonlinearity and high hysteresis in the electrolytic water hydrogen production system, the article particularly proposes a PID control strategy with expected dynamic equations (DDE), This method is to make use of the expected second-order dynamic model, which enables the system output to track the reference signal quickly and stably, and reduces the dependence on the exact mathematical model. The article firstly establishes a simplified model of the electrolyzed water system, and the article also derives the control law of the DDE PID controller and then proposes a set of parameter tuning methods based on the time scale information of the system, and this method makes the controller have good dynamic performance and robustness. Simulation and experimental results show that the article method compares with the Ziegler-Nichols and IMC-tuned PID controllers, and the DDE PID exhibits significant advantages in terms of regulation time of 3.8 s, overshooting amount of 0 %, and the recovery time of disturbance resistance of 1.9 s, which are the effects.

Thermoacoustic instability challenges combustion engine operation due to acoustic wave and heat release rate coupling. Mitigating instabilities is crucial but often hindered by the complexity of the mathematical expressions involved. In this study, we propose a novel approach that leverages the easily measurable frequency response characteristics of the system, specifically the dominant oscillation frequency of the pressure pulsations, to achieve robust active disturbance rejection control for thermoacoustic instability in the Rijke tube burner. Unlike existing feedback controller designs, our model-independent active disturbance rejection control synthesis offers a general and clear design flow, enabling effective control parameter tuning and aiming to achieve optimal control performance. This design flow employs an iterative method to find an optimal set of control parameters for practical engineering applications. The simulation and experimental results confirm the effectiveness of the proposed method in suppressing oscillations across a wide frequency range (200-2000 Hz and beyond). The method achieves a rapid decrease in oscillating pressure, resulting in an approximate 99.6% reduction in amplitude. Additionally, it effectively suppresses 20% of operational fluctuations and 400% of energy fluctuations without compromising control performance. These findings demonstrate the robustness and reliability of the proposed method, as supported by both simulation and experimental data. This study contributes to the development of robust and efficient active control strategies for thermoacoustic instability, with potential benefits for enhanced engine performance and reduced emissions.

This article proposes a Smith-like active disturbance rejection control (SLADRC) for a class of overdamped processes composed of multiple first-order inertial components, where the idea of the SLADRC comes from Smith predictor. The design principle of SLADRC is presented and its stability analysis is carried out theoretically, where the estimation error of the designed extended state observer and the regulation error of the control law are both bound. For the convenience of engineering applications, this article also provides a simple and effective parameter-tuning method. The comparative simulations illustrate its advantages in tracking and disturbance rejection performance with satisfactory robustness. Finally, the proposed SLADRC is applied to a low-pressure heater system of a 660MW power plant successfully, where running data further verify its practical significance in industrial processes.

In recent years, with the advancement of renewable energy technologies, hydropower has assumed an increasingly important regulatory and balancing role in the power system. It plays an important role in grid frequency stability. This requires a faster response speed and superior disturbance immunity of the hydropower regulation system. The characteristics of active disturbance rejection control (ADRC) make it suitable for solving these kinds of nonlinearities, oscillations, and disturbances of hydro-generating units. The traditional ADRC has a complex structure and a large amount of parameter adjustments. In this paper, an improved ADRC based on a generalized differentiator is proposed, and the control loop consists of only the proportional and integrator. The parameters to be adjusted are reduced to two. The structure of the traditional ADRC is simplified. In several types of typical linear systems, the improved ADRC can harvest almost the same dynamic performance as the traditional ADRC. After applying the improved method to the simulation of a hydraulic turbine speed control system, a satisfactory response speed, superior anti-interference ability, and robustness are obtained.

This paper presents a new design methodology for robust fractional-order controllers with more than three parameters for first-order plus dead time systems using the synthesis scheme of the 'more flat phase' idea for a fractional-order controller with [proportional integral derivative] (FO[PID]) structure. The stability region of the FO[PID] controller and the synthesis scheme with the 'more flat phase' idea are illustrated through a simulation example. The corresponding pseudo-codes of the synthesis scheme are also summarised. The implementation and approximation error of the FO[PID] controller are also discussed. Likewise, the superiority of the FO[PID] controller designed with the 'more flat phase' idea is verified by additional simulations and experimental results where the closed-loop system with FO[PID] controller is not sensitive to the variations of the loop gain, ensuring satisfactory control performance. Obtained results show high potential in practical industrial applications.

Model uncertainty creates a largely open challenge for industrial process control, which causes a trade-off between robustness and performance optimality. In such a case, we propose a generalized conditional feedback (GCF) system to largely eliminate conflicts between robustness and performance optimality. This approach leverages a nominal model to design an optimal control in the virtual domain and defines an ancillary feedback controller to drive the physical process to track the trajectory of the virtual domain. The effectiveness of the proposed GCF scheme is demonstrated in a simulation for six typical industrial processes and three model-based control methods, and in a half-quadrotor system control test. Furthermore, the GCF scheme is open to existing optimal control and robust control theories.

This article focuses the denitrification processes control of selective catalytic reduction, which faces great challenges caused by high-order dynamics, strong nonlinearity, wide-range load variations, and multisource disturbances. A modified active disturbance rejection control based on gain scheduling (MADRC-gs) is proposed. A parameter-switching methodology with the selected scheduling parameter is provided and the visual analyses of performance guarantees are analyzed. MADRC-gs is applied to a practical denitrification process of an in-service 660MW power plant. Actual operational data illustrate that MADRC-gs can reduce hourly average integral absolute error by about 22.61% and 43.18% in high-load and low-load ranges, respectively. Even though the power plant experiences lifting and lowering powers frequently, MADRCgs can still obtain better control performance compared to the original controller and MADRC, and show a promising application potential in energy and chemical industries.