State Estimation Research Articles

Feedback control of an experimental electrically-heated steam methane reformer

Steam methane reforming (SMR) is the most common industrial process to produce hydrogen (H2) from methane and water vapor. The SMR reactions are overall highly endothermic and traditionally, fossil fuels are burned to provide the necessary heat of reaction. However, it was found that electrifying the tubular SMR reactors using renewable electrons instead of conventional heating gives the opportunity of producing H2 with lower carbon emissions, lower reactor volumes, and higher carbon conversion. While current studies in this new technology focus on improving the catalysts or heating sources, a more efficient process control scheme can also significantly contribute to the understanding of potential challenges and opportunities of combining renewables and natural gas in the production of H2 at industrial scales. In order to further develop the electrically-heated SMR process and the associated control strategies, we have constructed an experimental Joule-heated SMR system at UCLA. The system contains a tubular reactor with a washcoated Ni/ZrO2 catalyst, two thermocouples connected to the top and bottom of the reactor, a power supply for providing electrical heating, and an on-line gas chromatograph (GC) for measuring outlet gas concentrations. The synthesis procedure of the catalyst, SMR data collection, and thermal considerations for catalyst degradation are described in this paper and are all accounted for experimentally when using a proportional integral (PI) controller to gradually increase the reactor temperature without harming the catalyst. Advanced control strategies, such as model predictive control (MPC), require a process model that uses measurement feedback to make predictions of the process time-evolution in order to optimize the control actions in real-time. We have previously developed a lumped-parameter modeling strategy for the SMR process. The MPC objective is to control the H2 production rate by manipulating the current flowing through the outer reactor shell. However, to use this model in an MPC, feedback values for all state variables should be provided by the sensors. In our experimental system, the on-line GC only gives discrete measurements with a long sampling period. To this end, the process model is incorporated into an extended Luenberger observer (ELO) that uses the reactor temperature and GC measurements to provide estimates of all the variables needed by the MPC. The ELO-based MPC system is then experimentally implemented on the process and it is demonstrated to be more efficient in terms of speed of the closed-loop response than the PI controller using delayed, measurement feedback by the GC.

Improved Deadbeat Predictive Current Control With Extended State Observer for Dual Three-Phase PMSMs

Improved Deadbeat Predictive Current Control With Extended State Observer for Dual Three-Phase PMSMs

An online battery–state of charge estimation method using the varying forgetting factor recursive least square - unscented Kalman filter algorithm on electric vehicles

Accurate and fast estimation of the state of charge is important for the battery management system of electric vehicles. This paper proposes a method to estimate the state of charge of Lithium-ion batteries by the <span lang="EN-US">variable</span> forgetting factor recursive least square (VFFRLS) – unscented Kalman filter (UKF) algorithm in real-time without the off-line battery testing data. Since the state observation requires an accurate model, an equivalent circuit model was constructed. Then, the VFFRLS algorithm is used to identify online the battery model parameters based on voltage and current measurements. An advantage of this algorithm is that it requires less initial information and shorter identification time than offline parameter identification. After the model parameters are well identified, the unscented Kalman filter estimates the state of charge and minimizes noise characteristics and uncertainty in the parameter identification process. The VFFRLS algorithm applied in this paper has shown a good result with the model output error of less than 1%, and the identification achieves real-time response. The state of charge obtained by the UKF algorithm has shown satisfactory estimation results with fast convergence speed and small errors. The UKF filter provides the results with a 1.5% error from the reference and converges after 10 cycles.

Model-free Predictive Trajectory Tracking Control and Obstacle Avoidance for Unmanned Surface Vehicle With Uncertainty and Unknown Disturbances via Model-free Extended State Observer

Model-free Predictive Trajectory Tracking Control and Obstacle Avoidance for Unmanned Surface Vehicle With Uncertainty and Unknown Disturbances via Model-free Extended State Observer

Hadronization of heavy quarks

Heavy-flavor hadrons produced in ultrarelativistic heavy-ion collisions are a sensitive probe for studying hadronization mechanisms of the quark-gluon-plasma. In this paper, we survey how different transport models for the simulation of heavy-quark diffusion through a quark-gluon plasma in heavy-ion collisions implement hadronization and how this affects final state observables. Utilizing the same input charm-quark distribution in all models at the hadronization transition, we find that the transverse-momentum dependence of the nuclear modification factor of various charm hadron species has significant sensitivity to the hadronization scheme. In addition, the charm-hadron elliptic flow exhibits a nontrivial dependence on the elliptic flow of the hadronizing partonic medium. Published by the American Physical Society 2024

Some Results on the Properties of Discrete-Time LTI State-Space Systems

Abstract This work brings forward several interesting facts about system properties of LTI discrete-time systems like output controllability, state controllability and state observability, trackability and input and state observability. Particularly, the work brings about the inter-relationships between these properties while taking a state-space formulation based approach to come up with simple facts that are backed up by proofs using preliminary linear algebra.

Neural adaptive dynamic surface control for position tracking of electrohydraulic servo systems based on extended state observer

High-performance motion tracking of electro-hydraulic servo systems plays an important role in developing industrial technology. However, the system itself has parameter uncertainty, uncertain nonlinearity, and measurement noise, significantly decreasing the performance of conventional controllers designed based on nominal models. To improve the tracking performance of electro-hydraulic servo systems, an adaptive dynamic surface control method combining extended state observer and radial basis function neural network is proposed. Firstly, an extended state observer combining neural network output and parameter adaptation technology is designed without the need for speed and pressure feedback to observe the system’s unknown state variables and nonlinear matched disturbance. The design of neural networks is used to approximate mismatched disturbance with significant nonlinearity online. Then, the proposed extended state observer is introduced into the neural adaptive backstepping design, effectively compensating for simultaneous matched and mismatched disturbances, thereby suppressing most of the uncertain nonlinearity of the system. Meanwhile, online update of uncertain parameters further improves the tracking performance of the controller. In addition, the introduction of dynamic surface overcomes the “explosion of complexity” issue in backstepping design. The rigorous stability of the closed-loop system is proved by the Lyapunov stability theory. Finally, the effectiveness of the proposed controller is validated through comparative experiments on valve-controlled hydraulic cylinder.

Systematic Control Design for Adaptive Rejection of Narrow-Band Disturbances Based on a Novel Resonant Generalized Extended State Observer

In this paper, the adaptive rejection of multiple narrow-band disturbances with time-varying frequencies is investigated. A systematic control approach based on a resonant generalized extended state observer (RGESO) is proposed. The frequency response of the RGESO is shaped into a desired form to reject the total disturbance, including the wide-band uncertainties and the narrow-band disturbances. The state-space realization of the RGESO is also provided to estimate both the states and the total disturbance. To handle the time-varying frequencies of the narrow-band disturbances, a direct frequency estimation approach based on the Levenberg–Marquardt method and an online supervision strategy is presented to improve convergence and reliability, and the estimations are then used to adapt the RGESO parameters. Parameter tuning and stability robustness analysis methods are also developed for the proposed scheme to facilitate its application. Finally, extensive simulations are conducted to demonstrate the effectiveness of our method.

Asymptotic adaptive output-feedback stabilisation of nonlinear systems with unknown growth rate and sensor uncertainty

For a class of nonlinear systems with sensor uncertainty, the problem of adaptive output feedback stabilisation is investigated in this paper. It is assumed that only the output is available for feedback control, which suffers from sensor uncertainty. At the same time, the nonlinear function in the system model has an unknown growth rate. To solve this problem, a set of state observers is designed to estimate the unknown system states based on the uncertain output, and an adaptive output-feedback control is designed based on this. By using the corollary of Barbalet's Lemma, it is shown that the equilibrium of the closed-loop system is asymptotically stable. Finally, simulation results verify the effectiveness of the control scheme

GESO based RISE Controller for Active Flutter Suppression for Aeroelastic System

Abstract The paper presents a Robust Integral of Signum of Error (RISE) controller for active suppression of flutter of a two dimensional aerofoil and it is integrated with a General Extended State Observer (GESO). Towards this, aerofoil model in state space is first changed into a canonical form. Then, the controller is designed using RISE control technique. As equations of system dynamics are not into integral chain form, a GESO is formulated to observe system states and disturbances. The controller is implemented using estimated states and it is robustified using estimated disturbance. Stability of the proposed GESO-RISE controller is established using the Lyapunov theory. Simulations are performed to check the proposed controller's performance against variations in airspeed, uncertainties in model parameters, external disturbances, time delay and unmodeled dynamics. Comparison of the proposed GESO-RISE controller is carried out with existing controllers using two performance criteria i.e. Control Efforts and Integral of Absolute Error (IAE). It is discovered from simulations that the proposed GESO-RISE controller significantly reduces IAE and control efforts. Additionally, Monte Carlo method is utilized to check robustness of the proposed GESO-RISE controller. The proposed GESO-RISE controller significantly enhances flutter boundary of aerofoil and is completely implementable.

Data-driven estimation of the algebraic Riccati equation for the discrete-time inverse linear quadratic regulator problem

In this paper, we propose a method for estimating the algebraic Riccati equation (ARE) with respect to an unknown discrete-time system from the system state and input observation. The inverse optimal control (IOC) problem asks, “What objective function is optimized by a given control system?” The inverse linear quadratic regulator (ILQR) problem is an IOC problem that assumes a linear system and quadratic objective function. The ILQR problem can be solved by solving a linear matrix inequality that contains the ARE. However, the system model is required to obtain the ARE, and it is often unknown in fields in which the IOC problem occurs, for example, biological system analysis. Our method directly estimates the ARE from the observation data without identifying the system. This feature enables us to economize the observation data using prior information about the objective function. We provide a data condition that is sufficient for our method to estimate the ARE. We conducted a numerical experiment to demonstrate that our method can estimate the ARE with less data than system identification if the prior information is sufficient.

Distributed finite-time adaptive consensus output-feedback control of multi-agent systems under switching topologies

The paper investigates the finite-time adaptive consensus control of nonlinear multi-agent systems (MASs) by output-feedback. During the process of control design, the fuzzy logic system (FLS) is employed to approximate nonlinear function, as well as constructing a fuzzy state observer to estimate unmeasured states. Combining the dynamic surface control (DSC) with adaptive backstepping method conquers the complexity explosion issue. Then, semi-global practical finite-time stability (SGPFS) for closed-loop system is obtained under arbitrary switching communication topologies. All the signals of the overall system are uniformly ultimately bounded (UUB). Finally, the availability of developed control approach will be demonstrated through a simulation.

Training task planning-based adaptive assist-as-needed control for upper limb exoskeleton using neural network state observer

Training task planning-based adaptive assist-as-needed control for upper limb exoskeleton using neural network state observer

Adaptive output feedback stabilisation control for cascaded systems with output constraints and disturbance

The system under consideration is a cascaded system composed of integral input-to-state stable inverse dynamics and a non-holonomic system. An adaptive output feedback stabilisation control is proposed for the system with disturbance and output constraints. The dynamic uncertainty is eliminated using the technique that changes the supply rate. An extended state observer is proposed by defining the non-vanishing disturbance as a new state variable of the system. The asymmetric time-varying output constraint is solved by utilising the tan-type barrier Lyapunov function. The result shows that the adaptive output feedback controller guarantees the stability of the closed-loop system without violating the asymmetric time-varying output constraints under the backstepping technique. Simulation results are given to verify the effectiveness of the control method.

Prescribed Performance Fault-Tolerant Attitude Tracking Control for UAV with Actuator Faults

This paper proposes a prescribed performance fault-tolerant control based on a fixed-time extended state observer (FXTESO) for a carrier-based unmanned aerial vehicle (UAV). First, the attitude motion model of the UAV is introduced. Secondly, the proposed FXTESO is designed to estimate the total disturbances including coupling, actuator faults and external disturbances. By using the barrier Lyapunov function (BLF), it is proved that under prescribed performance control (PPC), the attitude tracking error is stable within the prescribed range. The simulation results for tracking the desired attitude angle show that the average overshoot and stabilization time of PPC-FXTESO is 0.00455rad and 6.2s. Comparatively, the average overshoots of BSC-ESO and BSC-FTESO are 0.035rad and 0.027rad, with stabilization times of 14.97s and 12.56s, respectively. Therefore, the control scheme proposed in this paper outperforms other control schemes.

Sliding mode active disturbance rejection control for manipulator considering actuator saturation

<p style="text-align: justify;">Considering the issue of low control accuracy in joint trajectory tracking control for manipulator systems with actuator saturation due to external disturbances, modelling inaccuracies, and joint friction, a sliding mode active disturbance rejection control approach was proposed. An improved extended state observer is employed to observe and estimate the lumped disturbances affecting the system, providing feedback compensation. A variable gain reaching law is devised, coupled with a fast non-singular terminal sliding mode to design the system control law, which mitigates chattering inherent and ensuring precision control. Additionally, a novel output error compensation-based anti-windup scheme is introduced to compensate for the detrimental impacts caused by actuator saturation. Simulation results collectively demonstrate that the proposed tracking control algorithm exhibits better control performance and robustness against disturbances.</p>

Characteristic analysis and mitigation strategy for SSCI in series-compensated DFIG-based wind farm controlled by a virtual synchronous generator.

The proliferation of virtual synchronous generator (VSG) technology within series-compensated double-fed induction generator (DFIG)-based wind farms is substantially hampered by the attendant risk of subsynchronous control interaction (SSCI), resulting in a significant research deficiency on systematic control interaction analysis and the development of mitigation strategies. The paper proposes an advanced active disturbance rejection control (ADRC) framework, incorporating real-time compensation mechanisms to mitigate the inadequate suppression efficacy attributable to the VSG's diminished output impedance. Initially, the mathematical expression for the VSG output impedance is rigorously deduced, and the positive damping attributes of the VSG in relation to SSCI are elucidated from the perspective of underlying mechanistic principles. Subsequently, the suppressive mechanism of SSCI by the ADRC is revealed in the context of VSG involvement, and the consequent augmentation of SSCI attributed to PI control is systematically derived. In immediate succession, the quanta of oscillation and inductive cross-coupling are encapsulated as the system's aggregate disturbance, thereby streamlining the ADRC to its primary order configuration, permitting the utilization of an extended state observer (ESO) for the dynamic estimation of said disturbance. Furthermore, a fractional-order filter function is instituted to engineer an augmented ESO, which refines the output voltage of the grid-side converter. Concurrently, a meticulous discourse on the rectification strategy for the proposed ESO parameters and its stability ensues. Ultimately, the efficacy of the mechanism analysis, alongside the robustness of the proffered control strategy for SSCI mitigation under diverse perturbation conditions, is corroborated via impedance evaluation and time-domain simulation.

Research on improved active disturbance rejection control strategy for hydraulic-driven Stewart stabilization platform

Purpose In response to the severe lag in tracking the response of the Stewart stability platform after adding overload, as well as the impact of nonlinear factors such as load and friction on stability accuracy, a new error attenuation function and a parallel stable platform active disturbance rejection control (ADRC) strategy combining cascade extended state observer (ESO) are proposed. Design/methodology/approach First, through kinematic modeling of the Stewart platform, the relationship between the desired pose and the control quantities of the six hydraulic cylinders is obtained. Then, a linear nonlinear disturbance observer was established to observe noise and load, to enhance the system’s anti-interference ability. Finally, verification was conducted through simulation. Findings Finally, stability analysis was conducted on the cascaded observer. Experiments were carried out on a parallel stable platform with six degrees of freedom involving rotation and translation. In comparison to traditional PID and ADRC control methods, the proposed control strategy not only endows the stable platform with strong antiload disturbance capability but also exhibits faster response speed and higher stability accuracy. Originality/value A new error attenuation function is designed to address the lack of smoothness at d in the error attenuation function of the ADRC controller, reducing the system ripple caused by it. Finally, a combination of linear and nonlinear ESOs is introduced to enhance the system's response speed and its ability to observe noise and load disturbances. Stability analysis of the cascade observer is carried out, and experiments are conducted on a six-degree-of-freedom parallel stable platform with both rotational and translational motion.

Robust sliding-mode observer for unbounded state nonlinear systems

Designing a full-state observer for nonlinear systems has always been accompanied by challenges and restrictive constraints. Mainly, applying a state observer in nonlinear systems with non-minimum phase characteristics is more challenging when the limiting constraints are not satisfied due to diverging internal dynamics. In this paper, a robust sliding-mode observer approach has been successfully employed to estimate the states of nonlinear systems with unbounded and diverging dynamics. The design principles of this observer are based on applying a classifying algorithm in single-input single-output and multiple-input multiple-output nonlinear systems. It is noteworthy that this observer is highly robust against disturbance, uncertainty and measurement noise, and its conditions are less conservative compared to previous nonlinear sliding-mode observers. One novel feature of the proposed observer is that while the system's state gets unbounded and diverged in fault-occurring scenarios or critical circumstances, this observer retains accuracy. The efficiency of the proposed observer is verified in the simulation results for two nonlinear industrial systems, including a hydro-turbine power generation plant and a continuous stirred tank reactor.

Disturbance Rejection Control of Grid-Forming Inverter for Line Impedance Parameter Perturbation in Weak Power Grid

When a grid-forming (GFM) inverter is connected to a low- or medium-voltage weak power grid, the line impedance with resistive and inductive characteristics will cause power coupling. Typical GFM decoupling control strategies are designed under nominal line impedance parameters. However, there are deviations between the nominal line impedance and actual parameters, resulting in poor decoupling effects. Aiming at this problem, this paper proposes a power decoupling strategy based on a reduced-order extended state observer (RESO). Firstly, the power dynamic model of the GFM is established based on the dynamic phasor method. Then, the model deviation and power coupling due to line impedance parameter perturbation are estimated as internal disturbances of the system, and the disturbances are compensated on the basis of typical power control strategy and virtual impedance decoupling. Good decoupling performance is obtained under different impedance parameters, improving the control strategy’s robustness. Finally, the effectiveness of the proposed method is verified by the results of RT Box hardware-in-the-loop experiments.