State Observer Design Research Articles

Adaptive fuzzy optimal output-feedback fault-tolerant control for the USV system with intermittent actuator faults

This paper presents a novel fuzzy optimal output-feedback fault-tolerant control (FTC) method for uncertain nonlinear unmanned surface vehicle (USV) systems, which are subject to intermittent actuator failures and unmeasured states. The proposed optimal controller is composed of a fuzzy feedforward fault-tolerant output-feedback controller and a fuzzy error feedback optimal controller. The fuzzy feedforward fault-tolerant output-feedback controller is designed by using the fuzzy state observer and backstepping control design technique. The fuzzy optimal feedback controller is given by adopting adaptive dynamic programming (ADP) theory. It is proven that the presented fuzzy optimal FTC scheme is able to ensure that the USV system is uniformly ultimately bounded (UUB), and the optimal control performance is achieved. The validity is confirmed by computer simulation results.

Application of an Improved State Feedback Control in the Selective Catalytic Reduction Denitrification Systems of Coal Power Units Under Variable Load Conditions

Selective catalytic reduction (SCR) flue gas denitrification systems are inherently complex, typically embodying characteristics of non-linearity, significant time delays, and susceptibility to multiple disturbances. In the context of coal power units engaging in deep load cycling and rapid frequency adjustment, conventional proportional-integral-derivative (PID) control struggles to meet the demands of effective control. This study introduces a control strategy that incorporates a “state observer + Linear Quadratic Regulator (LQR) state feedback + Improved Quantum Genetic Algorithm (IQGA) optimized PID”. Initially, local linear mathematical models of an SCR denitrification system at 340 MW, 450 MW, and 540 MW loads were used to design state observer and LQR state feedback control parameters for each operational condition. At a single load point, the IQGA was employed to optimize the outer loop PID parameters, followed by simulation experiments of load increases and decreases between 340 MW and 540 MW. The results demonstrated that, compared to two other strategies, the proposed approach reduced the overshoot by a minimum of 1.5% and shortened the adjustment time by 31.7% under conditions of step disturbances and internal perturbations. Throughout variable operational conditions, the strategy consistently exhibited minimal output fluctuations, rapid adjustment capabilities, strong disturbance rejection, and robust stability. This algorithm proves to be an effective method for controlling NOx concentrations, offering insights for precise ammonia injection control in future applications.

Constrained solutions of generalized coupled discrete-time periodic matrix equations with application in state observer design for linear periodic systems

PurposeIt is desired to provide a diversified iterative scheme for solving the constrained solutions of the generalized coupled discrete-time periodic (GCDTP) matrix equations from the perspective of optimization.Design/methodology/approachThe paper considers generalized reflexive solutions of the GCDTP matrix equations by applying the Jacobi gradient-based iterative (JGI) algorithm, which is an extended variant of the gradient-based iterative (GI) algorithm.FindingsThrough numerical simulation, it is verified that the efficiency and accuracy of the JGI algorithm are better than some existing algorithms, such as the GI algorithm in Hajarian, the RGI algorithm in Sheng and the AGI algorithm in Xie and Ma.Originality/valueIt is the first instance in which the GCDTP matrix equations are solved applying the JGI algorithm.

Robust trajectory tracking for omnidirectional robots by means of anti-peaking linear active disturbance rejection

This article presents a Linear Active Disturbance Rejection scheme for the robust trajectory tracking control of an Omnidirectional robot, including an additional saturation element in the control design to improve the transient closed-loop response by including a saturation-input strategy in the Extended State Observer design, mitigating the possible arising peaking phenomenon. In addition, the controller is implemented in the kinematic model of the robotic system, assuming as the available information the position and orientation measurement and concerning the system structure, it is just known the order of the system and the control gain matrix as well. A wide set of laboratory experiments, including a comparison with a standard ADRC (i.e. without the proposed anti-peaking mechanism) and a PI-based control including an anti-peaking proposal, in the presence of different disturbance elements in the terrain of smooth and abrupt nature is carried out to formulate a comprehensive assessment of the proposal which validate the practical advantages of the proposal in robust trajectory tracking of the kind of robots.

On Observer and Controller Design for Nonlinear Hadamard Fractional-Order One-Sided Lipschitz Systems

This paper presents an extensive investigation into the state feedback stabilization, observer design, and observer-based controller design for a specific category of nonlinear Hadamard fractional-order systems. The research extends the conventional integer-order derivative to the Hadamard fractional-order derivative, offering a more universally applicable method for system analysis. Furthermore, the traditional Lipschitz condition is adapted to a one-sided Lipschitz condition, broadening the range of systems amenable to analysis using these techniques. The efficacy of the proposed theoretical findings is illustrated through several numerical examples. For instance, in Example 1, we select an order of derivative r = 0.8; in Example 2, r is set to 0.9; and in Example 3, r = 0.95. This study enhances the comprehension and regulation of nonlinear Hadamard fractional-order systems, setting the stage for future explorations in this domain.

LMI-based state observer design for supercavitating vehicles with time delay

Due to the existence of the planing force, the control of the supercavitating vehicle is difficult, and the vertical velocity which has a great influence on the planing force cannot be directly measured. Therefore, considering the time-delay effect of the planing force and the external disturbance, the state observer and controller based on linear matrix inequality (LMI) have been designed. By decomposing the planing force into two parts of time delay and non-time delay, and a longitudinal plane Linear Parameter Varying (LPV) time-delay model for supercavitating vehicles is derived. In addition, the controller and state observer for the supercavitating vehicle system with time-delay characteristics and external disturbances are simultaneously designed. The gains of the controller and observer are obtained by combining the theory of linear matrix inequalities and convex polytopes, ensuring the convergence of estimation error. At the same time, taking into account the possibility of exceeding the physical limits of the actuator when the input value is too large, the compensator has been added. Finally, the simulation results demonstrate that the designed controller exhibits good stability and tracking performance.

A Modified ADRC Scheme Based on Model Information for Maglev Train

During the operation of maglev trains, they are subjected to various disturbances. The presence of these disturbances presents a significant challenge for attaining high-performance control and even poses the risk of system instability. To further enhance the anti-disturbance capability of maglev trains, this paper proposes a model information-assisted modified active disturbance rejection control (MADRC) approach. A mathematical model of the single-point suspension system of maglev trains is constructed for the design of the extended state observer (ESO), which is a modified extended state observer (MESO), and a nonlinear mechanism is incorporated to boost the performance of the ESO. Owing to the introduction of model information, the estimated quantity of disturbances by MESO no longer considers the system model deviation as a disturbance. Hence, the linear feedback control law is modified accordingly. The MESO is regarded as an ESO with time-varying gain using the equivalent gain method, and its stability is proven using the Lyapunov method. The tracking and anti-disturbance performances of different controllers are compared via simulation experiments. Suspension and anti-disturbance experiments are conducted on the single-point suspension experimental platform, verifying that the proposed MADRC has a more potent suppression ability for load disturbances in the suspension system.

Unmanned Floating Object Transportation Applying Multiple Dynamic Positioning Tugboats: A Novel Cooperative Control Algorithm

Abstract To promote the automation and intelligence of marine floating object transportation, this paper proposes a cooperative consensus control algorithm for multiple unmanned dynamic positioning (DP) tugboats to transport an unactuated floating structure object using cables. The major concept of present algorithm is to implement a leader-follower formation strategy among distributed tugboats, with the aim of effectively maneuvering the object by adjusting the relative position between the virtual leader and the object in a reasonable manner. A cooperative consensus controller is integrated into the feedback controller of each tugboat local DP system in order to facilitate cooperative coordination among tugboats in a formation. A customized DP system, which incorporates the radial basis function neural network supervisor control into the DP controller design and introduces nonlinear disturbance observer into the low-frequency motion state observer design, is proposed to address cable tension disturbances, and thus, the tracking performance of the DP tugboat is improved. Full-scale nonlinear time domain simulations are performed under variable environmental conditions, verifying the effectiveness of the proposed automatic towing control scheme.

Research on Optimization of Nonlinear Extended State Observer for the Upper-Limb Rehabilitation Robot Controller

Background: In recent years, patents have shown that upper-limb rehabilitation robots play a significant role in home-based rehabilitation training for stroke hemiplegia patients. Changes in muscle tension during the flaccid paralysis phase cause the rehabilitation robot to deviate from the predetermined motion trajectory. This poses a challenge to the mathematical modeling of the rehabilitation robot and the design of the nonlinear extended state observer (NESO). Objective: To address the problem of trajectory tracking errors caused by the rehabilitation robot when the patient's muscle tension changes, a method based on optimizing the nonlinear function within the NESO is proposed. Methods: First, a mathematical model of the upper-limb rehabilitation robot is established to obtain the dynamic relationship between the robot's velocity and the input voltage. Second, the nonlinear function of NESO is optimized by adjusting the gain values of the sine and tangent functions to effectively estimate the muscle tension and reduce the problem of accumulative error due to changes in muscle tension. Finally, comparative simulations of trajectory tracking including the optimized nonlinear function as well as the sine, tangent and power functions are performed on the MATLAB platform. Results: NESO is constructed to estimate changes in muscle tension based on sine, tangent, and power functions, as well as optimized nonlinear functions. The equivalent gain values of each function and the muscle tension estimation curves of NESO are compared. The simulation results show that the equivalent gain value of the optimized nonlinear function acting in NESO is increased to more than 8 and the convergence time is reduced by 11.9% accordingly. This conclusion is validated by simulations and practical tests. Conclusion: The optimized nonlinear function shortens the estimation time of the NESO for changes in muscle tension, which can provide a reference value for the design of observers for upper-limb rehabilitation robots of patients in the flaccid paralysis stage.

Secure state estimation of networked switched systems under denial-of-service attacks

This paper studies the problem of secure state estimation of networked switched systems in the presence of denial-of-service (DoS) attacks, as well as disturbances and measurement noise. Firstly, a state transformation rule is designed to partition the original system into two subsystems, facilitating the design of discrete and continuous state observers. Secondly, by modifying the traditional super-twisting sliding-mode method and taking into account the frequency and duration characteristics of DoS attacks, we employ dynamic differential properties between different modes to design a switching law identification strategy. We show that this strategy can accurately estimate the switching state without imposing any requirement on the switching times and sequences. Thirdly, based on the identified activated mode, a set of mode-dependent continuous state sliding-mode observers is designed, that achieves continuous state estimation in finite time. The practicality and applicability of the developed results are validated through numerical simulations.

Event-Triggered State Observer Design for a Class of Nonlinear Time-Delay Fractional-Order Systems

Event-Triggered State Observer Design for a Class of Nonlinear Time-Delay Fractional-Order Systems

A class of adaptive predefined‐time extended state observers for high‐order strict‐feedback systems

AbstractFast state estimation for nonlinear systems has been a key issue in control theory and the recently developed predefined‐time stability acts as an effective tool for the problem. However, the studies of predefined‐time state observer for nonlinear systems are rare. In this article, we consider the predefined‐time extended state observer (PTESO) design for a class of high‐order strict‐feedback systems subject to Hölder continuous nonlinearities and lumped disturbance. By developing an adaptive mechanism and using time‐varying functions, a class of adaptive PTESOs is designed to estimate the unavailable states and the lumped disturbance, in which the convergence time can be tightly and explicitly preset by only one parameter, irrelevant to the initial conditions. The adaptive mechanism is used to improve the transient performance under wide‐range lumped disturbance. Moreover, thanks to the design of the time‐varying gains, the PTESO could realize fast observation with trivial peaking observation errors. Finally, simulation results are provided to illustrate the effectiveness of the proposed observer.

Double-Observer-Based Bumpless Transfer Control of Switched Positive Systems

This paper investigates the bumpless transfer control of linear switched positive systems based on state and disturbance observers. First, state and disturbance observers are designed for linear switched positive systems to estimate the state and the disturbance. By combining the designed state observer, the disturbance observer, and the output, a new controller is constructed for the systems. All gain matrices are described in the form of linear programming. By using co-positive Lyapunov functions, the positivity and stability of the closed-loop system can be ensured. In order to achieve the bumpless transfer property, some additional sufficient conditions are imposed on the control conditions. The novelties of this paper lie in that (i) a novel framework is presented for positive disturbance observer, (ii) double observers are constructed for linear switched positive systems, and (iii) a bumpless transfer controller is proposed in terms of linear programming. Finally, two examples are given to illustrate the effectiveness of the proposed results.

A Walking Trajectory Tracking Control Based on Uncertainties Estimation for a Drilling Robot for Rockburst Prevention

A walking trajectory tracking control approach for a walking electrohydraulic control system is developed to reduce the walking trajectory tracking deviation and enhance robustness. The model uncertainties are estimated by a designed state observer. A saturation function is used to attenuate sliding mode chattering in the designed sliding mode controller. Additionally, a walking trajectory tracking control strategy is proposed to improve the walking trajectory tracking performance in terms of response time, tracking precision, and robustness, including walking longitudinal and lateral trajectory tracking controllers. Finally, simulation and experimental results are employed to verify the trajectory tracking performance and observability of the model uncertainties. The results testify that the proposed approach is better than other comparative methods, and the longitudinal and lateral trajectory tracking average absolute errors are controlled in 10.23 mm and 22.34 mm, respectively, thereby improving the walking trajectory tracking performance of the walking electrohydraulic control system for the coal mine drilling robot for rockburst prevention.

Existence conditions for functional ODE observer design of descriptor systems revisited

This paper is devoted to the problem of designing functional observers for linear time-invariant (LTI) descriptor systems. The observers are realized by using state–space systems governed by ordinary differential equations (ODEs). Available existence results for functional ODE observers in the literature are extended by introducing new and milder sufficient conditions. These conditions are purely algebraic and provided directly in terms of the system coefficient matrices. The proposed observer has an order less than or equal to the dimension of the functional vector to be estimated. The observer parameter matrices are obtained by using simple matrix theory, and the design algorithm is illustrated by numerical examples.

Observer-based MPC for fuzzy cyber–physical system with hybrid attacks via a dynamic event-triggered mechanism

In this article, a secure model predictive control (MPC) algorithm is addressed for a nonlinear cyber–physical system (CPS) subject to hybrid attacks and parameter uncertainties via a dynamic event-triggered mechanism (DETM). The nonlinear CPS with parameter uncertainties is represented by the interval type-2 Takagi–Sugeno (IT2 T–S) fuzzy model. Considering that the full states of system are unmeasurable and aiming at decreasing the transmission burden, a DETM is proposed in the observer-based MPC scheme. Moreover, the hybrid attacks, including denial-of-service (DoS) attacks and deception attacks, are investigated in a unified framework due to the vulnerability of communication network. Furthermore, a secure MPC algorithm is presented, which consists of an off-line designed state observer and an on-line optimized MPC algorithm. Besides, by considering the internal dynamic variable in DETM, a new formula for updating estimation errors bounds is proposed to guarantee the feasibility of proposed algorithm. Finally, a practical example and comparative studies confirm the effectiveness of the proposed scheme.

Fully actuated system approach for spacecraft rendezvous system with actuator saturation

This paper explores the application of a fully actuated system (FAS) approach to a spacecraft rendezvous system with actuator saturation. A FAS model for the spacecraft rendezvous system is developed, followed by the design of an extended state observer (ESO) to estimate unmeasurable states and the system's nonlinear terms. The saturation issue is addressed using the convex hull method. By the designed ESO, a state feedback controller for the system is designed using the FAS approach, resulting in a constant linear closed-loop system whose eigenvalues can be arbitrarily assigned. This method simplifies the controller design process and provides a more accurate system model without the linearisation of nonlinear terms, thereby improving control accuracy. Simulation results show the effectiveness and usefulness of the proposed method.

Finite time fault estimation and fault‐tolerant control for a class of uncertain nonlinear systems based on cascaded observers

AbstractIn this paper, a finite time fault estimation and fault‐tolerant control method is proposed for a class of uncertain nonlinear systems that have both actuator faults and sensor faults. First, the outputs of the original system pass through the low‐pass filters to obtain the augmented states, and then an augmented system is composed of the states of the low‐pass filters and the original system, so as to realize the conversion of the sensor faults of the original system into partial actuator faults of the augmented system. Next, design state observers to reconstruct the unknown states of the augmented system, and develop extended state observers to estimate the actuator faults and disturbance of the augmented system. Again, the fault‐tolerant controllers are completed based on the backstepping control and the finite time control, and the finite time convergences of the designed observers and controllers are proved by theoretical analyses. Finally, based on a permanent magnet synchronous motor (PMSM) speed system, the simulation research and dSPACE simulated experiment research are conducted to verify the effectiveness of the proposed control method and its feasibility in the actual application.

Compliant-Control-Based Assisted Walking with Mobile Manipulator.

In this paper, a new approach involving the use of a mobile manipulator to assist humans with mobility impairments to walk is proposed. First, in order to achieve flexible interaction between humans and mobile manipulators, we propose a variable admittance controller that can adaptively regulate the virtual mass and damping parameters based on the interaction forces and the human motion intention predicted using the fuzzy theory. Moreover, a feedforward velocity compensator based on a designed state observer is proposed to decrease the inertia resistance of the manipulator, effectively enhancing the compliance of the human-robot interaction. Then, the configuration of the mobile manipulator is optimized based on a null-space approach by considering the singularity, force capacity, and deformation induced by gravity. Finally, the proposed assisted walking approach for the mobile manipulator is implemented using the human-robot interaction controller and the null-space controller. The validity of the proposed controllers and the feasibility of assisted human walking are verified by conducting a set of tests involving different human volunteers.

Target layer state estimation in multi-layer complex dynamical networks considering nonlinear node dynamics

In many engineering networks, only a part of target state variables are required to be estimated. On the other hand, multi-layer complex network exists widely in practical situations. In this paper, the state estimation of target state variables in multi-layer complex dynamical networks with nonlinear node dynamics is studied. A suitable functional state observer is constructed with the limited measurement. The parameters of the designed functional observer are obtained from the algebraic method and the stability of the functional observer is proven by the Lyapunov theorem. Some necessary conditions that need to be satisfied for the design of the functional state observer are obtained. Different from previous studies, in the multi-layer complex dynamical network with nonlinear node dynamics, the proposed method can estimate the state of target variables on some layers directly instead of estimating all the individual states. Thus, it can greatly reduce the placement of observers and computational cost. Numerical simulations with the three-layer complex dynamical network composed of three-dimensional nonlinear dynamical nodes are developed to verify the effectiveness of the method.