High-order Systems Research Articles

Rotorcraft Flight Control Design for Rotor Noise Abatement

This article presents the development and implementation of active noise abatement flight control laws utilizing redundant control allocation in rotorcraft. The study starts by finding a periodic equilibrium of coupled rotorcraft flight dynamics and acoustics using a modified harmonic balance trim solution method. Next, the rotorcraft nonlinear time-periodic dynamics are linearized about its periodic equilibrium and transformed into an equivalent higher-order linear time-invariant system in harmonic decomposition form. Composite aeroacoustic measures are formulated as outputs of this system. To enable faster runtime and tractable control design, a reduced 8‐state model representative of the coupled rigid‐body dynamics and acoustics is obtained through residualization. An explicit model following control law with pseudoinverse allocation to redundant control surfaces–an active horizontal stabilizer in this study–is synthesized using the 8‐state model. The article further assesses the impact of noise alleviation control on handling qualities of conventional and compound rotorcraft in forward flight. The results demonstrate that redundant control allocation is an effective method for active reduction of unsteady rotor noise, with increasing effectiveness during aggressive maneuvers. Future-generation rotorcraft, particularly future vertical lift configurations featuring high control redundancy and aggressive maneuvering capabilities, can significantly benefit from noise abatement through redundant control allocation. Furthermore, the article highlights that while implementing noise abatement control in conventional helicopters can degrade handling qualities, the use of redundant control allocation in compound configurations offers noise reduction without compromising handling qualities.

A novel dynamic finite-time prescribed performance control strategy with constraint and robustness

This paper is devoted to the design of adaptive nonlinear prescribed performance controllers for balancing constraint and robustness. Firstly, a shift function is introduced to enhance robustness in the initial stage. Secondly, a new finite-time performance function and a regulation of dynamic adjustments are developed for the first time. Due to the regulation, it can be prevented by the proposed scheme that tracking errors approach or exceed performance boundaries during operation, which ensures both robustness and constraint, and the performance function is differentiable of order n, which can be used in backstepping design for higher-order systems without approximators. Finally, the designed controller is more robust in both transient and stable states, whose effectiveness and superiority are validated by stability analysis, matlab simulation, and an actual test on a real robotic arm.

A Semi-Global Finite-Time Decentralized Control Method for High-Order Large-Scale Nonlinear Systems

This study focuses on the decentralized stabilization issue of high-order large-scale nonlinear systems with unknown disturbances. A novel decentralized semi-global finite-time control approach is suggested by constructing a Lyapunov function with both quadratic and higher-order components and employing the method of homogeneous domination. Based on the designed Lyapunov function, a state-feedback controller is constructed for the nominal system. Subsequently, the scaling gain is flexibly introduced to enable semi-globally finite-time stabilization of the nonlinear system. Besides, the approach is extended to the problem of decentralized tracking control of high-order large-scale nonlinear systems. Finally, numerical and practical examples validate the effectiveness of the presented control strategy.

High-order allpass cascade-connected phase-system design utilizing fractional polynomial errors

ABSTRACT This paper proposes a nonlinear optimization method for designing a high-order recursive allpass digital phase system that comprises several cascade-connected second-order (SO) allpass sections. This method first splits a given phase design specification (approximation target) into a set of equal sub-specifications, and then the equal sub-specification acts as the ideal phase for each of the SO sections. Since an SO section can be designed via employing a linear programming to minimize a linear fractional error function, this splitting process generates an excellent starting point (good initial values for the coefficients of the cascaded SO sections) for further minimizing the overall approximation error. This paper first derives a wide variety of fractional polynomial error functions for designing cascade-connected allpass phase systems of different high orders, and then shows that a high-order cascade-connected allpass phase system can be designed by utilizing a nonlinear solver to minimize the peak deviation of such a fractional polynomial error. Using the derived fractional polynomial error functions in the system design enables the system designer to find an excellent starting point for further minimizing the approximation error and thus reach a convergent design solution. This paper first derives a set of fractional polynomial errors, and then adopts the eighth-order cascade-connected phase system design to exemplify the effectiveness of the fractional-polynomial-error-based design tactic. Furthermore, the stability of the cascade-connected high-order allpass system can be readily checked via confirming that all of the cascaded SO sections have their poles inside the unit circle in the complex plane.

Reconfigurations of cortical manifold structure during reward-based motor learning

Adaptive motor behavior depends on the coordinated activity of multiple neural systems distributed across the brain. While the role of sensorimotor cortex in motor learning has been well established, how higher-order brain systems interact with sensorimotor cortex to guide learning is less well understood. Using functional MRI, we examined human brain activity during a reward-based motor task where subjects learned to shape their hand trajectories through reinforcement feedback. We projected patterns of cortical and striatal functional connectivity onto a low-dimensional manifold space and examined how regions expanded and contracted along the manifold during learning. During early learning, we found that several sensorimotor areas in the dorsal attention network exhibited increased covariance with areas of the salience/ventral attention network and reduced covariance with areas of the default mode network (DMN). During late learning, these effects reversed, with sensorimotor areas now exhibiting increased covariance with DMN areas. However, areas in posteromedial cortex showed the opposite pattern across learning phases, with its connectivity suggesting a role in coordinating activity across different networks over time. Our results establish the neural changes that support reward-based motor learning and identify distinct transitions in the functional coupling of sensorimotor to transmodal cortex when adapting behavior.

Reconfigurations of cortical manifold structure during reward-based motor learning

Adaptive motor behavior depends on the coordinated activity of multiple neural systems distributed across the brain. While the role of sensorimotor cortex in motor learning has been well established, how higher-order brain systems interact with sensorimotor cortex to guide learning is less well understood. Using functional MRI, we examined human brain activity during a reward-based motor task where subjects learned to shape their hand trajectories through reinforcement feedback. We projected patterns of cortical and striatal functional connectivity onto a low-dimensional manifold space and examined how regions expanded and contracted along the manifold during learning. During early learning, we found that several sensorimotor areas in the dorsal attention network exhibited increased covariance with areas of the salience/ventral attention network and reduced covariance with areas of the default mode network (DMN). During late learning, these effects reversed, with sensorimotor areas now exhibiting increased covariance with DMN areas. However, areas in posteromedial cortex showed the opposite pattern across learning phases, with its connectivity suggesting a role in coordinating activity across different networks over time. Our results establish the neural changes that support reward-based motor learning and identify distinct transitions in the functional coupling of sensorimotor to transmodal cortex when adapting behavior.

Theoretical analysis of higher-order system of difference equations with generalized balancing numbers

Theoretical analysis of higher-order system of difference equations with generalized balancing numbers

Kinematic Parameter Identification and Error Compensation of Industrial Robots Based on Unscented Kalman Filter with Adaptive Process Noise Covariance

Kinematic calibration plays a pivotal role in enhancing the absolute positioning accuracy of industrial robots, with parameter identification and error compensation constituting its core components. While the conventional parameter identification method, based on linearization, has shown promise, it suffers from the loss of high-order system information. To address this issue, we propose an unscented Kalman filter (UKF) with adaptive process noise covariance for robot kinematic parameter identification. The kinematic model of a typical 6-degree-of-freedom industrial robot is established. The UKF is introduced to identify the unknown constant parameters within this model. To mitigate the reliance of the UKF on the process noise covariance, an adaptive process noise covariance strategy is proposed to adjust and correct this covariance. The effectiveness of the proposed algorithm is then demonstrated through identification and error compensation experiments for the industrial robot. Results indicate its superior stability and accuracy across various initial conditions. Compared to the conventional UKF algorithm, the proposed approach enhances the robot’s accuracy stability by 25% under differing initial conditions. Moreover, compared to alternative methods such as the extended Kalman algorithm, particle swarm optimization algorithm, and grey wolf algorithm, the proposed approach yields average improvements of 4.13%, 26.47%, and 41.59%, respectively.

Event-triggered prescribed-time control for a class of uncertain nonlinear systems using finite time-varying gain

This paper addresses the event-triggered prescribed-time control problem for a class of high-order nonlinear systems based on finite time-varying gain. Due to the existence of unknown gain functions and system uncertainties, the resultant control with prescribed-time convergence performance becomes nontrivial. The problem becomes even more complex due to the use of event-based communication instead of continuous communication. To tackle the aforementioned challenges, this paper proposes an event-triggered prescribed-time stabilization approach with the following key steps. Firstly, we establish a new prescribed-time stability lemma to overcome the technical difficulty arising from the prescribed-time controller design, and stability analysis. Secondly, we give the controller design procedure upon using the backstepping technique. Thirdly, we redesign the event-triggering threshold condition based on time-varying functions, which allows the controller terminal jitter to be mitigated and the controller to be implemented straightforwardly in practice. Furthermore, the proposed control scheme avoids Zeno behavior. The numerical simulation confirms the effectiveness of the proposed control scheme.

Composite predictive trajectory control of HS-PMSM with LCL filter for hydrogen electric vehicle at low fuel condition

Limitations in current fuel cell technology lead to instability in output voltage for hydrogen fuel cells, particularly under the influence of temperature variations and fuel flow fluctuations, thereby affecting the normal operation of hydrogen-powered vehicles. Improving the motor drive control system and optimizing energy management are crucial for enhancing overall vehicle performance. To improve dynamic response speed while suppressing harmonics, this paper proposes a predictive control strategy for high-speed permanent magnet synchronous motors with LCL filter in hydrogen fuel cell electric vehicles. The proposed control strategy suppresses high-frequency current harmonics by sampling only the current on the motor side, enabling fast predictive control of the high-order system motor-side current. Additionally, to mitigate the issue of unstable torque output of the electric motor at low fuel levels, this paper proposes a new composite predictive torque trajectory control strategy based on the previous control strategy. This strategy ensures rapid and accurate tracking of motor output torque, particularly during decreases in fuel cell output voltage. Experimental results validate the feasibility and effectiveness of the proposed control strategies in this paper.

High-Capacity Coherent WDM Networks Empowered by Probabilistic Shaping and End-to-End Deep Learning

To optimize the functionality of coherent optical fiber communication (OFC) systems and enhance their capacity related to long-haul transmissions, wavelength-division multiplexing (WDM) and probabilistic constellation shaping (PCS) techniques have been used. This paper develops an end-to-end (E2E) deep learning (DL)-based PCS algorithm, i.e., autoencoder (AE) for a high-order modulation format WDM system that minimizes nonlinear effects while ensuring high capacity and considers system parameters, in particular those related to the OFC channel. Only the AE of the central channel is trained to meet the specified performance objective, as the system design employs identical AEs in each WDM channel. The simulation results show that the architecture should consist of two hidden layers, with thirty two nodes per hidden layer and a ”32×modulation order” batch size to obtain optimal system performance, when designing AE using a dense layer neural network. The behavior of the AE is examined to determine the optimum launch-power ranges that enhance the system's performance. The developed AE-based PCS-WDM provides a 0.4 shaping gain and outperforms conventional solutions.

Discrete-Time Impedance Control for Dynamic Response Regulation of Parallel Soft Robots.

Accurately controlling the dynamic response and suppression of undesirable dynamics such as overshoots and vibrations is a vital requirement for soft robots operating in industrial environments. Pneumatically actuated soft robots usually undergo large overshoots and significant vibrations when deactuated because of their highly flexible bodies. These large vibrations not only decrease the reliability and accuracy of the soft robot but also introduce undesirable characteristics in the system. For example, it increases the settling time and damages the body of the soft robot, compromising its structural integrity. The dynamic behavior of the soft robots on deactuation needs to be accurately controlled to increase their utility in real-world applications. The literature on pneumatic soft robots still does not sufficiently address the issue of suppressing undesirable vibrations. To address this issue, we propose the use of impedance control to regulate the dynamic response of pneumatic soft robots since the superiority of impedance control is already established for rigid robots. The soft robots are highly nonlinear systems; therefore, we formulated a nonlinear discrete sliding mode impedance controller to control the pneumatic soft robots. The formulation of the controller in discrete-time allows efficient implementation for a high-order system model without the need for state-observers. The simplification and efficiency of the proposed controller enable fast implementation of an embedded system. Unlike other works on pneumatic soft robots, the proposed controller does not require manual tuning of the controller parameters and automatically calculates the parameters based on the impedance value. To demonstrate the efficacy of the proposed controller, we used a 6-chambered parallel soft robot as an experimental platform. We presented the comparative results with an existing state-of-the-art controller in SMC control of pneumatic soft robots. The experiment results indicate that the proposed controller can effectively limit the amplitude of the undesirable vibrations.

Design of event-based sliding mode controller for high-order systems via a reduced-order method

Design of event-based sliding mode controller for high-order systems via a reduced-order method

Optimal control problem for higher-order non-instantaneous impulsive fractional system with non-local conditions

The purpose of this article is to study the optimal control problem of higher-order non-instantaneous impulsive fractional system with non-local conditions by virtue of cosine operator theory in the Hilbert space. Initially, the sufficient conditions for the existence of a mild solution of the proposed system are verified by applying the fixed point theorem in infinite dimensional space. Further, we formulate and prove the existence results for optimal control of the proposed system with the corresponding cost functional by using Balder's theorem. Finally, an example is provided to illustrate the main results.

Robust distributed Nash equilibrium seeking for high-order systems with disturbances and coupling constraints

The objective of this article is to tackle the problem of distributed searching for generalized Nash equilibrium (GNE) for high-order multi-agent systems (MASs) that are subject to external disturbances and coupling constraints. To address disturbances and linear equality constraints while ensuring that high-order agents achieve the task of seeking a GNE, a novel approach has been developed that utilizes gradient descent algorithms, extended state observers, and state feedback control. By utilizing the proposed algorithm, the agents' behavior will ultimately converge to a small range around the GNE points. The proposed algorithm's effectiveness is validated through two numerical simulations.

Fixed-time consensus control for uncertain heterogeneous multi-agent systems with high-order dynamics and time-varying delay under generic topologies

This article is concerned with the fixed-time control problem of uncertain high-order heterogeneous multi-agent systems with time-varying delays for both directed and undirected topologies. Applying the free-weighting matrix approach, a sliding mode controller is designed through the Lyapunov–Krasovskii functional and the conditions are derived with the help of linear matrix inequalities to attain fixed-time consensus tracking control of such systems. Two numerical simulations are included to verify the capability of the derived control law with respect to different initializations.

A state feedback control with compensation for permanent magnet synchronous machine drives

Using the linear approach to design a controller is still prevalent. The state feedback control (SFC) is applied in this paper to improve the dynamic response of permanent magnet synchronous machine (PMSM) speed regulation systems. First, a third-order augmented system is constructed for the reason that a higher-order system has better disturbance rejection. It can be found through analysis and comparison that the order of the proposed speed controller is increased. The parameters of SFC are selected by utilizing the linear quadratic regulator (LQR), and the influence of matrix Q on dynamic performance is detailed through the Bode diagram. Additionally, considering parametric uncertainties and unmodeled dynamics, a disturbance observer (DOB) using the Luenberger observer is designed to further boost anti-disturbance performance. Finally, plenty of experimental results verify the effectiveness of the proposed methods.

Identification and Control of Flexible Joint Robots Based on a Composite-Learning Optimal Bounded Ellipsoid Algorithm and Prescribe Performance Control Technique

This paper presents an indirect adaptive neural network (NN) control algorithm tailored for flexible joint robots (FJRs), aimed at achieving desired transient and steady-state performance. To simplify the controller design process, the original higher-order system is decomposed into two lower-order subsystems using the singular perturbation technique (SPT). NNs are then employed to reconstruct the aggregated uncertainties. An adaptive prescribed performance control (PPC) strategy and a continuous terminal sliding mode control strategy are introduced for the reduced slow subsystem and fast subsystem, respectively, to guarantee a specified convergence speed and steady-state accuracy for the closed-loop system. Additionally, a composite-learning optimal bounded ellipsoid algorithm (OBE)-based identification scheme is proposed to update the NN weights, where the tracking errors of the reduced slow and fast subsystems are integrated into the learning algorithm to enhance the identification and tracking performance. The stability of the closed-loop system is rigorously established using the Lyapunov approach. Simulations demonstrate the effectiveness of the proposed identification and control schemes.

Using Affine Arithmetic to Design a Controller for Large Uncertain System

This study presents a approach for creating the supervisor of expansive uncertain systems. The Controller for a particular high order system is designed using a reduced order model. The numerator and denominator polynomial in the suggested reduction approach is derived using modified polynomial differential method. A lower order model with least ISE optimization is obtained. Assuming that the initial high-order system is stable, the proposed approach guarantees the stability of the streamlined model. Through With reference to the original high-order systems, a PID controller is created for the suggested low-order model. In order to explain the method's efficiency, a few numerical examples were taken into consideration. It has been demonstrated that applying Control from the lower order model to the higher order system is improved and the controlled system's performance. Common numerical illustrations seen in the literature have been used to test the method, and the results show that it works satisfactorily.

Scaled Position Consensus of High-Order Uncertain Multiagent Systems Over Switching Directed Graphs.

We investigate the scaled position consensus of high-order multiagent systems with parametric uncertainties over switching directed graphs, where the agents' position states reach a consensus value with different scales. The intricacy arises from the asymmetry inherent in information interaction. Achieving scaled position consensus in high-order multiagent systems over directed graphs remains a significant challenge, particularly when confronted with the following complex features: 1) uniformly jointly connected switching directed graphs; 2) complex agent dynamics with unknown inertias, unknown control directions, parametric uncertainties, and external disturbances; 3) interacting with each other via only relative scaled position information (without high-order derivatives of relative position); and 4) fully distributed in terms of no shared gains and no global gain dependency. To address these challenges, we propose a distributed adaptive algorithm based on a acrlong MRACon scheme, where a linear high-order reference model is designed for every individual agent employing relative scaled position information as input. A new transformation is proposed which converts the scaled position consensus of high-order linear reference models to that of first-order ones. Theoretical analysis is presented where agents' positions achieve the scaled consensus over switching directed graphs. Numerical simulations are performed to validate the efficacy of our algorithm and some collective behaviors on traditional consensus, bipartite consensus, and cluster consensus are shown by precisely choosing the scales of the agents.