Error Dynamics Research Articles

Prescribed performance tracking control of multi-link robotic manipulator with uncertainties

<p style='text-indent:20px;'>This paper addresses the trajectory tracking problem with prescribed performance for a multi-link robotic manipulator subject to unknown dynamics and external disturbances. A predefined performance function is adopted to describe tracking errors' desired transient and steady-state performance. Then, the output error dynamics with performance constraints are transformed into an equivalent unconstrained system, whose stabilization is sufficient to guarantee the prescribed performance of the original system. An extended state observer with a friction model is designed to approximate unknown dynamics together with the unmeasurable velocity state, which extends the applicability of the proposed controller to manipulators with only position signals available. The friction model is lumped into it to improve the precision and velocity of estimation. It is proved via Lyapunov analysis that the proposed controller can theoretically guarantee the satisfaction of prescribed performance in the presence of uncertainties. The simulation results verify the reliability and effectiveness of the proposed method.</p>

Exploiting Equivariance in the Design of Tracking Controllers for Euler-Poincare Systems on Matrix Lie Groups

The trajectory tracking problem is a fundamental control task in the study of mechanical systems. Hamiltonian systems are posed on the cotangent bundle of configuration space of a mechanical system, however, symmetries for the full cotangent bundle are not commonly used in geometric control theory. In this paper, we propose a group structure on the cotangent bundle of a Lie group and leverage this to define momentum and configuration errors for trajectory tracking, drawing on recent work on equivariant observer design. We show that this error definition leads to error dynamics that are themselves “Euler-Poincare like” and use these to derive simple, almost global trajectory tracking control for fully-actuated Euler-Poincare systems on a Lie group state space.

A Receding-Horizon $\mathcal {H}_\infty$ Model-Free Control for Application to Robot Manipulators

Although robot manipulators are widely used in advanced industrial applications, their dynamics has very high complexity and uncertainties, making exact mathematical modeling difficult and preventing high-precision tracking control. Herein, we propose a practical high-performance model-free controller for robot manipulators that attenuates the undesirable side effects of a time-delayed state-based estimation (TDE) technique in terms of the receding-horizon <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_\infty$</tex-math></inline-formula> performance. By constructing tracking error dynamics with a sliding variable, the effects of TDE errors are identified and suppressed each time in terms of the fixed-horizon <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_\infty$</tex-math></inline-formula> performance. All initial states are shown to converge to a certain bounded set within a precomputed finite time. The proposed approach is beneficial for sudden transient responses and the temporarily unbounded TDE errors that cannot be handled by existing TDE-based controllers. Finally, the stability of the proposed controller is proven based on the comparison Lemma, and simulations and experiments show that its tracking performance and robustness are superior to those of conventional control algorithms.

Nonlinear Guidance Laws for Anti-tank Guided Missile to Intercept Maneuvering Tank Targets Using Optimal Error Dynamics and Relative Virtual Model

Nonlinear Guidance Laws for Anti-tank Guided Missile to Intercept Maneuvering Tank Targets Using Optimal Error Dynamics and Relative Virtual Model

Proportional Observer for the Nonlinear Parameter Varying Systems: A Matrix-Multiplier-based LMI Approach

This article delves into the design of a proportional observer scheme for a class of Nonlinear Parameter-Varying (NLPV) systems. The objective is to formulate a less conservative Linear Matrix Inequality (LMI) condition than the existing ones, ensuring the exponential stability of the error dynamics in the proposed observer. Through the incorporation of the reformulated Lipschitz property, Young's inequalities and a generalized matrix multiplier, two new LMI conditions are established. Due to the judicious use of these mathematical tools, the obtained LMI conditions contain a larger number of decision variables. As a result, these LMIs have enhanced feasibility than the one presented in the literature. The effectiveness of the newly designed LMI-based proportional observer is highlighted through a numerical example.

Neuroadaptive Output-Feedback Tracking Control for Stochastic Nonlower Triangular Nonlinear Systems With Dead-Zone Input.

For stochastic nonlower triangular nonlinear systems subject to dead-zone input, a neuroadaptive tracking control frame is constructed by applying the dynamic surface technique with a state observer in this work. Its primary contribution lies in extending the stability criteria to encompass stochastic nonlinear systems characterized by nonlower triangular structures and unmeasured states. The control strategy is delineated as follows. First, the state observer is designed to address the issue of unmeasured states, thereby facilitating the generation of an error dynamics system for subsequent analysis. Second, within the backstepping design framework, a neural network-based tracking controller is devised using dynamic surface control technique and variable separation approaches, ensuring system performance despite the presence of unmeasured states. Finally, stability analysis is conducted to guarantee that all the system signals remain bounded. Simulation examples are presented to illustrate the validity and practicality of the framework.

Unifying the Generalized Jacobian Matrix and prioritized task hierarchies, with application to free-floating VMSs

Free-floating vehicle manipulator systems (VMSs), such as those in space or underwater, experience a coupling effect between the motion of the manipulator arm and the vehicle base, since the motion of the joints induces a motion of the base relative to the system's center of gravity (CG). In this work a control framework is proposed that takes this coupling effect into account, selecting the motion of the CG as the highest priority task in a dynamically consistent task hierarchy in order to reduce the need for counteracting disturbances while controlling the position of the manipulator workspace. The proposed approach generalizes previous works using the Generalized Jacobian matrix to allow the completion of several prioritized tracking tasks. Control allocation is performed in a manner ensuring that the thrusters are used only for controlling the overall position of the VMS, while the joints are used for tasks requiring higher accuracy. The set in which all tracking error dynamics are zero is shown to be uniformly asymptotically stable, and the performance of the proposed control method is validated in a simulation study.

Virtual-Target based Path-Following in the 3D Underwater Environment

This work focuses on the design of a 3D path-following strategy for under-actuated underwater vehicles. The modeling of the problem relies on the Serret-Frenet apparatus, leading to the definition of the position error dynamics, with respect to a generic smooth curve in the operational 3D space. On the basis of such a model, a virtual-target based non-linear guidance law, derived by the exploitation of Lyapunov methodology, is designed. The theoretical proof and simulation results prove the functionality and reliability of the proposed approach.

Dynamic error modeling and compensation of a scanning probe on CMM

Dynamic error modeling and compensation of a scanning probe on CMM

Association Rule Mining for Dynamic Error Classification in the Automotive Manufacturing Industry

Association rule mining (ARM) is a data mining technique that extracts relationships between variables in dataset. This paper presents an application of ARM for dynamic error classification in the automotive manufacturing industry. The method involves the extraction of frequent patterns from historical vehicle configuration data to build a rule-based system for error classification. The presented approach includes frequent item sets, rule mining and the estimation of conditional error probabilities. The results show that ARM is a promising approach for dynamic error classification in the automotive manufacturing industry and has potential to improve product quality.

Finite-Horizon H∞ State Estimation for Complex Networks With Uncertain Couplings and Packet Losses: Handling Amplify-and-Forward Relays.

This article is concerned with the state estimation problem for a class of complex networks (CNs) with uncertain inner couplings and packet losses over communication networks. The inner couplings are allowed to be uncertain and varying in a specific interval. The amplify-and-forward (AaF) relay protocols are introduced to improve the communication quality and enhance the propagation distance. The Bernoulli random variables are used to characterize the randomly occurring packet losses encountered in communication channels. The focus of this article is on the design of a state estimator for each node of CNs such that a prescribed H∞ performance constraint is satisfied for the dynamical error system over a finite horizon. A sufficient condition is first provided to verify the existence of the desired H∞ state estimator, and the estimator gain is then determined by solving two coupled backward Riccati difference equations (RDEs). Subsequently, a recursive state estimation algorithm is put forward that is suitable for online computation. Finally, a numerical example is given to demonstrate the effectiveness of the proposed estimation method.

Characteristics Extraction and Constrained Signal Modeling Method for Dynamic Errors Testing in Electricity Meters

Characteristics Extraction and Constrained Signal Modeling Method for Dynamic Errors Testing in Electricity Meters

Theory of Run-Length Domain Modal Decomposition for Assessing Dynamic Errors in Electricity Meter (May 2024)

Theory of Run-Length Domain Modal Decomposition for Assessing Dynamic Errors in Electricity Meter (May 2024)

A flexible soft error mitigation framework leveraging dynamic partial reconfiguration technology

Fault tolerance is crucial for mission-critical FPGA-based systems in radiation environments. Soft-core processors in these systems, performing both control and computational tasks, require efficient soft error mitigation techniques to enhance their fault tolerance. In this paper, we investigate the variation trends in the fault tolerance of various processor components as the software workload changes. Based on our investigation, we propose a reconfigurable soft error mitigation framework that dynamically switches the hardening strategies for the processor according to the running workloads. The innovative application of dynamic partial reconfiguration technique in FPGAs enables time-multiplexing of the same circuit region to accommodate various hardening schemes, consequently achieving high area efficiency. We apply the framework to an open-source dual-issue superscalar RISC-V processor on a Xilinx ZCU102 FPGA board. Compared to traditional spatial redundancy-based hardening techniques, the proposed framework achieves a 20.84 % reduction in LUT utilization and a 20.53 % reduction in flip-flop utilization. The effectiveness of our framework has been evaluated through fault injection campaigns. The results indicate that, on average, only 0.05 % of faults would lead to system failure after hardening. Therefore, our work offers a new perspective on dynamic soft error mitigation in reconfigurable systems.

Nonfragile containment control of nonlinear multi‐agent systems via a disturbance observer‐based approach

AbstractIn this article, we consider the nonfragile containment control problem of nonlinear multi‐agent systems (MASs) with exogenous disturbance where the communication links among agents under consideration is directed. Firstly, based on relative output measurements between the agent and its neighbors, a disturbance observer‐based control protocol is proposed to solve the containment control problem of MASs with inherent nonlinear dynamics and exogenous disturbances. Secondly, because of the additional tuning of parameters in the real control systems, uncertainties in the designing of observer and controller gains always occur, and as a result, an output feedback controller with disturbance rejection is conceived and the containment control problem of nonlinear MASs with nonfragility is thoroughly investigated. Then, depending on matrix transformation and inequality technique, sufficient conditions of the designed controller gains exist, which is derived from the asymptotic stability analysis problem of some containment error dynamics of MASs. Finally, two simulation examples are exploited to illustrate the effectiveness of the proposed techniques.

Elastodynamic modeling and structural error compensation for a 5-DOF parallel mechanism with subclosed loops

In order to reduce the adverse effects of structural errors on a novel 5-degrees of freedom (DOF) parallel kinematic mechanism (PKM) with subclosed loops, studies on the elastodynamic modeling and structural error compensation are conducted in this paper. First, considering that introduction of subclosed loops significantly increased the complexity and difficulty of elastodynamic modeling, an equivalent unit modeling method for the branch chain with subclosed loop is proposed based on force analysis and deformation compatibility condition. Then, elastodynamic model of the whole 5-DOF PKM is established with the matrix structural analysis based method. Second, by defining a six-dimensional error (three translational errors and three rotational errors) for each node, structural error model of the PKM is constructed based on closed-loop vector method. To consider the coupling effects of static and dynamic structural errors, the dynamic structural errors derived by above elastodynamic model would be substituted into the structural error model along with given static structural errors. Finally, structural error compensation optimization model is established and structural errors are compensated by adjusting the driven parameters based on the improved particle swarm optimization (PSO) algorithm. Numerical simulations are conducted to verify the proposed elastodynamic modeling and structural error compensation methods. After compensation, the position errors along x, y, and z directions are respectively decreased by 68.036%, 81.409%, and 90.625%, and the angle errors around x and y directions are respectively decreased by 91.426% and 62.042%.

An Interval Observer for a Class of Cyber–Physical Systems with Disturbance

This paper investigates the problem of interval estimation for cyber–physical systems with unknown disturbance. In order to realize the interval estimation of cyber–physical systems, two technical methods are adopted. The first one requires the observer dynamic error system to be non-negative, and the second one relaxes this limitation by coordinate transformation. The sufficient conditions are established using both Lyapunov stability and positive system theory. Furthermore, according to the Schur complement, the linear matrix inequality is solved to determine the observer gains. Finally, the effectiveness and feasibility of the designed interval observer are verified by one numerical simulation.

A high-load current low-dropout regulator with adaptive ESR compensation

This paper presents a dynamic pseudo equivalent series resistance (DPESR) zero-point compensation technology applied to high-current high-precision low-dropout (LDO) regulators. The DPESR circuit tracks the poles of the LDO output and adaptively generates zeros to improve stability. This compensation scheme allows the equivalent series resistance (ESR) of the output capacitor to be reduced to zero, enabling the use of miniaturized and low-ESR ceramic capacitors while reducing voltage peaks. In addition, a dynamic bias error amplifier (EA) is designed to improve transient response while ensuring that the LDO has adequate load and line regulation. The proposed LDO is designed and tested using the 0.18μm CMOS process. The test results demonstrated that the load and line regulations are 0.0028 mV/mA and 0.655 mV/V, respectively. When the input voltage VIN is 1.9 V, the output voltage VOUT is 1.5 V, and the load current is varied from 10 mA to 1.2 A, the undershoot and overshoot are 58 mV and 45 mV, respectively.

Fault estimation for persistent dwell time switched systems with actuator and sensor faults

This paper investigates the fault estimation (FE) problem for a class of switched systems with external disturbances, actuator faults and sensor faults. A new adaptive FE observer is proposed to estimate the sensor and actuator faults simultaneously. Meanwhile, a more general and flexible persistent dwell time (PDT) switching signal is utilized to depict slow switching and fast switching phenomenon of switched systems. Then, sufficient conditions can be achieved to guarantee the stability of the estimation error dynamics. Finally, a simulation example of the circuit system is presented to show the effectiveness of the proposed FE scheme.

Path-following control for an unmanned aerial vehicle slung load system

A multirotor unmanned aerial vehicle (UAV) slung load system (SLS) is a nonlinear dynamics with eight degrees of freedom and four inputs that can be used for load transportation. The suspended payload can be modelled as a two degree-of-freedom pendulum attached to the UAV. This paper presents a path-following control (PFC) for an SLS. The PFC renders motions along any smooth Jordan curve in R 3 for payload position controlled-invariant. This property has practical benefits over traditional time-based trajectory tracking. Furthermore, the PFC prescribes UAV yaw and a desired payload speed profiles along the path. The PFC adopts dynamic extension and input-output state feedback linearisation. The closed-loop has a 1-dimensional zero-dynamics which is shown to be bounded. Hence, the PFC error dynamics is exponentially stable. Simulations are provided to validate the design.