Single-link Flexible Joint Robot Research Articles

Robust tracking control of flexible manipulators using hybrid backstepping/nonlinear reduced-order active disturbance rejection control

This study presents a novel hybrid control strategy for single-link flexible-joint robot manipulators, addressing inherent uncertainties and nonlinear dynamics. By integrating nonlinear reduced-order active disturbance rejection control (NRADRC) with backstepping control, the proposed method effectively estimates and mitigates nonlinear dynamics and external disturbances. Utilizing a nonlinear reduced-order extended state observer (NRESO) enhances resilience to internal and external uncertainties. The global stability of the proposed controller is rigorously established using the Lyapunov approach. Numerical comparisons with state-of-the-art nonlinear control methods demonstrate the superior efficiency and robustness of the proposed approach, especially under varying payloads and disturbances, advancing robotic control solutions.

Sensor fault estimation based on L∞ unknown input observer

Abstract This study investigates the fault estimation problem for a class of Lipschitz non-linear systems with sensor faults and disturbances. An augmented system consisting of system states and sensor faults is constructed to estimate sensor faults by designing an augmented state. A novel L∞ performance index is presented to reduce the influence of disturbances on fault estimation results. An unknown input observer (UIO) is proposed based on the L∞ performance index to achieve an asymptotic estimation of sensor faults. The design conditions of the L∞ UIO are deduced and solved using linear matrix inequalities. The effectiveness of the proposed L∞ UIO and the fault estimation performance are demonstrated via numerical simulations of a single-link flexible joint robot.

Finite-time observer–based robust fault estimation for nonlinear systems

This article investigates the finite-time fault-estimation problem for a class of Lipschitz nonlinear systems with actuator faults and unknown input disturbances. Specifically, the original system is preliminarily decoupled into two reduced-order subsystems using a linear nonsingular transformation. A novel finite-time observer is proposed to estimate actuator faults in finite time. Subsequently, the proposed finite-time observer is extended to nonlinear systems with unknown input disturbances to investigate the robust fault-estimation problem. The actuator fault and unknown input disturbance are estimated simultaneously using two finite-time observations. Furthermore, a fault-estimation scheme is designed based on finite-time observers. The finite-time stability of the observers is then analysed using the Moreno–Lyapunov function method. The analytical proofs presented herein demonstrate that estimation errors can converge to a region of zero in finite time. Finally, the effectiveness of the developed finite-time observers and fault-estimation scheme was validated through simulations of a sample single-link flexible-joint robot.

Adaptive PID Fault-Tolerant Tracking Controller for Takagi-Sugeno Fuzzy Systems with Actuator Faults: Application to Single-Link Flexible Joint Robot

This paper considers the problem of Fault Tolerant Tracking Control (FTTC) strategy design for nonlinear systems using Takagi-Sugeno (T-S) fuzzy models with measurable premise variables affected by actuator faults subject to unknown bounded disturbances (UBD). Firstly, the Adaptive Fuzzy Observer (AFO) is proposed to estimate the faults. Based on the information provided by this observer, an active fault tolerant tracking controller described by an adaptive Proportional-Integral-Derivative (PID) structure has been developed to compensate for the actuator fault effects and to guarantee the trajectory tracking of desired outputs to the reference model despite the presence of actuator faults. The stability and the trajectory tracking performances of the proposed approach are analyzed based on the Lyapunov theory. Sufficient conditions can be obtained and solved for the design of the controller, and the observer gains using Linear Matrix Inequalities (LMIs). Finally, the effectiveness of the proposed technique is illustrated by using a single-link flexible joint robot.

H − / L ∞ UIO‐based actuator and sensor fault diagnosis design in the finite frequency domain for discrete‐time Lipschitz nonlinear systems

This study investigates the problem of fault diagnosis observer design in the finite frequency domain for discrete-time Lipschitz nonlinear systems simultaneously subjected to actuator and sensor faults and unknown input disturbances. An augmented descriptor system is developed by constructing an augmented state consisting of system states and sensor faults. A novel H−/L∞ unknown input observer (UIO) is proposed in the finite frequency domain using the generalized Kalman–Yakubovich–Popov lemma to render the residual sensitive to actuator faults and robust against disturbances, which can achieve a better fault diagnosis result compared with existing observers in the full frequency domain. In the fault diagnosis scheme, a time-varying threshold is presented based on the L∞ performance index to detect actuator faults, and the sensor fault estimation is simultaneously achieved through an asymptotical estimation of the augmented state. Design conditions for the proposed H−/L∞ UIO are derived and converted into linear matrix inequalities to solve its design matrices together. The effectiveness of the developed H−/L∞ UIO and the fault diagnosis scheme are validated via simulations of an example of a single-link flexible joint robot.

Nonlinear Model Predictive Control of Single-Link Flexible-Joint Robot Using Recurrent Neural Network and Differential Evolution Optimization

A recurrent neural network (RNN) and differential evolution optimization (DEO) based nonlinear model predictive control (NMPC) technique is proposed for position control of a single-link flexible-joint (FJ) robot. First, a simple three-layer recurrent neural network with rectified linear units as an activation function (ReLU-RNN) is employed for approximating the system dynamic model. Then, using the RNN predictive model and model predictive control (MPC) scheme, an RNN and DEO based NMPC controller is designed, and the DEO algorithm is used to solve the controller. Finally, comparing numerical simulation findings demonstrates the efficiency and performance of the proposed approach. The merit of this method is that not only is the control precision satisfied, but also the overshoots and the residual vibration are well suppressed.

Robust Output Feedback Control of Single-Link Flexible-Joint Robot Manipulator with Matched Disturbances Using High Gain Observer.

This article focuses on the output feedback control of single-link flexible-joint robot manipulators (SFJRMs) with matched disturbances and parametric uncertainties. Formally, four sensing elements are required to design the controller for single-link manipulators. We have designed a robust control technique for the semiglobal stabilization problem of the angular position of the link in the SFJRM system, with the availability of only a position sensing device. The sliding mode control (SMC) based output feedback controller is devised for SFJRM dynamics. The nonlinear model of SFJRM is considered to estimate the unknown states utilizing the high-gain observer (HGO). It is shown that the output under SMC using HGO-based estimated states coincides with that using original states when the gains of HGO are sufficiently high. Finally, the results are presented showing that the designed control technique works well when the SFJRM model is uncertain and matched perturbations are expected.

Adaptive Fuzzy Event-Triggered Control for Single-Link Flexible-Joint Robots With Actuator Failures

This article studies the finite-time tracking control problem for the single-link flexible-joint robot system with actuator failures and proposes an adaptive fuzzy fault-tolerant control strategy. More precisely, the issue of "explosion of complexity" is successfully solved by incorporating the command filtering technology and the backstepping method. The unknown nonlinearities are identified with the help of the fuzzy logic system. An event-triggered mechanism with the relative threshold strategy is exploited to save communication resources. Furthermore, the proposed control design can guarantee that the tracking error converges to a small neighborhood of origin within a finite time by taking full advantage of the finite-time stability theory. Finally, the simulation example is presented to further verify the validity of the proposed control method.

Simultaneous state and fault estimation for Takagi-Sugeno implicit models with Lipschitz constraints

This paper presents a state and fault observer design for a class of Takagi-Sugeno implicit models (TSIMs) with unmeasurable premise variables satisfying the Lipschitz constraints. The fault variable is constituted by the actuator and sensor faults. The actuator fault affects the state and the sensor fault affects the output of the system. The approach is based on the separation between dynamic and static relations in the TSIM. Firstly, the method begins by decomposing the dynamic equations of the algebraic equations. Secondly, the fuzzy observer design that satisfies the Lipschitz conditions and permits to estimate simultaneously the unknown states, actuator and sensor faults is developed. The aim of this approach for the observer design is to construct an augmented model where the fault variable is added to the state vector. The exponential convergence of the state estimation error is studied by using the Lyapunov theory and the stability condition is given in term of only one linear matrix inequality (LMI). Finally, numerical simulation results are given to highlight the performances of the proposed method by using a TSIM of a single-link flexible joint robot.

Observer-based adaptive fractional-order control of flexible-joint robots using the Fourier series expansion: theory and experiment

In this paper, fractional-order observer/controller design for flexible-joint robots is developed. In order to eliminate the need for obtaining the regressor matrix, the Fourier series expansion is applied for uncertainty estimation. Voltage saturation nonlinearities are compensated in the control law; hence, knowledge of the actuator/manipulator dynamics model is not required in the proposed method. Uniformly ultimately boundedness of observer estimation error and joint position tracking error are guaranteed through Lyapunov stability concept. The case study is a single-link flexible-joint robot actuated by permanent magnet DC motors. Experimental results are presented to emphasize the successful practical implementation of the proposed algorithm. Based on the experimental results, the proposed controller considerably outperforms some previous related works using various criteria.

A new estimation/decoupling approach for robust observer-based fault reconstruction in nonlinear systems affected by simultaneous time varying actuator and sensor faults

This paper presents an estimation/decoupling approach to design a fault estimation observer for nonlinear systems affected by a simultaneous actuator and sensor faults. In this approach, the sensor fault is treated as unknown inputs while the state and the actuator faults are estimated by recalling the extended state observer (ESO) idea. A Takagi-Sugeno Multiple-Integral Unknown Input Observer (TSMIUIO) is used to achieve this approach. First, the TSMIUIO estimates an extended state consists of the original system state and the actuator faults by using the ESO idea. On the other hand, the sensor faults are decoupled from the estimation of the extended state by treating such faults as unknown inputs. Then, the TSMIUIO permits an implicit estimation of sensor faults by using the output signals. The benefits earned by such an approach are: (1) the approach does not presume constraints on the time behaviour of the sensor faults. (2) By decoupling the sensor faults, the approach eliminates the bi-directional interaction (BDI) between the estimated signals. (3) It offers an implicit estimation of sensor faults by using the output signals. The design algorithm is given in a linear matrix inequality (LMI) form. The single-link flexible joint robot and the FAST 5MW benchmark wind turbine have been used to show the effectiveness of the proposed method.

Robust fault tolerant control based on adaptive observer for Takagi-Sugeno fuzzy systems with sensor and actuator faults: Application to single-link manipulator

In this work, we investigate the problem of control for nonlinear systems represented by Takagi-Sugeno (T-S) fuzzy models affected by both sensor and actuator faults subject to an unknown bounded disturbances (UBD). For this, we design an adaptive observer to estimate state, sensor and actuator fault vectors simultaneously despite the presence of external disturbances. Based on this observer, we develop a fault tolerant control (FTC) law not only to stabilize closed loop system, but also to compensate the fault effects. For the observer-based controller design, we propose less conservative conditions formulated in terms of linear matrix inequalities (LMIs). Moreover, both observer and controller gains are calculated via solving a set of LMIs only in single step. Finally, comparative results and an application to single-link flexible joint robot are afforded to prove the efficiency of the proposed design.

Optimal state estimation and fault diagnosis for a class of nonlinear systems

This study proposes a scheme for state estimation and, consequently, fault diagnosis in nonlinear systems. Initially, an optimal nonlinear observer is designed for nonlinear systems subject to an actuator or plant fault. By utilizing Lyapunov &#x02BC s direct method, the observer is proved to be optimal with respect to a performance function, including the magnitude of the observer gain and the convergence time. The observer gain is obtained by using approximation of Hamilton-Jacobi-Bellman &#x0028 HJB &#x0029 equation. The approximation is determined via an online trained neural network &#x0028 NN &#x0029 . Next a class of affine nonlinear systems is considered which is subject to unknown disturbances in addition to fault signals. In this case, for each fault the original system is transformed to a new form in which the proposed optimal observer can be applied for state estimation and fault detection and isolation &#x0028 FDI &#x0029 . Simulation results of a singlelink flexible joint robot &#x0028 SLFJR &#x0029 electric drive system show the effectiveness of the proposed methodology.

Similar Fault Isolation of Discrete-Time Nonlinear Uncertain Systems: An Adaptive Threshold Based Approach

In this paper, a new concept of “similar fault” is introduced to the field of fault isolation (FI) of discrete-time nonlinear uncertain systems, which defines a new and important class of faults that have small mutual differences in fault magnitude and fault-induced system trajectories. Effective isolation of such similar faults is rather challenging as their small mutual differences could be easily concealed by other system uncertainties (e.g., modeling uncertainty/disturbances). To this end, a novel similar fault isolation (sFI) scheme is proposed based on an adaptive threshold mechanism. Specifically, an adaptive dynamics learning approach based on the deterministic learning theory is first introduced to locally accurately learn/identify the uncertain system dynamics under each faulty mode using radial basis function neural networks (RBF NNs). Based on this, a bank of sFI estimators are then developed using a novel mechanism of absolute measurement of fault dynamics differences. The resulting residual signals can be used to effectively capture the small mutual differences of similar faults and distinguish them from other system uncertainties. Finally, an adaptive threshold is designed for real-time sFI decision making. One important feature of the proposed sFI scheme is that: it is capable of not only isolating similar faults that belong to a pre-defined fault set (used in the training/learning process), but also identifying new faults that do not match any pre-defined faults. Rigorous analysis on isolatability conditions and isolation time is conducted to characterize the performance of the proposed sFI scheme. Simulation results on a practical application example of a single-link flexible joint robot arm are used to show the effectiveness and advantages of the proposed scheme over existing approaches.

Estimation/decoupling approach for robust Takagi–Sugeno UIO-based fault reconstruction in nonlinear systems affected by a simultaneous time-varying actuator and sensor faults

ABSTRACTThis paper presents a robust design of Takagi–Sugeno Multiple-Integral Unknown Input Observer (TSMIUIO) for nonlinear systems affected by a simultaneous time-varying actuator and sensor faults, sensor noise and unknown input by using novel estimation/decoupling approach. In comparison to the available literature, the motivation for this approach is to: (1) attain robust fault reconstruction against the effects of bi-directional interaction accompanying the use of extended state observer (ESO) to simultaneously estimate actuator and sensor faults. (2) Guarantee accurate fault reconstruction despite the time behaviour of the fault. (3) Reduce the order of the TSMIUIO by avoiding the use of ESO for estimating all faults. The -norm minimisation has been exploited to ensure robust global stability against system disturbances. The design algorithm has been formulated using linear matrix inequality framework. Finally, the effectiveness of the proposal is illustrated by using a single-link flexible joint robot.

Adaptive sliding mode fault tolerant control design for uncertain nonlinear systems with multiplicative faults: Takagi–Sugeno fuzzy approach

The present article deals with adaptive sliding mode fault tolerant control design for uncertain nonlinear systems, affected by multiplicative faults, that is described under Takagi–Sugeno fuzzy representation. First, we propose to conceive robust adaptive observer in order to achieve states and multiplicative faults estimation in the presence of nonlinear system uncertainties. Under the nonlinear Lipschitz condition, the observer gains are attained by solving the multi-objective optimization problem. Second, sliding mode controller is suggested to offer a solution of the closed-loop system stability even the occurrence of real fault effects. The main objective is to compensate multiplicative fault effects based on output feedback information. Sufficient conditions are developed with [Formula: see text] performances and expressed as a set of linear matrix inequalities subject to compute controller gains. Finally, simulation results, using the nonlinear model of a single-link flexible joint robot system, are given to illustrate the capability of the suggested fault tolerant control strategy to treat multiplicative faults.

Hybrid approach to design Takagi–Sugeno observer‐based FTC for non‐linear systems affected by simultaneous time varying actuator and sensor faults

This study uses a novel approach, integrating fault estimation and fault decoupling methods, in designing a new Takagi–Sugeno multiple integral unknown input observer (TSMIUIO)-based fault tolerant control (FTC) system. The motivation is to tackle the challenges underlined in designing observer-based FTC for non-linear systems affected by simultaneous time-varying actuator and sensor faults, exogenous input, and sensor noise. In such systems, the FTC design challenges are the constraints imposed by the structure of input/output matrices, the need of extending the order of the observer to estimate simultaneous faults, the bi-directional interaction caused by the state and faults’ estimation errors, and the unpredictable time behaviour of fault signals. These challenges motivate the proposal of TSMIUIO to (i) ensure acceptable FTC performance, irrespective of the time behaviour of sensor fault; (ii) relax the complexity of TSMIUIO by avoiding the use of extended state approach for estimating simultaneous faults; and (iii) eliminate the BDI in the estimated signals that feed the controller. The effectiveness of the proposed method is illustrated using a single-link flexible joint robot and translational oscillator with an eccentric rotational proof mass actuator benchmark.

A Novel Discrete-time Nonlinear Model Predictive Control Based on State Space Model

This paper proposes a novel finite dimensional discrete-time Nonlinear Model Predictive Control. This technique is based on discrete-time state-space models, Taylor series expansion for prediction and performance index optimization. Furthermore, the technique extends the concept of the Lie derivative for the discrete time case using Euler backwards method. The performance validation for the discrete-time Nonlinear Model Predictive Control uses the simulation of a single-link flexible joint robot and the inverted pendulum. Comparison of the proposed finite dimensional discrete-time Nonlinear Model Predictive Control technique with Feedback Linearization Control is also discussed. Analytical and numerical results show excellent performances for both, the single-link flexible joint and inverted pendulum controllers using the proposed discrete-time Nonlinear Model Predictive Control technique.

H∞ observer-based event-triggered sliding mode control for a class of discrete-time nonlinear networked systems with quantizations

This paper investigates the problem of H∞ observer-based event-triggered sliding mode control (SMC) for a class of uncertain discrete-time Lipschitz nonlinear networked systems with quantizations occurring in both input and output channels. The event-triggered strategy is used to save the limited network bandwidth. Then, based on the zero-order-hold (ZOH) measurement, a state observer is designed to reconstruct the system state, which facilitates the design of the discrete-time sliding surface. Considering the effects of quantizations, networked-induced constraints and event-triggered scheme, the nonlinear state error dynamics and sliding mode dynamics are converted into a unified linear parameter varying (LPV) time-delay system with the aid of a reformulated Lipschitz property. By using the Lyapunov-Krasovskii functional and free weighting matrix, a new sufficient condition is derived to guarantee the robust asymptotic stability of the resulting closed-loop system with prescribed H∞ performance. And then the observer gain, event-triggering parameter and sliding mode parameter are co-designed. Furthermore, a novel SMC law is synthesized to force the trajectories of the observer system onto a pre-specified sliding mode region in a finite time. Finally, a single-link flexible joint robot example is utilized to demonstrate the effectiveness of the proposed method.

Mixed H∞ and passivity control for a class of stochastic nonlinear sampled-data systems

In this paper, we consider the problem of mixed H∞ and passivity control for a class of stochastic nonlinear systems with aperiodic sampling. The system states are unavailable and the measurement is corrupted by noise. We introduce an impulsive observer-based controller, which makes the closed-loop system a stochastic hybrid system that consists of a stochastic nonlinear system and a stochastic impulsive differential system. A time-varying Lyapunov function approach is presented to determine the asymptotic stability of the corresponding closed-loop system in mean-square sense, and simultaneously guarantee a prescribed mixed H∞ and passivity performance. Further, by using matrix transformation techniques, we show that the desired controller parameters can be obtained by solving a convex optimization problem involving linear matrix inequalities (LMIs). Finally, the effectiveness and applicability of the proposed method in practical systems are demonstrated by the simulation studies of a Chua’s circuit and a single-link flexible joint robot.