Time-delay estimation based computed torque control with robust adaptive RBF neural network compensator for a rehabilitation exoskeleton

MIMO ultra-local model-based adaptive enhanced model-free control using extremum-seeking for coupled mechatronic systems

Multiple degree-of-freedom (DOF) mechatronic systems, such as robots and robotic arms, play a crucial role in modern life and production. However, due to strong coupling, uncertain dynamics, and external disturbance, accurately modeling these systems is challenging, making traditional model-based control methods impractical. To address this, this paper proposes an extremum-seeking-based adaptive enhanced model-free control for multi-input multi-output (MIMO) mechatronic systems to realize robust trajectory tracking. Unlike previous model-free control methods that decouple and reorganize the MIMO system into several single-input single-output ultra-local models, this paper develops a MIMO ultra-local model with a non-diagonal gain matrix α to approximate the system dynamics within an ultra-short time window. Time-delay estimation (TDE), Proportional-Derivative (PD) control law and accuracy compensation compose an TDE-based enhanced intelligent PD control that ensures the closed-loop stability. Furthermore, an extremum-seeking (ES) technique is designed to optimize the gain matrix α to enhance control performance. The main contributions of this paper are the development of a model-free control framework based on the MIMO ultra-local model and the successful application of ES to optimize the non-diagonal gain matrix α. Stability analysis of the closed-loop system is conducted using Lyapunov theorem. Finally, numerical simulations on a 2-DOF robotic manipulator and co-simulation results on a 3-DOF PUMA 560 robotic manipulator validate the effectiveness and superiority of the proposed methods.

Active Disturbance Rejection Control via Neural Networks for a Lower-Limb Exoskeleton

This article presents the design of a control algorithm based on Artificial Neural Networks (ANNs) applied to a lower-limb exoskeleton, which is aimed to carry out walking trajectories during lower-limb rehabilitation. The interaction between the patient and the exoskeleton leads to model uncertainties and external disturbances that are always present. For this reason, the proposed control considers that the non-linear part of the model is unknown and is perturbed by external disturbances, which are estimated by an active disturbance rejection control via Artificial Neural Networks. To validate the proposed approach, a numerical simulation and an experimental implementation of the ANN-Controller are developed.

Prediction of potentially toxic elements in water resources using MLP-NN, RBF-NN, and ANFIS: a comprehensive review

Water resources are constantly threatened by pollution of potentially toxic elements (PTEs). In efforts to monitor and mitigate PTEs pollution in water resources, machine learning (ML) algorithms have been utilized to predict them. However, review studies have not paid attention to the suitability of input variables utilized for PTE prediction. Therefore, the present review analyzed studies that employed three ML algorithms: MLP-NN (multilayer perceptron neural network), RBF-NN (radial basis function neural network), and ANFIS (adaptive neuro-fuzzy inference system) to predict PTEs in water. A total of 139 models were analyzed to ascertain the input variables utilized, the suitability of the input variables, the trends of the ML model applications, and the comparison of their performances. The present study identified seven groups of input variables commonly used to predict PTEs in water. Group 1 comprised of physical parameters (P), chemical parameters (C), and metals (M). Group 2 contains only P and C; Group 3 contains only P and M; Group 4 contains only C and M; Group 5 contains only P; Group 6 contains only C; and Group 7 contains only M. Studies that employed the three algorithms proved that Groups 1, 2, 3, 5, and 7 parameters are suitable input variables for forecasting PTEs in water. The parameters of Groups 4 and 6 also proved to be suitable for the MLP-NN algorithm. However, their suitability with respect to the RBF-NN and ANFIS algorithms could not be ascertained. The most commonly predicted PTEs using the MLP-NN algorithm were Fe, Zn, and As. For the RBF-NN algorithm, they were NO3, Zn, and Pb, and for the ANFIS, they were NO3, Fe, and Mn. Based on correlation and determination coefficients (R, R2), the overall order of performance of the three ML algorithms was ANFIS > RBF-NN > MLP-NN, even though MLP-NN was the most commonly used algorithm.

A novel adaptive neural network-based time-delayed estimation control for nonlinear systems subject to disturbances and unknown dynamics

This paper presents an adaptive backstepping-based model-free control (BSMFC) for general high-order nonlinear systems (HNSs) subject to disturbances and unstructured uncertainties to enhance the system tracking performance. The proposed methodology is constructed based on the backstepping control (BSC) with radial basis function neural network (RBFNN) -based time-delayed estimation (TDE) to overcome the obstacle of unknown system dynamics. Additionally, a command-filtered (CF) approach is involved to address the complexity explosion of the BSC design. As the errors arising from approximation, new control laws are established to reduce the effects in this regard. The stability of the closed-loop system is guaranteed through the Lyapunov theorem and the superiority of the proposed methodology is confirmed through a comparative simulation with other model-free approaches.

High-precision dynamic torque control of high stiffness actuator for humanoids

The high stiffness actuator (HSA), applied to each joint of an electrical driven humanoid robot, can directly affect the motion performance of the torque-controlled humanoid robots. For high control performance of HSA, a high-precision dynamic torque control (HDTC) is proposed. The HDTC consists of two phases: (1) A novel dynamic current control is used to linearize high stiffness actuator torque control system, which can estimate and compensate the nonlinear coupling parts; (2) An enhanced internal model control is designed to ensure high tracking accuracy in the system containing noisy torque signal and even numerical differentiation signals. Benefitting from dynamic current control and the enhanced internal model control, the proposed HDTC is accurate and adaptable. Finally, the superiority of the HDTC is verified with comparative experiments.

sEMG-Based Adaptive Cooperative Multi-Mode Control of a Soft Elbow Exoskeleton Using Neural Network Compensation

Soft rehabilitation exoskeletons have gained much attention in recent years, striving to assist the paralyzed individuals restore motor functions. However, it is a challenge to promote human-robot interaction property and satisfy personalized training requirements. This article proposes a soft elbow rehabilitation exoskeleton for the multi-mode training of disabled patients. An adaptive cooperative admittance backstepping control strategy combined with surface electromyography (sEMG)-based joint torque estimation and neural network compensation is developed, which can induce the active participation of patients and guarantee the accomplishment and safety of training. The proposed control scheme can be transformed into four rehabilitation training modes to optimize the cooperative training performance. Experimental studies involving four healthy subjects and four paralyzed subjects are carried out. The average root mean square error and peak error in trajectory tracking test are 3.18° and 5.68°. The active cooperation level can be adjusted via admittance model, ranging from 4.51 °/Nm to 10.99 °/Nm. In cooperative training test, the average training mode value and effort score of healthy subjects (i.e., 1.58 and 1.50) are lower than those of paralyzed subjects (i.e., 2.42 and 3.38), while the average smoothness score and stability score of healthy subjects (i.e., 3.25 and 3.42) are higher than those of paralyzed subjects (i.e., 1.67 and 1.71). The experimental results verify the superiority of proposed control strategy in improving position control performance and satisfying the training requirements of the patients with different hemiplegia degrees and training objectives.

Trajectory tracking control of a coaxial rotor drone: Time-delay estimation-based optimal model-free fuzzy logic approach

This paper proposes a control algorithm for controlling the position and attitude of a coaxial rotor drone without knowing the model dynamics. To overcome the major drawback of model-dependent approaches, an optimal model-free fuzzy controller (OMFFC) based on the estimation of the unknown dynamic function of the system is proposed. A time-delay estimation (TDE) technique is effectively exploited to approximate the unknown dynamic function of the system. The estimation error is then offset using a robust adaptive fuzzy logic compensator. Based on Lyapunov stability arguments, the global asymptotic stability of the coaxial rotor drone system is proven. Moreover, a flower pollination-based algorithm is also proposed to generate the optimal parameters to address the trade-off between optimal tracking performance and the design conditions related to the closed-loop stability requirements. The numerical simulations illustrate how the proposed methodology leads to the best performance, as well as less computational complexity compared to the standard proportional-integral-derivative and time-delay estimation-based controllers in the presence of external disturbances.

A new adaptive sliding mode controller based on the RBF neural network for an electro-hydraulic servo system

Accuracy and robust trajectory tracking for electro-hydraulic servo systems in the presence of load disturbances and model uncertainties are of great importance in many fields. In this work, a new adaptive sliding mode control method based on the RBF neural networks (SMC-RBF) is proposed to improve the performances of a robotic excavator. Model uncertainties and load disturbances of the electro-hydraulic servo system are approximated and compensated using the RBF neural networks. Adaptive mechanisms are designed to adjust the connection weights of the RBF neural networks in real time to guarantee the stability. A nonlinear term is introduced into the sliding mode to design an adaptive terminal sliding mode control structure to improve dynamic performances and the convergence speed. Moreover, a sliding mode chattering reduction method is proposed to suppress the chattering phenomenon. Three types of step, ramp and sine signals are used as the simulation reference trajectories to compare different controllers on a co-simulation platform. Experiments with leveling and triangle conditions are presented on a robotic excavator. Results show that the proposed SMC-RBF controller is superior to existing proportional integral derivative (PID) and sliding mode controller (SMC) in terms of tracking accuracy and disturbance rejection.

Optimization Algorithm for Delay Estimation Based on Singular Value Decomposition and Improved GCC-PHAT Weighting

The accuracy of time delay estimation seriously affects the accuracy of sound source localization. In order to improve the accuracy of time delay estimation under the condition of low SNR, a delay estimation optimization algorithm based on singular value decomposition and improved GCC-PHAT weighting (GCC-PHAT-ργ weighting) is proposed. Firstly, the acoustic signal collected by the acoustic sensor array is subjected to singular value decomposition and noise reduction processing to improve the signal-to-noise ratio of the signal; then, the cross-correlation operation is performed, and the cross-correlation function is processed by the GCC-PHAT-ργ weighting method to obtain the cross-power spectrum; finally, the inverse transformation is performed to obtain the generalized correlation time domain function, and the peak detection is performed to obtain the delay difference. The experiment was carried out in a large outdoor pool, and the experimental data were processed to compare the time delay estimation performance of three methods: GCC-PHAT weighting, SVD-GCC-PHAT weighting (meaning: GCC-PHAT weighting based on singular value decomposition) and SVD-GCC-PHAT-ργ weighting (meaning: GCC-PHAT-ργ weighting based on singular value decomposition). The results show that the delay estimation optimization algorithm based on SVD-GCC-PHAT-ργ improves the delay estimation accuracy by at least 37.95% compared with the other two methods. The new optimization algorithm has good delay estimation performance.

Adaptive interaction torque-based AAN control for lower limb rehabilitation exoskeleton

In this paper, an adaptive interaction torque-based assist-as-needed (AITAAN) control method for the lower limb rehabilitation exoskeleton is proposed. Firstly, a desired input torque for the wearer's lower limb is designed based on computed torque control (CTC). A nonlinear disturbance observer (NDO) is used to assess the lower limb muscle torque. Subtract the estimated muscle torque from the desired input torque, the exoskeleton only provides the remaining torque through interaction torque. Then, the interaction torque tracking problem can be converted to the exoskeleton trajectory tracking problem by using the spring-damper like dynamics model of the interaction force. A flexible boundary prescribed performance controller (PPC) is designed for the exoskeleton to achieve fast and accurate trajectory tracking. The coupled wearer-exoskeleton system is established in SolidWorks and imported to MATLAB/Simulink with SimMechanics. The AITAAN controller's effectiveness and superiority were then verified through co-simulations.

Soft Sensor Modeling Method Based on Improved KH-RBF Neural Network Bacteria Concentration in Marine Alkaline Protease Fermentation Process

Marine alkaline protease (MAP) fermentation is a complex multivariable, multi-coupled, and nonlinear process. Some unmeasured parameters will affect the quality of protease. Aiming at the problem that some parameters are difficult to be detected online, a soft sensing modeling method based on improved Krill Herd algorithm RBF neural network (LKH-RBFNN) is proposed in this paper. Based on the multi-parameter RBFNN model, the adaptive RBF neural network algorithm and control law are used to approximate the unknown parameters. The adaptive Levy flight strategy is used to improve the traditional Krill Herd algorithm, improve the global search ability of the algorithm, and avoid falling into local optimization. At the same time, the location update formula of Krill Herd algorithm is improved by using the calculation methods of similarity and agglomeration degree, and the parameters of adaptive RBFNN are optimized to improve its over correction and large amount of calculation. Finally, the soft sensing prediction model of bacterial concentration and relative active enzyme in map process based on LKH-RBFNN is established. The root mean square error and maximum absolute error of this model are 0.938 and 0.569, respectively, which are less than KH-RBFNN and PSO-RBFNN prediction models. It proves that the prediction error of LKH-RBFNN model is smaller and can meet the needs of online prediction of key parameters of map fermentation.

Periodic event-triggered sliding mode control for lower limb exoskeleton based on human-robot cooperation

This paper presents a periodic event-triggered sliding mode control (SMC) scheme based on human-robot cooperation for lower limb exoskeletons. Firstly, a Genetic Algorithm-Back propagation (GA-BP) neural network is proposed to estimate the motion intention of the wearer through electromyography (EMG) signals. Secondly, the periodic event-triggered SMC strategy based on tanh function is designed to ensure the asymptotic convergence of the exoskeleton system and save communication resources, where the detailed expressions of sampling period and control gain are designed. Finally, comparative simulation and experimental analysis is presented to verify the effectiveness of the proposed control method.

Mechanism Analysis and Self-Adaptive RBFNN Based Hybrid Soft Sensor Model in Energy Production Process: A Case Study

Despite hard sensors can be easily used in various condition monitoring of energy production process, soft sensors are confined to some specific scenarios due to difficulty installation requirements and complex work conditions. However, industrial process may refer to complex control and operation, the extraction of relevant information from abundant sensors data may be challenging, and description of complicated process data patterns is also becoming a hot topic in soft-sensor development. In this paper, a hybrid soft sensor model based mechanism analysis and data-driven is proposed, and ventilation sensing of coal mill in a power plant is conducted as a case study. Firstly, mechanism model of ventilation is established via mass and energy conservation law, and object-relevant features are identified as the inputs of data-driven method. Secondly, radial basis function neural network (RBFNN) is used for soft sensor modeling, and genetic algorithm (GA) is adopted for quick and accurate determination of the RBFNN hyper-parameters, thus self-adaptive RBFNN (SA-RBFNN) is proposed to improve the soft sensor performance in energy production process. Finally, effectiveness of the proposed method is verified on a real-world power plant dataset, taking coal mill ventilation soft sensing as a case study.

Nonlinear time delay estimation based model reference adaptive impedance control for an upper-limb human-robot interaction

A nonlinear Time Delay Estimation (TDE) based model reference adaptive impedance controller was developed for Tarbiat Modares University Upper Limbs Rehabilitation Robot (TUERR). The proposed controller uses a stable reference impedance model, which produces desired dynamic relationship between applied force and position error for the robot End-effector to track the desired trajectory. TDE based model reference adaptive controller estimates unknown system dynamics and uncertainties, and the adaption law modifies the controller gains. Using a Lyapunov function was shown trajectory tracking errors in the overall system are bounded. In addition, a performance-based velocity profile proposed to modify the pace of trajectory planning considering the deviation from the desired path. Finally, the performance of the presented controller and rehabilitation process is experimentally investigated for TUERR.

Robust LQR-Based Neural-Fuzzy Tracking Control for a Lower Limb Exoskeleton System with Parametric Uncertainties and External Disturbances

The design of an accurate control scheme for a lower limb exoskeleton system has few challenges due to the uncertain dynamics and the unintended subject's reflexes during gait rehabilitation. In this work, a robust linear quadratic regulator- (LQR-) based neural-fuzzy (NF) control scheme is proposed to address the effect of payload uncertainties and external disturbances during passive-assist gait training. Initially, the Euler-Lagrange principle-based nonlinear dynamic relations are established for the coupled system. The input-output feedback linearization approach is used to transform the nonlinear relations into a linearized state-space form. The architecture of the adaptive neuro-fuzzy inference system (ANFIS) and used membership function are briefly explained. While varying mass parameters up to 20%, three robust neural-fuzzy datasets are formulated offline with the joint error vector and LQR control input. Thereafter, to deal with external interferences, an error dynamics with a disturbance estimator is presented using an online adaptation of the firing strength matrix. The Lyapunov theory is carried out to ensure the asymptotic stability of the coupled human-exoskeleton system in view of the proposed controller. The gait tracking results for the proposed control scheme (RLQR-NF) are presented and compared with the exponential reaching law-based sliding mode (ERL-SM) controller. Furthermore, to investigate the robustness of the proposed control over LQR control, a comparative performance analysis is presented for two cases of parametric uncertainties and external disturbances. The first case considers the 20% raise in mass values with a trigonometric form of disturbances, and the second case includes the effect of the 30% increment in mass values with a random form of disturbances. The simulation runs have shown the promising gait tracking aspects of the designed controller for passive-assist gait training.

Nonlinear Nonsingular Fast Terminal Sliding Mode Control Using Deep Deterministic Policy Gradient

Background: As a control strategy of industrial robots, sliding mode control has the advantages of fast response and simple physical implementation, but it still has the problems of chattering and low tracking accuracy caused by chattering. This paper proposes a new sliding mode control strategy for the application of industrial robot control, which effectively solves these problems. Methods: In this paper, a deep deterministic policy gradient–nonlinear nonsingular fast terminal sliding mode control (DDPG–NNFTSMC) strategy is proposed for industrial robot control. In order to improve the tracking control accuracy and anti-interference ability, DDPG is used to approach the uncertainties of the system in real time, which ensures the robustness of the system in various uncertain environments. Lyapunov function is used to prove the stability and finite time convergence of the system. Compared with the nonsingular terminal sliding mode control (NTSMC), the time to reach the equilibrium point is shorter. With the help of MATLAB/Simulink, the tracking accuracy and control effects are compared with traditional terminal sliding mode control (TSMC), NTSMC and radial basis function–sliding mode control (RBF–SMC), the results showed that it had the advantages of nonsingularity, finite time convergence, small tracking error. The motion accuracy and anti-interference ability of the uncertain manipulator system was further improved, and the chattering problem of the system in the motion process is effectively eliminated.

Application of artificial neural networks to predict the heavy metal contamination in the Bartin River

In this study, copper (Cu), iron (Fe), zinc (Zn), manganese (Mn), nickel (Ni), and lead (Pb) analyses were performed, and the results were modelled by artificial neural networks (ANN) and adaptive neuro-fuzzy inference system (ANFIS). Samples were taken from 3 stations selected on the Bartin River for 1 year between December 2012 and December 2013. Radial basis neural network (RBANN), multilayer perceptron (MLP) neural networks models, and adaptive neuro-fuzzy inference system (ANFIS) were applied to the data in order to predict the heavy metal concentrations. As a result of the study, the RMSE and MAE values of all the heavy metal models were found to have very low error values during the test phase, and it was found that the models created using MLP had R² values higher than 0.77 during the test phase; the test phase R² values of the models using RBN method were found to be ranging between 0.773 and 0.989, and the test phase R² value of the ANFIS model was higher than 0.80. If sorted from the best model to the worst by taking the MAE and RMSE values into consideration based on the test evaluation results, according to the heavy metal types, where all of the MLP, RBN, and ANFIS models were generally approximate to each other, RBN was successful for Cu, Zn, and Mn, while MLP model was successful for Ni and ANFIS model for Fe and Pb. According to the results, it can be inferred that the heavy metal contents can be estimated approximately with artificial intelligence models and relatively easy-to-measure parameters; it will be possible to detect heavy metals which are harmful to the viability of the rivers, both quickly and economically.

A MBSE Application to Controllers of Autonomous Underwater Vehicles Based on Model-Driven Architecture Concepts

In this paper, a hybrid realization model is proposed for the controllers of autonomous underwater vehicles (AUVs). This model is based on the model-based systems engineering (MBSE) methodology, in combination with the model-driven architecture (MDA), the real-time unified modeling language (UML)/systems modeling language (SysML), the extended/unscented Kalman filter (EKF/UKF) algorithms, and hybrid automata, and it can be reused for designing controllers of various AUV types. The dynamic model and control structure of AUVs were combined with the specialization of MDA concepts as follows. The computation-independent model (CIM) was specified by the use-case model combined with the EKF/UKF algorithms and hybrid automata to intensively gather the control requirements. Then, the platform-independent model (PIM) was specialized using the real-time UML/SysML to design the capsule collaboration of control and its connections. The detailed PIM was subsequently converted into the platform-specific model (PSM) using open-source platforms to promptly realize the AUV controller. On the basis of the proposed hybrid model, a planar trajectory-tracking controller, which allows a miniature torpedo-shaped AUV to autonomously track the desired planar trajectory, was implemented and evaluated, and shown to have good feasibility.

Variable Bandwidth Adaptive Course Keeping Control Strategy for Unmanned Surface Vehicle

This paper proposes a new and original course keeping control strategy for an unmanned surface vehicle in the presence of modeling error, external disturbance and input saturation. The trajectory linearization control method is used as the basic algorithm to design the course keeping strategy, and the radial basis function neural network and disturbance observer are used to compensate modeling error and external disturbance respectively to enhance the robustness of the control system. Moreover, a robust term is used to compensate various compensation errors to further improve the robustness of the system. In addition, hyperbolic tangent function and Nussbaum function are hired to deal with the potential input saturation problem, and the neural shunting model is adopted to avoid the computational explosion caused by the derivation of virtual control law. Taking the above facts into account will help to further realize engineering practice. Finally, the control strategy proposed in this paper is compared with the classical proportional–integral–derivative control strategy. The simulation results show that the course control results of the proposed control strategy are more robust than proportional–integral–derivative control, regardless of whether the external disturbance is weak or strong.