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The purpose of this review paper is to address the substantial challenges of the outdated exoskeletons used for rehabilitation and further study the current advancements in this field. The shortcomings and technological developments in sensing the input signals to enable the desired motions, actuation, control and training methods are explained for further improvements in exoskeleton research.

Search platforms such as Web of Science, IEEE, Scopus and PubMed were used to collect the literature. The total number of recent articles referred to in this review paper with relevant keywords is filtered to 143.

Exoskeletons are getting smarter often with the integration of various modern tools to enhance the effectiveness of rehabilitation. The recent applications of bio signal sensing for rehabilitation to perform user-desired actions promote the development of independent exoskeleton systems. The modern concepts of artificial intelligence and machine learning enable the implementation of brain–computer interfacing (BCI) and hybrid BCIs in exoskeletons. Likewise, novel actuation techniques are necessary to overcome the significant challenges seen in conventional exoskeletons, such as the high-power requirements, poor back drivability, bulkiness and low energy efficiency. Implementation of suitable controller algorithms facilitates the instantaneous correction of actuation signals for all joints to obtain the desired motion. Furthermore, applying the traditional rehabilitation training methods is monotonous and exhausting for the user and the trainer. The incorporation of games, virtual reality (VR) and augmented reality (AR) technologies in exoskeletons has made rehabilitation training far more effective in recent times. The combination of electroencephalogram and electromyography-based hybrid BCI is desirable for signal sensing and controlling the exoskeletons based on user intentions. The challenges faced with actuation can be resolved by developing advanced power sources with minimal size and weight, easy portability, lower cost and good energy storage capacity. Implementation of novel smart materials enables a colossal scope for actuation in future exoskeleton developments. Improved versions of sliding mode control reported in the literature are suitable for robust control of nonlinear exoskeleton models. Optimizing the controller parameters with the help of evolutionary algorithms is also an effective method for exoskeleton control. The experiments using VR/AR and games for rehabilitation training yielded promising results as the performance of patients improved substantially.

Robotic exoskeleton-based rehabilitation will help to reduce the fatigue of physiotherapists. Repeated and intention-based exercise will improve the recovery of the affected part at a faster pace. Improved rehabilitation training methods like VR/AR-based technologies help in motivating the subject.

The paper describes the recent methods for signal sensing, actuation, control and rehabilitation training approaches used in developing exoskeletons. All these areas are key elements in an exoskeleton where the review papers are published very limitedly. Therefore, this paper will stand as a guide for the researchers working in this domain.

The purpose of this paper is to develop a combined control (CC) technique based on the direct torque control (DTC) strategy and vector control (VC) method, to improve the overall performance of a three-phase induction machine (TPIM) drives.

The proposed control scheme includes a table-based DTC strategy in connection with a proportional-integral-sliding mode controller and pulse width modulation switching strategy. The control system has merits of DTC technique such as simple structure, less dependent on machine parameters, fast dynamic response and merits of VC technique such as high accuracy and constant switching frequency.

To validate the effectiveness of the proposed control system, simulation and experimental studies are carried out for a 0.75 kW TPIM in different operating conditions. The achieved results show the superiority of the proposed method in terms of fast dynamics and simple structure compared to the VC strategy and low speed and torque ripples and constant switching frequency compared to the DTC method.

Compared to the conventional CC strategies, the control law of the proposed method is based on DTC theory and modulation is established based on VC. In other words, the variable switching frequency which is one of the main disadvantages of the conventional CC strategies is rectified using the proposed CC scheme.

The control charts are used in many production areas because they give an idea about the quality characteristic(s) of a product. The control limits are calculated and the data are examined whether the quality characteristic(s) is/are within these limits. At this point, it may be confusing to comment, especially if it is slightly below or above the limit values. In order to overcome this situation, it is suitable to use fuzzy numbers instead of crisp numbers. The purpose of this paper is to demonstrate how to create control limits of X ¯ -R control charts for a specified data set of interval type-2 fuzzy sets.

There are methods in the literature, such as defuzzification, distance, ranking and likelihood, which may be applicable for interval type-2 fuzzy set. This study is the first that these methods are adapted to the X ¯ -R control charts. This methodology enables interval type-2 fuzzy sets to be used in X ¯ -R control charts.

It is demonstrated that the methods – such as defuzzification, distance, ranking and likelihood for interval type-2 fuzzy sets – could be applied to the X ¯ -R control charts. The fuzzy control charts created using the methods provide similar results in terms of in/out control situations. On the other hand, the sample points depicted on charts show similar pattern, even though the calculations are different based on their own structures. Finally, the control charts obtained with interval type-2 fuzzy sets and the control charts obtained with crisp numbers are compared.

Based on the related literature, research works on interval type-2 fuzzy control charts seem to be very limited. This study shows the applicability of different interval type-2 fuzzy methods on X ¯ -R control charts. For the future study, different interval type-2 fuzzy methods may be considered for X ¯ -R control charts.

The unique contribution of this research to the relevant literature is that interval type-2 fuzzy numbers for quantitative control charts, such as X ¯ -R control charts, is used for the first time in this context. Since the research is the first adaptation of interval type-2 fuzzy sets on X ¯ -R control charts, the authors believe that this study will lead and encourage the people who work on this topic.

THE improvement in the British standard of living is generally desired. Politicians have not only subscribed to that ideal but some of them have indicated the rate at which we should advance. There are, however, certain trends in the country's economic life which must be reversed if we are to make any progress in that direction.

The purpose of this paper is to measure the performance of a sampling method through the average number of samples drawn in control.

Matching the adjusted average time to signal (AATS) of sampling methods, using as a reference the AATS of one of them the paper obtains the design parameters of the others. Thus, it will be possible to obtain, in control, the average number of samples required, so that the AATS of the mentioned sampling methods may be equal to the AATS of the method that the paper uses as the reference.

A more robust performance measure to compare sampling methods because in many cases the period of time where the process is in control is greater than the out of control period. With this performance measure the paper compares different sampling methods through the average total cost per cycle, in systems with Weibull lifetime distributions: three systems with an increasing hazard rate (shape parameter β=2, 4 and 7) and one system with a decreasing failure rate (β=0, 8).

In a usual production cycle where the in control period is much larger than the out of control period, particularly if the sampling costs and false alarms costs are high in relation to malfunction costs, the paper thinks that this methodology allows us a more careful choice of the appropriate sampling method.

To compare the statistical performance between different sampling methods using the average number of samples need to be inspected when the process is in control. Particularly, the paper compares the statistical and economic performance between different sampling methods in contexts not previously considered in literature. The paper presents an approximation for the average time between the instant that failure occurs and the first sample with the process out of control, as well.

The purpose of this paper is to propose a kind of fuzzy adaptive control method to control non‐linear system that has the characteristic of small time delay and fast respond speed.

The paper analyzes the production process and the actual condition of the preheat process of the plating zinc and painting plastic scribbled of double layer welded pipe that has the small time delay and fast respond speed, and also gives the preheat process mathematical model. Fuzzy adaptive control method with hierarchical structure is used which aims at one non‐linear system that has the characteristic of small time delay and fast responds speed. Through the simulation, it proves the mentioned method is effective to control the temperature system for double layers welded pipe in welding process.

Based on the mathematical model proposed about the production process and the actual condition of the preheat process, the fuzzy adaptive control method is effective to control the temperature system for double layers welded pipe in welding process.

The paper proposes fuzzy adaptive control method with hierarchical structure which has the basic fuzzy control grade, adaptive adjust grade, and process state judgment grade.

A very useful method in welding process for double layers welded pipe.

The new mathematical model is proposed about the production process, and the new control method is used in the temperature system for double layers welded pipe in welding process.

The purpose of this paper is to propose a new method based on goodness of fit tests for shift detection problems.

In this method, although the distribution of gathered data from the process is the subject of control, but any out-of-control signal could also be generalized to the overall state of the process including the parameters of the distribution.

Results of simulation study denote that among goodness of fit tests, the χ2 test has a better performance than the Kolmogorov-Smirnov test in detecting shifts of process. Also comparison of proposed method with traditional methods denotes that, proposed method generally has smaller probabilities of first and second type errors.

To the best of author’s knowledge, no attention has previously been paid to application of goodness of fit tests in process control.

This study discusses the tracking trajectory issue of the exoskeleton under the bounded disturbance and designs an useful tracking trajectory control method to solve it. By using the proposed control method, the tracking error can be successfully convergence to the assigned boundary. Meanwhile, the chattering effect caused by the actuators is already reduced, and the tracking performance of the pneumatic artificial muscles (PAMs) elbow exoskeleton is improved effectively.

A prescribed performance sliding mode control method was developed in this study to fulfill the joint position tracking trajectory task on the elbow exoskeleton driven by two PAMs. In terms of the control structure, a dynamic model was built by conforming to the adaptive law to compensate for the time variety and uncertainty exhibited by the system. Subsequently, a super-twisting algorithm-based second-order sliding mode control method was subjected to the exoskeleton under the boundedness of external disturbance. Moreover, the prescribed performance control method exhibits a smooth prescribed function with an error transformation function to ensure the tracking error can be finally convergent to the pre-designed requirement.

From the theoretical perspective, the stability of the control method was verified through Lyapunov synthesis. On that basis, the tracking performance of the proposed control method was confirmed through the simulation and the manikin model experiment.

As revealed by the results of this study, the proposed control method sufficiently applies to the PAMs elbow exoskeleton for tracking trajectory, which means it has potential application in the actual robot-assisted passive rehabilitation tasks.

Voltage source inverter-fed permanent magnet synchronous motors (VSI-PMSMs) are widely used in industrial actuation and mechatronic systems in water pumping stations, as well as in the traction of transportation systems (such as electric vehicles and electric trains or ships with electric propulsion). The dynamic model of VSI-PMSMs is multivariable and exhibits complicated nonlinear dynamics. The inverters’ currents, which are generated through a pulsewidth modulation process, are used to control the stator currents of the PMSM, which in turn control the rotational speed of this electric machine. So far, several nonlinear control schemes for VSI-PMSMs have been developed, having as primary objectives the precise tracking of setpoints by the system’s state variables and robustness to parametric changes or external perturbations. However, little has been done for the solution of the associated nonlinear optimal control problem. The purpose of this study/paper is to provide a novel nonlinear optimal control method for VSI-fed three-phase PMSMs.

The present article proposes a nonlinear optimal control approach for VSI-PMSMs. The nonlinear dynamic model of VSI-PMSMs undergoes approximate linearization around a temporary operating point, which is recomputed at each iteration of the control method. This temporary operating point is defined by the present value of the voltage source inverter-fed PMSM state vector and by the last sampled value of the motor’s control input vector. The linearization relies on Taylor series expansion and the calculation of the system’s Jacobian matrices. For the approximately linearized model of the voltage source inverter-fed PMSM, an H-infinity feedback controller is designed. For the computation of the controller’s feedback gains, an algebraic Riccati equation is iteratively solved at each time-step of the control method. The global asymptotic stability properties of the control method are proven through Lyapunov analysis. Finally, to implement state estimation-based control for this system, the H-infinity Kalman filter is proposed as a state observer. The proposed control method achieves fast and accurate tracking of the reference setpoints of the VSI-fed PMSM under moderate variations of the control inputs.

The proposed H-infinity controller provides the solution to the optimal control problem for the VSI-PMSM system under model uncertainty and external perturbations. Actually, this controller represents a min–max differential game taking place between the control inputs, which try to minimize a cost function that contains a quadratic term of the state vector’s tracking error, the model uncertainty, and exogenous disturbance terms, which try to maximize this cost function. To select the feedback gains of the stabilizing feedback controller, an algebraic Riccati equation is repetitively solved at each time-step of the control algorithm. To analyze the stability properties of the control scheme, the Lyapunov method is used. It is proven that the VSI-PMSM loop has the H-infinity tracking performance property, which signifies robustness against model uncertainty and disturbances. Moreover, under moderate conditions, the global asymptotic stability properties of this control scheme are proven. The proposed control method achieves fast tracking of reference setpoints by the VSI-PMSM state variables, while keeping also moderate the variations of the control inputs. The latter property indicates that energy consumption by the VSI-PMSM control loop can be minimized.

The proposed nonlinear optimal control method for the VSI-PMSM system exhibits several advantages: Comparing to global linearization-based control methods, such as Lie algebra-based control or differential flatness theory-based control, the nonlinear optimal control scheme avoids complicated state variable transformations (diffeomorphisms). Besides, its control inputs are applied directly to the initial nonlinear model of the VSI-PMSM system, and thus inverse transformations and the related singularity problems are also avoided. Compared with backstepping control, the nonlinear optimal control scheme does not require the state-space description of the controlled system to be found in the triangular (backstepping integral) form. Compared with sliding-mode control, there is no need to define in an often intuitive manner the sliding surfaces of the controlled system. Finally, compared with local model-based control, the article’s nonlinear optimal control method avoids linearization around multiple operating points and does not need the solution of multiple Riccati equations or LMIs. As a result of this, the nonlinear optimal control method requires less computational effort.

Voltage source inverter-fed permanent magnet synchronous motors (VSI-PMSMs) are widely used in industrial actuation and mechatronic systems in water pumping stations, as well as in the traction of transportation systems (such as electric vehicles and electric trains or ships with electric propulsion), The solution of the associated nonlinear control problem enables reliable and precise functioning of VSI-fd PMSMs. This in turn has a positive impact in all related industrial applications and in tasks of electric traction and propulsion where VSI-fed PMSMs are used. It is particularly important for electric transportation systems and for the wide use of electric vehicles as expected by green policies which aim at deploying electromotion and at achieving the Net Zero objective.

Unlike past approaches, in the new nonlinear optimal control method, linearization is performed around a temporary operating point, which is defined by the present value of the system’s state vector and by the last sampled value of the control input vector and not at points that belong to the desirable trajectory (setpoints). Besides, the Riccati equation, which is used for computing the feedback gains of the controller, is new, as is the global stability proof for this control method. Comparing with nonlinear model predictive control, which is a popular approach for treating the optimal control problem in industry, the new nonlinear optimal (H-infinity) control scheme is of proven global stability, and the convergence of its iterative search for the optimum does not depend on initial conditions and trials with multiple sets of controller parameters. It is also noteworthy that the nonlinear optimal control method is applicable to a wider class of dynamical systems than approaches based on the solution of state-dependent Riccati equations (SDRE). The SDRE approaches can be applied only to dynamical systems that can be transformed to the linear parameter varying form. Besides, the nonlinear optimal control method performs better than nonlinear optimal control schemes which use approximation of the solution of the Hamilton–Jacobi–Bellman equation by Galerkin series expansions.

The aim of the paper is to conduct an analytical study of a new method of induction motor torque and flux direct control with nonlinear controllers.

The method is based on the inverter state predictive determination in order to minimize the torque and flux errors.

The proposed method allows one to eliminate known DTC disadvantages, i.e. the hexagonal flux shape and nonsinusoidal current at a low motor speed, and also secures a decrease of torque and flux pulsation.

This new method enables a more precise reproduction of the motor torque and flux command signals, working with the same sampling frequency of the control processor as in the case of the standard DTC method. The decreased torque pulsations cause a decrease of the motor speed pulsation.

An innovative optimal control method is presented. The correctness of the initial assumptions as well as the expected final results have been verified in practice.