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The flexible arm easily vibrates due to its thin structural characteristics, which affect the operation accuracy, so reducing the vibration of the flexible arm is a significant issue. Smart materials are very widely used in the research topic of vibration suppression. Considering the hysteresis characteristic of the smart materials, based on previous simulation research, this paper proposes an experimental system design of nonlinear vibration control by using the interactive actuation from shape memory alloy (SMA) for a flexible arm. The experiment system was an interactive actuator–sensor–controller combination. The vibration suppression strategy was integrated with an operator-based vibration controller, a designed integral compensator and the designed n-times feedback loop. In detail, a nonlinear vibration controller based on operator theory was designed to guarantee the robust stability of the flexible arm. An integral compensator based on an estimation mechanism was designed to optimally reduce the displacement of the flexible arm. Obtaining the desired tracking performance of the flexible arm was a further step, by increasing the n-times feedback loop. From the three experimental cases, when the vibration controller was integrated with the designed integral compensator, the vibration displacement of the flexible arm was much reduced compared to that without the integral compensator. Increasing the number of n-times feedback loops improves the tracking performance. The desired vibration control performance can be satisfied when n tends to infinity. The conventional PD controller stabilizes the vibration displacement after the 7th vibration waveform, while the vibration displacement approaches zero after the 4th vibration waveform using the proposed vibration control method, which is proved to be faster and more effective in controlling the flexible arm’s vibration. The experimental cases verify the effectiveness of the proposed interactive actuation vibration control approach. It is observed from the experimental results that the vibration displacement of the flexible arm becomes almost zero within less time and with lower input power, compared with a traditional controller.

In this paper, an operator-based voltage control method for TENGs is investigated, achieving output voltage tracking without compensators and uncertainty suppression using robust right coprime factorization. Initially, a comprehensive simulation-capable circuit model for TENGs is developed, integrating their open-circuit voltage and variable capacitance characteristics. This model is implemented to simulate the behavior of TENGs with a rectifier bridge and capacitive load. To address the high-voltage, low-current pulsating nature of TENG outputs, a storage capacitor switching model is designed to effectively transfer the pulsating energy. This switching model is directly connected to a buck converter and operates under a unified control strategy. A complete TENG power management system was established based on this model, incorporating an operator theory-based control strategy. This strategy ensures steady output voltage under varying load conditions without using compensators, thereby reducing disturbances. Simulation results validate the feasibility of the proposed TENG system and the efficacy of the control strategy, providing a robust framework for optimizing TENG energy harvesting and management systems with significant potential for practical applications.

This paper investigates the problem of trajectory tracking control in the presence of bounded model uncertainty and external disturbance. To cope with this problem, we propose a novel intelligent operator-based sliding mode control scheme for stability guarantee and control performance improvement in the closed-loop system. Firstly, robust stability is guaranteed by using the operator-based robust right coprime factorization method. Secondly, in order to further achieve the asymptotic tracking and enhance the responsiveness to disturbance, a finite-time integral sliding mode control law is designed for fast convergence and non-zero steady-state error in accordance with Lyapunov stability analysis. Lastly, the controller’s parameters are automatically adjusted by the proved stabilizing particle swarm optimization with the linear time-varying inertia weight, which significantly saves tuning time with a remarkable performance guarantee. The effectiveness and efficiency of the proposed method are verified on a highly nonlinear ionic polymer metal composite application. The extensive numerical simulations are conducted and the results show that the proposed method is superior to the state-of-the-art methods in terms of tracking accuracy and high robustness against disturbances.

A new operator-based nonlinear robust control design scheme for wireless power transfer systems with uncertainties is proposed in this paper. In the proposed control design system, to deal with the uncertainties in the wireless power transfer system, operator-based robust right coprime factorization approach is adopted to guarantee the robust stability. Moreover, the tracking performance is improved by using the proposed control design scheme. Simulations and experiments are tested to show the effectiveness of this proposed control design scheme.

In this study, the passivity‐based robust control and tracking for Hamiltonian systems with unknown perturbations by using the operator‐based robust right coprime factorisation method is concerned. For the system with unknown perturbations, a design scheme is proposed to guarantee the uncertain non‐linear systems to be robustly stable while the equivalent non‐linear systems is passive, meanwhile the asymptotic tracking property of the plant output is discussed. Moreover, the design scheme can be also used into the general Hamiltonian systems while the simulation is used to further demonstrate the effectiveness of the proposed method.

In this paper, an operator-based robust nonlinear multivariable tracking control for a manipulator with uncertainties is proposed by using a robust right coprime factorization approach. In general, there exist unknown modelling errors in measuring structural parameters of the manipulator and external disturbances in real situations. In the present control system design, the effect of the modelling errors and disturbance on system performance is considered to be uncertainties in the manipulator dynamics. Considering the uncertainties, an operator-based robust nonlinear multivariable tracking control using robust right coprime factorization is studied. That is, firstly a robustly stable control based on robust right coprime factorization is designed. Secondly, a robust nonlinear multivariable tracking system is proposed for improving the trajectory of the manipulator, and the output tracking performance is evaluated based on the exponential iteration theorem. Finally, the effectiveness of the designed system is confirmed by simulation results.

In this paper, operator based robust control for nonlinear uncertain system with unknown backlash-like hysteresis is considered. In detail, a continuous backlash-like hysteresis operator is proved to be corresponding to a one-to-one operator, that is, it is suitable to be used in operator theoretic based control theory. Moreover, an internal model control (IMC) structure with one parallel compensating operator is proposed for nonlinear uncertain system with unknown backlash-like hysteresis. Based on the proposed control scheme, the designed system is robustly stable and the desired output tracking performance can be realized simultaneously. Finally, a simulation example about nonlinear plant preceded by backlash is given to show the design procedure of the proposed method.

[abstFig src='/00280006/07.jpg' width='300' text='The asymptotic tracking performance and the passivity property' ] The tracking control problem for the uncertain nonlinear feedback systems is considered in this paper by using passivity-based robust right coprime factorization method. Concerned with the passivity for the nonlinear feedback system, two stable controllers are designed such that the nonlinear feedback system is robust stable and the plant output asymptotically tracks to the reference output. A numerical example is given to show the validity of the control scheme as well as the tracking performance.

In this paper, a robust nonlinear tracking control design for a bio-inspired robot arm with human-like motion mechanism is investigated, and the bio-inspired operator controller based on human multi-joint viscoelastic properties is designed by using operator-based robust right coprime factorization approach. The motion mechanism of human multi-joint arm is used, and the measurement uncertainties of human multi-joint arm viscoelasticity are considered in designing bio-inspired operator controller. Based on the proposed design scheme, the sufficient conditions for the robust stability are derived in considering the coupling effects and measurement uncertainties, and the output tracking performance is realized. The effectiveness of the proposed design scheme was confirmed by the simulation results based on experimental data, and the time-varying estimated experimental data of human multi-joint arm viscoelasticity is used in simulation.