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This paper aims to develope a novel fractional hybrid impedance control (FHIC) approach for high-sensitive contact stress force tracking control of the series elastic muscle-tendon actuator (SEM-TA) in uncertain environments.

In three different cases, the fractional parameters of the FHIC were optimized with the particle swarm optimization algorithm. Its adaptability to the pressure of the sole of the foot on real environments such as grass (soft), carpet (medium) and solid floors (hard) is far superior to traditional impedance control. The main aim of this paper is to derive the dynamic simulation models of the SEM-TA, to develop a control architecture allowing for high-sensitive contact stress force control in three cases and to verify the simulation models and the proposed controller with experimental results. The performance of the optimized controllers was evaluated according to these parameters, namely, maximum overshoot, steady-state error, settling time and root mean squared errors of the positions. Moreover, the frequency robustness analysis of the controllers was made in three cases.

Different simulations and experimental results were conducted to verify the control performance of the controllers. According to the comparative results of the performance, the responses of the proposed controller in simulation and experimental works are very similar.

Origin approach and origin experiment.

The purpose of this paper is to address a fractional order fuzzy PID (FOFPID) control approach for solving the problem of enhancing high precision tracking performance and robustness against to different reference trajectories of a 6-DOF Stewart Platform (SP) in joint space.

For the optimal design of the proposed control approach, tuning of the controller parameters including membership functions and input-output scaling factors along with the fractional order rate of error and fractional order integral of control signal is tuned with off-line by using particle swarm optimization (PSO) algorithm. For achieving this off-line optimization in the simulation environment, very accurate dynamic model of SP which has more complicated dynamical characteristics is required. Therefore, the coupling dynamic model of multi-rigid-body system is developed by Lagrange-Euler approach. For completeness, the mathematical model of the actuators is established and integrated with the dynamic model of SP mechanical system to state electromechanical coupling dynamic model. To study the validness of the proposed FOFPID controller, using this accurate dynamic model of the SP, other published control approaches such as the PID control, FOPID control and fuzzy PID control are also optimized with PSO in simulation environment. To compare trajectory tracking performance and effectiveness of the tuned controllers, the real time validation trajectory tracking experiments are conducted using the experimental setup of the SP by applying the optimum parameters of the controllers. The credibility of the results obtained with the controllers tuned in simulation environment is examined using statistical analysis.

The experimental results clearly demonstrate that the proposed optimal FOFPID controller can improve the control performance and reduce reference trajectory tracking errors of the SP. Also, the proposed PSO optimized FOFPID control strategy outperforms other control schemes in terms of the different difficulty levels of the given trajectories.

To the best of the authors’ knowledge, such a motion controller incorporating the fractional order approach to the fuzzy is first time applied in trajectory tracking control of SP.