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In this paper, based on the extended state observer (ESO) and on a fractional order controller (FOC), composed of an integer order PID cascaded with a fractional order filter (FOF), a new control scheme for an n th order integer plant is proposed. The ESO is used to estimate and cancel the unknown internal dynamics and the external disturbance. Afterwards, an FOC is designed to resolve the set-point tracking problem. An analytical and systematic method is proposed to design the FOC. This method is based on the Internal Model Control (IMC) and the Bode's Ideal Transfer Function (BITF). Therefore, the proposed control structure improves the robustness and performance of the traditional linear active disturbance rejection control (LADRC), especially for the open-loop gain variation. In addition, since the system be controlled is an n th order, a general form of the BITF is also proposed. Numerical simulations on a nonlinear model and experimental results on a cart-pendulum system design illustrate the effectiveness of the suggested ESO-PID-FOF scheme for the disturbance rejection, the set-point tracking and robustness. A comparison with the results obtained using the standard LADRC is also presented. [ABSTRACT FROM AUTHOR]

As one of the most promising topics in complex control processes, data-driven techniques have been widely used in numerous industrial sectors and have developed over the past two decades. In addition, the fractional-order controller has become more attractive in applied studies. In this article, a fractional integral control is implemented for a rotary flexible joint system. Moreover, an adjusted virtual reference feedback tuning (VRFT) technique is used to tune the fractional-order integrator. In this method, fractional integral control is designed based on state feedback control. Then, VRFT is adjusted and applied to the fractional integral controller. The effectiveness of the proposed adjusted VRFT method is discussed and presented through simulation and experimental results. The tracking performance of the rotary arm and the minimization of the vibration tip is evaluated based on the proposed method. In this article, the comparison of our proposed VRFT fractional scheme is made with the classical state feedback as well as a recently developed state feedback-based fractional order integral (SF-FOI) controller. The current investigations determine the performance improvement of our proposed scheme of comparable structure to the recent SF-FOI, with the introduction of the VRFT to the SF-FOI scheme. [ABSTRACT FROM AUTHOR]

• A 2DOF fractional order control of a nonlinear and unstable system is investigated in this paper. • Analytical model based method is developed to design the parameters of the fractional order PD controller. • The fractional order controllers of the inner and outer loops are tuned to have a constant phase margin of the open-loop. • Based on experiment on a real ball and beam system, performance of the proposed controller is highlighted. Control engineers and researchers face challenges to design an efficient controller for Ball and beam system due to its nonlinear and unstable properties. This paper investigates two Degrees of Freedom fractional order control of the ball and beam system. It involves the model based method to design controllers' parameters for the corresponding linear model. The fractional order controllers are specially tuned to have a constant phase margin of the open-loop. This characteristic ensures the robustness of the controllers to the variations of system gain. This paper presents a proper evaluation and comparison between integer and fractional order controllers. Performance of each controller is evaluated in terms of set-point tracking, disturbance rejection, and robustness. The comparison between two controllers is validated through both simulation and experimental results. Strengths and weaknesses in the real-time control are also indicated. [ABSTRACT FROM AUTHOR]

Analytical methods are usually applied for tuning fractional controllers. The present paper proposes an empirical method for tuning a new type of fractional controller known as PID-Fractional-Order-Filter (FOF-PID). Indeed, the setpoint overshoot method, initially introduced by Shamsuzzoha and Skogestad, has been adapted for tuning FOF-PID controller. Based on simulations for a range of first order with time delay processes, correlations have been derived to obtain PID-FOF controller parameters similar to those obtained by the Internal Model Control (IMC) tuning rule. The setpoint overshoot method requires only one closed-loop step response experiment using a proportional controller (P-controller). To highlight the potential of this method, simulation results have been compared with those obtained with the IMC method as well as other pertinent techniques. Various case studies have also been considered. The comparison has revealed that the proposed tuning method performs as good as the IMC. Moreover, it might offer a number of advantages over the IMC tuning rule. For instance, the parameters of the fractional controller are directly obtained from the setpoint closed-loop response data without the need of any model of the plant to be controlled. [ABSTRACT FROM AUTHOR]

Rotary double inverted pendulum is a highly nonlinear complex system and requires a high performance controller for its control. Using gain matrix which is obtained through state feedback technique may create complexity while removing the steady-state error for all states. Incorporating an integral action can be an alternative for these errors. Therefore, a state space–based fractional order controller with fractional integral action is designed and tested on a rotary double inverted pendulum in this article. The fractional integral controller is designed based on Bode's ideal transfer function. Two degree of freedom is considered for tuning purpose as well. The integer order controller based on the state space approach is also shown for comparison. Simulation and experimental results are presented for both controllers of this rotary double inverted pendulum system. [ABSTRACT FROM AUTHOR]