State feedback with fractional integral control design based on the Bode’s ideal transfer function

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.

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“…The details of the proof of this result can be found in Al-Saggaf et al 21 Mathematical modeling of rotary double inverted pendulum…”

Section: Fractional Integral Control Combined With State Feedbackmentioning

confidence: 85%

Stabilization of a double inverted rotary pendulum through fractional order integral control scheme

Mehedi

Al‐Saggaf

Mansouri

et al. 2019

International Journal of Advanced Robotic Systems

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“…The reference model is based on ideal open loop transfer function used in feedback amplifier that gives the best performance on terms of robustness to the gain variation, the ideal transfer function of Bode is [30][31][32].…”

Section: Bode's Ideal Transfer Function and Fractional Controller De mentioning

confidence: 99%

“…This paper presents a direct torque fractional order control design to PMSM, in this approach, a fractional-order controller PI λ D γ [5,28,29], is synthesized using Bode's ideal transfer function as a reference model [30][31][32]. The proposed technique of the PMSM speed control is compared to the conventional PID controller.…”

Section: Introductionmentioning

confidence: 99%

Fractional Order Direct Torque Control of Permanent Magnet Synchronous Machine

Walid¹,

Rahem²,

Meddour³

et al. 2019

EJEE

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This paper designs a fractional order PID direct torque control strategy for permanent magnet synchronous machine (PSMS) based on on fractional calculus. The fractional order controller to control the speed of the machine was synthesized, referring to Bode's ideal transfer function. In the controller, the fractional order integrator was approximated by Charef's method. The fractional PID order control was compared with classical PID control, showing that the former has the better accuracy and robustness. Finally, MATLAB/ SIMULINK simulation proved the advantages of our control strategy under oscillating torque load or magnetic field.

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“…The stabilization issue of commensurate fractional order systems is studied using system augmentation, and used in [31,32]. Fractional order tuning is performed in several recent works [33][34][35]. Therefore, the current study introduced in this paper designs a state space based fractional order integral controller.…”

Section: Introductionmentioning

confidence: 99%

State feedback based fractional order control scheme for linear servo cart system

Mehedi¹

2018

J. vibroeng.

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Fractional order control schemes are being actively investigated for various systems. Fractional order concept is incorporated in integral (I), proportional integral (PI), proportional derivative (PD) or proportional integral derivative (PID) controller to investigate the performance of different state variables of the system. These techniques are often used for the purpose of technology transfer but very scanty research has so far been conducted using state space approach. The current investigation is initiated to observe the effect of fractional order controller using state space approach for the system's performance while tracking the position and regulating the speed of a linear servo cart system. Integer order controller based on proportional derivative (PD) approach is also shown for comparison. Simulation responses are presented and analyzed, in this investigation. The superiority of state space approach based fractional order controller is shown in the results. The paper contains a literature review on several control techniques used to control position and speed of a servo-cart system. An over view of mathematical modeling of servo cart system and a description of a proposed fractional controller is presented in this paper. A brief description of integer order control scheme is also presented. Simulated results are compared and discussed for both fractional order controller and integer order controller at the end of this paper.

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State feedback with fractional integral control design based on the Bode’s ideal transfer function

Cited by 42 publications

References 12 publications

Stabilization of a double inverted rotary pendulum through fractional order integral control scheme

Stabilization of a double inverted rotary pendulum through fractional order integral control scheme

Fractional Order Direct Torque Control of Permanent Magnet Synchronous Machine

State feedback based fractional order control scheme for linear servo cart system

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