• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.229-241
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• 2007

Multi-term fractional differential equations have been used to simulate fractional-order control system. It has been demonstrated the necessity of the such controllers for the more efficient control of fractional-order dynamical system. In this paper, the multi-term fractional ordinary differential equations are transferred into equivalent a system of equations. The existence and uniqueness of the new system are proved. A fractional order difference approximation is constructed by a decoupled technique and fractional-order numerical techniques. The consistence, convergence and stability of the numerical approximation are proved. Finally, some numerical results are presented to demonstrate that the numerical approximation is a computationally efficient method. The new method can be applied to solve the fractional-order control system.

• Journal of Electrical Engineering and Technology
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• v.11 no.6
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• pp.1863-1871
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• 2016

This paper presents an application of fractional order controller for the control of multi input multi output twin rotor aerodynamic system. Dynamics of the considered system are highly nonlinear and there exists a significant cross-coupling between the horizontal and vertical axes (pitch & yaw). In this paper, a fractional order model of twin rotor aerodynamic system is identified using input output data from nonlinear system. Based upon identified fractional order model, a fractional order PID controller is designed to control the angular position of level bar of twin rotor aerodynamic system. The parameters of controller are tuned using Nelder-Mead optimization and compared with particle swarm optimization techniques. Simulation results on the nonlinear model show a significant improvement in the performance of fractional order PID controller as compared to a classical PID controller.

• Journal of Institute of Control, Robotics and Systems
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• v.21 no.8
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• pp.718-722
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• 2015

This paper proposes a fractional-order PID (Proportional-Integral-Derivative) control used electromagnetic strip stabilization controller in a continuous galvanizing line. Compared to a conventional PID controller, a fractional-order PID controller has integration-fractional-order and derivation-fractional-order as additional control parameters. Thanks to increased control parameters, more precise controller adjustment is available. In addition, accurate transfer function of a real system generally has a fractional-order form. Therefore, it is more adequate to use a fractional-order PID controller than a conventional PID controller for a real world system. Finite element models of a $1200{\times}2000{\times}0.8mm$ strip, which were extracted using a commercial software ANSYS were used as simulation plants, and Gaussian mixture models were used to find optimized control parameters that can reduce the strip vibrations to the lowest amplitude. Simulation results show that a fractional-order PID controller significantly reduces strip vibration and transient response time than a conventional PID controller.

• Journal of Electrical Engineering and Technology
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• v.13 no.4
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• pp.1705-1714
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• 2018

This paper develops a novel controller called iterative learning sliding mode (ILSM) to control linear and nonlinear fractional-order systems. This control applies a combination structures of continuous and discontinuous controller, conducts the system output to the desired output and achieve better control performance. This controller is designed in the way to be robust against the external disturbance. It also estimates unknown parameters of fractional-order systems. The proposed controller unlike the conventional iterative learning control for fractional systems does not need to apply direct control input to output of the system. It is shown that the controller perform well in partial and complete observable conditions. Simulation results demonstrate very good performance of the iterative learning sliding mode controller for achieving the desired control objective by increasing the number of iterations in the control loop.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.47.2-47
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• 2001

This paper is concerned with the limiting zeros, as the sampling period tends to zero, of a multivariable discrete-time system composed of an approximate fractional-order hold (AFROH), a continuous-time plant and a sampler in cascade. An approximate fractional-order hold is proposed to implement fractional-order hold (FROH) and is applied to instead of the zero-order hold (ZOH). The implementing problem of the fractional-order hold is overcome. The properties of the limiting zeros are studied and the location problem of them is solved. In addition, a stability condition of the zeros for sufficiently small sampling period is derived ...

• Journal of the Korean Society for Precision Engineering
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• v.23 no.1 s.178
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• pp.121-128
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• 2006

This paper deals with the application of enhanced perturbation estimation (SMCEPE) to sliding mode control of a dynamic system in the presence of perturbations including external disturbances, unpredictable parameter variations, and unstructured dynamics. Compared to conventional sliding mode control (SMC) and sliding mode control with perturbation estimation (SMCPE), the proposed one can offer robust control performances under serious control conditions, such as fast dynamic perturbations and slow loop-closure speeds, without a priori knowledge on upper bounds of perturbations. The perturbation estimator in SHCEPE also has more adaptability owing to the fractional-order hold technique. The effectiveness and superiority of the proposed control strategy are demonstrated by a series of simulations on the position tracking control of a two-link robot manipulator.

• Steel and Composite Structures
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• v.48 no.6
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• pp.611-623
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• 2023

This work considered an optimal control formulation in the sense of Caputo derivatives. The optimality of the fractional optimal control problem. The tumor immune interaction in fractional form provides an excellent tool for the description of memory and hereditary properties of inter and intra cells. So the interaction between effector-cells, tumor cells and are modeled by using the definition of Caputo fractional order derivative that provides the system with long-time memory and gives extra degree of freedom. In addiltion, existence and local stability of fixed points are investigated for discrete model. Moreover, in order to achieve more efficient computational results of fractional-order system, a discretization process is performed to obtain its discrete counterpart. Our technique likewise allows the advancement of results, such as return time to baseline that are unrealistic with current model solvers.

• Journal of Advanced Marine Engineering and Technology
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• v.13 no.2
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• pp.78-88
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• 1989

The fundamental objective of this paper has been to develop a means for incoporating the concept of the linear fractional transformation more generally and easily into multivariable feedback design procedure. When we design a continuous system, generally, we are constrained by design methods which arise specifically for the system. Also, in the design of descrete systems, it is the same concept. But the approach developed in this paper is very flexible in the view that in spite of being the continuous or discrete, the design can be done using a well known design method in both cases. That is, when we design a contnuous system or discrete system, the design can be done by a standard design method of continuous systmes or discrete ones, depending on the choice of the linear fractional transformation. Therefore, it is noted that this concept has broken the unflexibility of the conventional design rules for multivariable control system. In essence, the concept shows that if a given system is controllable, some desirable design, for examples, pole assignment within prespecified region, optimal controllers with poles within prespecified region etc., could be done easily by transforming a desirable region into a standard region, such as the complex left-half plane or the unit disk, by the chosen linear fractional transformation, and then by designing the transformed system using the well known standard results.

• The Journal of the Korea institute of electronic communication sciences
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• v.16 no.3
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• pp.503-510
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• 2021

This study intends to apply the mathematical method of fractional order differentiation to a controller that controls the response of the system. Therefore, we design integrator for the fractional index by converting it into discrete time to construct a controller. The IP controller composes an integral controller for errors and the proportional controller applies only the system output. The controller is designed by using the fractional order integrator to the integral controller of the IP controller. First, the performance of the PI controller and the IP controller is compared, and the designed controller is applied to the speed control of the motor. As a result, the motor output speed was uniformed and precise control performance could be obtained. It was confirmed that the speed error in the steady state is within 0.1 [%], and it has precise and uniform speed control performance without overshoot.

• Journal of Power Electronics
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• v.16 no.4
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• pp.1526-1540
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• 2016

This work mainly discusses an accurate and fast islanding detection based on fractional wavelet packet transform (FRWPT)for multibus microgrid systems. The proposed protection scheme uses combined desirable features retrieved from discrete fractional Fourier transform (FRFT) and wavelet packet transform (WPT) techniques, which provides precise time-frequency information on minute perturbation signals introduced in the system. Moreover, this study focuses on the design of decoupling control with a distributed controller based on state feedback for the efficient operation of microgrid systems that are transitioning from the grid-connected mode to the islanded mode. An IEEE 9-bus test system with inverter based distributed generation (DG) units is considered for islanding assessment and smooth operation. Finally, tracking errors are greatly reduced with stability improvement based on the proposed controller. FRWPT based islanding detection is demonstrated via a time domain simulation of the system. Simulated results show an improvement in system stability with the application of the proposed controller and accurate islanding detection based on the FRWPT technique in comparison with the results obtained by applying the wavelet transform (WT) and WPT.