Abstract: The fractional–order proportional integral (FOPI) controller tuning rules based on the fractional calculus for the cascade control system are systematically proposed in this paper. Accordingly, the ideal controller is obtained by using internal model control (IMC) approach for both the inner and outer loops, which gives the desired closed-loop responses. On the basis of the fractional calculus, the analytical tuning rules of FOPI controller for the inner loop can be established in the frequency domain. Besides, the outer loop is tuned by using any integer PI/PID controller tuning rules in the literature. The simulation study is considered for the stable process model and the results demonstrate the simplicity, flexibility, and effectiveness of the proposed method for the cascade control system in compared with the other methods.
Abstract: In this paper, a fraction-order model for pad parasitic effect of GaN HEMT on Si substrate is developed and validated. Open de-embedding structure is used to characterize and de-embed substrate loading parasitic effects. Unbiased device measurements are implemented to extract parasitic inductances and resistances. The model shows very good simulation for S-parameter measurements under different bias conditions. It has been found that this approach can improve the simulation of intrinsic part of the transistor, which is very important for small- and large-signal modeling process.
Abstract: In this paper, Backstepping method is proposed to synchronize two fractional-order systems. The simulation results show that this method can effectively synchronize two chaotic systems.
Abstract: This work aims to generalize the integer order Sallen-Key filters into the fractional-order domain. The analysis in the case of two different fractional-order elements introduced where the general transfer function becomes four terms which is unusual in the conventional case. In addition, the effect of the transfer function parameters on the filter poles and hence the stability is introduced and closed forms for the filter critical frequencies are driven. Finally, different examples for the fractional order Sallen-Key filter design are presented with circuit simulations using ADS where a great matching between the numerical and simulation results is obtained.
Abstract: A novel and efficient approach to realize
fractional-order capacitors is investigated in this paper. Meanwhile, a
new approach which is more efficient for semiconductor
implementation of fractional-order capacitors is proposed. The
feasibility of the approach has been verified with the preliminary
measured results.
Abstract: This paper analyses the performance of a genetic algorithm using a new concept, namely a fractional-order dynamic fitness function, for the synthesis of combinational logic circuits. The experiments reveal superior results in terms of speed and convergence to achieve a solution.
Abstract: In process control applications, above 90% of the
controllers are of PID type. This paper proposed a robust PI
controller with fractional-order integrator. The PI parameters were
obtained using classical Ziegler-Nichols rules but enhanced with the
application of error filter cascaded to the fractional-order PI. The
controller was applied on steam temperature process that was
described by FOPDT transfer function. The process can be classified
as lag dominating process with very small relative dead-time. The
proposed control scheme was compared with other PI controller
tuned using Ziegler-Nichols and AMIGO rules. Other PI controller
with fractional-order integrator known as F-MIGO was also
considered. All the controllers were subjected to set point change and
load disturbance tests. The performance was measured using Integral
of Squared Error (ISE) and Integral of Control Signal (ICO). The
proposed controller produced best performance for all the tests with
the least ISE index.
Abstract: In this paper, a fractional-order FIR differentiator
design method using the differential evolution (DE) algorithm is
presented. In the proposed method, the FIR digital filter is designed to
meet the frequency response of a desired fractal-order differentiator,
which is evaluated in the frequency domain. To verify the design
performance, another design method considered in the time-domain is
also provided. Simulation results reveal the efficiency of the proposed
method.
Abstract: Fractional-order controller was proven to perform better than the integer-order controller. However, the absence of a pole at origin produced marginal error in fractional-order control system. This study demonstrated the enhancement of the fractionalorder PI over the integer-order PI in a steam temperature control. The fractional-order controller was cascaded with an error compensator comprised of a very small zero and a pole at origin to produce a zero steady-state error for the closed-loop system. Some modification on the error compensator was suggested for different order fractional integrator that can improve the overall phase margin.
Abstract: In this paper, the finite-time stabilization of a class of multi-state time delay of fractional-order system is proposed. First, we define finite-time stability with the fractional-order system. Second, by using Generalized Gronwall's approach and the methods of the inequality, we get some conditions of finite-time stability for the fractional system with multi-state delay. Finally, a numerical example is given to illustrate the result.
Abstract: This paper analyses the performance of a genetic algorithm using a new concept, namely a fractional-order dynamic fitness function, for the synthesis of combinational logic circuits. The experiments reveal superior results in terms of speed and convergence to achieve a solution.
Abstract: In this paper, some brief sufficient conditions for the stability of FO-LTI systems dαx(t) dtα = Ax(t) with the fractional order are investigated when the matrix A and the fractional order α are uncertain or both α and A are uncertain, respectively. In addition, we also relate the stability of a fractional-order system with order 0 < α ≤ 1 to the stability of its equivalent fractional-order system with order 1 ≤ β < 2, the relationship between α and β is presented. Finally, a numeric experiment is given to demonstrate the effectiveness of our results.
Abstract: This paper at first presents approximate analytical
solutions for systems of fractional differential equations using the
differential transform method. The application of differential
transform method, developed for differential equations of integer
order, is extended to derive approximate analytical solutions of
systems of fractional differential equations. The solutions of our
model equations are calculated in the form of convergent series with
easily computable components. After that a drive-response
synchronization method with linear output error feedback is
presented for “generalized projective synchronization" for a class of
fractional-order chaotic systems via a scalar transmitted signal.
Genesio_Tesi and Duffing systems are used to illustrate the
effectiveness of the proposed synchronization method.