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![The result of the sine and cosine functions in (36) and (37) for the next stage [26].](publication/347295181/figure/fig1/AS:1024114789732352@1621179401329/The-result-of-the-sine-and-cosine-functions-in-36-and-37-for-the-next-stage-26.png)
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![Figure 7. Sine and cosine functions within the range of [−2, 2] allow a...](publication/347295181/figure/fig2/AS:1024114789732357@1621179401493/Sine-and-cosine-functions-within-the-range-of-2-2-allow-a-way-to-move-around-inside_Q320.jpg)
The focus of present research endeavor was to design a robust fractional-order proportional-integral-derivative (FOPID) controller with specified phase margin (PM) and gain cross over frequency (ωgc) through the reduced-order model for continuous interval systems. Currently, this investigation is two-fold: In the first part, a modified Routh approx...
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... MOR techniques have also been extended to reduce interval systems [2,4,5,[11][12][13][15][16][17][18]. However, the techniques presented for interval systems are limited in number. ...
In this contribution, two general expressions for Markov parameters (MPs) and time moments (TMs) of continuous interval systems (CISs) are proposed. The TMs and MPs are derived in such a way that they do not require the inversion of the denominator of the transfer function of a given system. Additionally, there is no requirement for the solution of interval equations for obtaining TMs and MPs. The applicability of derived TMs and MPs is shown with the help of CIS model order reduction (MOR). The method utilized for the CIS MOR is the Routh-Padé approximation. The whole MOR procedure is explained with the help of one test case where the third-order system is reduced to first-order and second-order models. To establish the efficacy of the proposed method, the step and impulse responses of the system and model are plotted. For a fair comparative study, time domain specifications such as the peak value, rise time, settling time, peak time and steady-state value for the lower and upper limits of the model are presented. Furthermore, the integral-square-error, integral-absolute-error, integral of time multiplied absolute-error, and integral of time multiplied square-error for the difference between the responses of the system and model are tabulated. The results presented prove the applicability and effectiveness of the proposed method.
... Frequency domain techniques are frequently applied due to their simple analysis and application (Chinesta et al., 2011). These MOR techniques are further applied for reduction of interval systems as well (Soliman, 2016;Lien et al., 2019;Singh et al., 2017;Bandyopadhyay et al., 2008;Deveerasetty and Nagar, 2020;Singh and Chandra, 2010;Singh et al., 2020Dewangan et al., 2020;Bokam et al., 2020aBokam et al., , 2020bPadhy et al., 2020). But application of these reduction techniques is very limited for interval systems. ...
... Frequency domain techniques are frequently applied due to their simple analysis and application (Chinesta et al., 2011). These MOR techniques are further applied for reduction of interval systems as well (Soliman, 2016;Lien et al., 2019;Singh et al., 2017;Bandyopadhyay et al., 2008;Deveerasetty and Nagar, 2020;Singh and Chandra, 2010;Singh et al., 2020Dewangan et al., 2020;Bokam et al., 2020aBokam et al., , 2020bPadhy et al., 2020). But application of these reduction techniques is very limited for interval systems. ...
This paper proposes method of reduced order modeling for Cuk converter using state-space-averaging (SSA) technique in which combined state-space description is obtained and output to control for Cuk converter transfer function is determined. However, there may be some variation in parameters of system due to uncertainties and imperfect modelling that are addressed using interval modeling. Thus obtained interval model is reduced further using Kharitonov polynomials. Routh-Padé approximation is employed for model order reduction. This procedure of model order reduction is explained for Cuk converter model. Fourth-order system is reduced to its respective first, second and third-order reduced models. To signify efficacy of technique proposed, frequency and step responses of models and system are plotted. Comparative study is performed using time domain specifications. Further, difference between responses of model and system are presented in terms of performance indices. The results prove effectiveness and simplicity of proposed technique.
Designing a controller for higher-order system is tough, as the system order grows, mathematical analysis gets more complicated and time-consuming. As a result, it is preferable to reduce higher-order systems to lower-order systems. A new stability preserving order reduction approach is proposed in this paper for the reduction of higher order multi input multi output (MIMO) continuous time systems. With the help of bilinear transformation technique, the proposed method becomes more flexible compared to available conventional methods. It is a one to one transformation from s-domain to z-domain and vice-versa. This method is free of aliasing effect. This method always generates stable reduced order models for stable high order systems which can be used for the stability analysis and design of high order MIMO continuous time systems. The method is extended for the design of proportional integral derivative (PID), fractional order PID (FOPID) controllers tuned by Genetic Algorithm (GA). From the results, it can be observed that GA tuned FOPID gives less settling time than the GA tuned PID and auto tuned PID.
In the current paper, a hybrid Tilt-Derivative Tilt-Integral (TD-TI) controller is added to the synchronous generator automatic voltage regulation (AVR) system to improve the rotor angle stability of a three-machine system and damp the power system oscillations. Moreover, the Sine Cosine algorithm (SCA), a relatively new robust optimization technique is used to tune the proposed controller parameters. The SCA based TD-TI controller results are presented in the form of time domain simulation using MATLAB. The proposed controller response is compared with the normal AVR excitation controller on the IEEE three-machine system. Simulation results show the effectiveness of the proposed controller in damping the oscillations of rotor speed and terminal voltage of the three machines when the system is subjected to three phase short circuit.
