• East Asian mathematical journal
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• v.34 no.3
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• pp.295-303
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• 2018

Gautam et al. [9] introduced the multivariable A-function, which is very general, reduces to yield a number of special functions, in particular, the multivariable H-function. Here, first, we aim to establish two very general integral formulas involving product of the general class of Srivastava multivariable polynomials and the multivariable A-function. Then, using those integrals, we find a solution of partial differential equations of heat conduction at zero temperature with radiation at the ends in medium without source of thermal energy. The results presented here, being very general, are also pointed out to yield a number of relatively simple results, one of which is demonstrated to be connected with a known solution of the above-mentioned equation.

• Journal of the Korean Institute of Telematics and Electronics
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• v.27 no.6
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• pp.921-928
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• 1990

A multivariable equalizer is designed which compensates transmission distortion for coaxial transmission line. The characteristic transfer function with bilateral parameter domain is approximated using the expansion method of orthonormal function and Gram Schmidt orthogonal function, but the parameter domain of approximated function is limited to unilateral. To solve that problem, Bode type transfer function is used to give bilateral variable characteristic to approximated function. The multivariable equalizer in this paper can be substituted for the current equalizer which consist of a fixed equalizer and a variable equalizer.

• Kyungpook Mathematical Journal
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• v.47 no.4
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• pp.495-500
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• 2007

The aim of this paper is to derive a fractional derivative of the multivariable H-function of Srivastava and Panda [7], associated with a general class of multivariable polynomials of Srivastava [4] and the generalized Lauricella functions of Srivastava and Daoust [9]. Certain special cases have also been discussed. The results derived here are of a very general nature and hence encompass several cases of interest hitherto scattered in the literature.

• Nuclear Engineering and Technology
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• v.55 no.3
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• pp.850-860
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• 2023

An industrial control process multiple-input multiple-output (MIMO) coupled system is analyzed in this study as an example of a Loss of Coolant Accident (LOCA) simulation system. Ordinary control algorithms can complete the steady state of the control system and even reduce the response time to some extent, but the entire system still consumes a large amount of energy after reaching the steady state. So a multivariable decoupled energy-saving control method is proposed, and a novel energy-saving function (economic function, Eco-Function) is specially designed based on the active disturbance rejection control algorithm. Simulations and LOCA simulation system tests show that the Eco-function algorithm can cope with the uncertainty of the multivariable system's internal parameters and external disturbances, and it can save up to 67% of energy consumption in maintaining the parameter steady state.

• Kyungpook Mathematical Journal
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• v.50 no.2
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• pp.229-235
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• 2010

In the present paper, we obtain a new formula for the generalized Weyl differintegral operator in a compact form avoiding the occurrence of infinite series and thus making it useful in applications. Our findings provide interesting generalizations and unifications of the results given by several authors and lying scattered in the literature.

• International Journal of Computer Science & Network Security
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• v.21 no.8
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• pp.212-218
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• 2021

The Proportional Integral Derivative (PID) controller is the most popular industrial controller and more than 90% process industries use this controller. During the past 50 years, numerous good tuning methods have been proposed for Single Input Single Output Systems. However, design of PI/PID controllers for multivariable processes is a challenge for the researchers. A comparative study of three PID controllers design methods has been carried-out. These methods include the DS (Direct Synthesis) method, IMC (Internal model Control) method and ETF (Effective Transfer Function) method. MIMO PID controllers are designed for a number of 2×2, 3×3 and 4×4 process models with multiple delays. The performance of the three methods has been evaluated through simulation studies in Matlab/Simulink environment. After extensive simulation studies, it is found that the Effective Transfer Function (ETF) Method produces better output responses among two methods. In this work, only decentralized methods of PID controllers have been studied and investigated.

• International Journal of Computer Science & Network Security
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• v.21 no.9
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• pp.11-18
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• 2021

The Proportional Integral Derivative (PID) controller is the most popular industrial controller and more than 90% process industries use this controller. During the past 50 years, numerous good tuning methods have been proposed for Single Input Single Output Systems. However, design of PI/PID controllers for multivariable processes is a challenge for the researchers. A comparative study of three PID controllers design methods has been carried-out. These methods include the DS (Direct Synthesis) method, IMC (Internal model Control) method and ETF (Effective Transfer Function) method. MIMO PID controllers are designed for a number of 2×2, 3×3 and 4×4 process models with multiple delays. The performance of the three methods has been evaluated through simulation studies in Matlab/Simulink environment. After extensive simulation studies, it is found that the Effective Transfer Function (ETF) Method produces better output responses among two methods. In this work, only decentralized methods of PID controllers have been studied and investigated.

• Journal of Institute of Control, Robotics and Systems
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• v.5 no.7
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• pp.808-813
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• 1999

A fuzzy learning method to control an unstable and multivariable system is presented in this paper, Because the multivariable system has generally a coupling effect between the inputs and outputs, it is difficult to find its modeling equation or parameters. If the system is unstable, initial condition rules are needed to make it stable because learning is nearly impossible. Therefore, this learning method uses the initial rules and introduces a cost function composed of the actual error and error-rate of each output without the modeling equation. To minimize the cost function, we experimentally got the Jacobian matrix in the operating point of the system. From the Jacobian matrix, we can find the direction of the convergence in the learning, and the optimal control rules are finally acquired when the fuzzy rules are updated by changing the portion of the errors and error rates.

• 제어로봇시스템학회:학술대회논문집
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• 1986.10a
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• pp.238-243
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• 1986

Distillation columns are widely used in almost every chemical plant. The use of multivariable control for such units is attractive because of the strong interactions exhibited between outputs and inputs and the desire to control simultaneously both top and bottom products. In this research design of a robust multivariable controller for distillation column was considered; output feedback controller with proportional and integral modes was designed using pole assignment. The transfer function matrix was obtained by fitting the step response realtions between single input double output pairs of variables. This matrix was then converted to linear time invariant state space model by multivariable realization technique. With the proposed multivariable proportional and integral controller applied to the process, the result of the digital computer simulation showed a good performance of asymtotic tracking. The limited experimental performance of this multivariable control was compared with the result from simulation. It was found that the proposed controller performed satisfactorily for the distillation column which separated binary mixture of methanol and water.

• Kyungpook Mathematical Journal
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• v.45 no.2
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• pp.153-159
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• 2005

In the present paper, we obtain two Theorems connecting the unified fractional integral operators and the Laplace transform. Due to the presence of a general class of polynomials, the multivariable H-function and general functions ${\theta}$ and ${\phi}$ in the kernels of our operators, a large number of (new and known) interesting results involving simpler polynomials (which are special cases of a general class of polynomials) and special functions involving one or more variables (which are particular cases of the multivariable H-function) obtained by several authors and hitherto lying scattered in the literature follow as special cases of our findings. Thus the Theorems obtained by Srivastava et al. [9] follow as simple special cases of our findings.