Dominant pole placement with fractional order PID controllers: D-decomposition approach

Mandić, Petar; Šekara, Tomislav B.; Lazarević, Mihailo P.; Bošković, Marko

doi:10.1016/j.isatra.2016.11.013

Cited by 56 publications

(20 citation statements)

References 28 publications

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“…Many real world applications of fractional calculus and differential equations exist where Bayesian methods and estimation is important. These range from viscoelastic diffusion in complex fluids [30], anomalous diffusion [31], fractional order control problems [32], biological systems [33], and a lot more [18]. Determining the accuracy of the numeric solver and its impact on inferences should be examined to ensure that the choice of numeric solver does not unduly influence any parameter inferences or predictive distributions.…”

Section: Discussionmentioning

confidence: 99%

Using the Bayesian Framework for Inference in Fractional Advection-Diffusion Transport System

Boone¹,

Ghanam²,

Malik³

et al. 2020

Int. J. of Appl. Math.

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Section: Discussionmentioning

confidence: 99%

Using the Bayesian Framework for Inference in Fractional Advection-Diffusion Transport System

Boone¹,

Ghanam²,

Malik³

et al. 2020

Int. J. of Appl. Math.

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“…[13,14]. Efficient optimization techniques are available in scientific and professional literature for tuning parameters of PID controller with empirical adopted filter time constant [15][16][17][18][19][20][21][22][23][24][25][26][27][28], while complex methods use filter time constant as an integral part of classic optimization procedure [29][30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Particle Swarm Optimization of PID Controller under Constraints on Performance and Robustness

Bošković

Rapaić²,

Jeličić³

2019

IJEEC

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This paper presents a design procedure of the PID controller where optimal parameters of controller * * * *p i d f (k ,k ,k ,T ) areobtained by solving the constrained optimization problem. The objective function is given in the form of the Integral of Absolute Error(IAE) under specifications to achieve predictable performance and robustness. The constraints within the optimization problem setupare desired maximum sensitivity, desired maximum complementary sensitivity and maximum sensitivity to measurement noise underhigh frequencies. The optimization problem is transformed to an unconstrained problem using penalty function approach. Solution tothe optimization problem is obtained using Particle Swarm algorithm (PSO) which leads to an efficient suppression of disturbance aswell as an adequate reference tracking performance of the closed-loop system with negligible overshoot. The suggested method isapplicable to the large class of stable, integral and unstable processes, processes with oscillatory dynamics with and without dead-time.Effectiveness of the proposed design procedure is verified via numerical simulations on test batch consisting of processes typicallyencountered in industry. Paper also provides two another solutions of the defined optimization problem using genetic algorithm (GA)and fminunc trust region based approach (TR). Performance of the PSO, GA, and TR based control system is compared with thoseusing recently proposed maximization of proportional gain denoted with max(kp) method. Although the present paper is focused to tunethe PID controller, the same procedure may be used to design PI controller, lead and lag compensators, high-order controllers as well asfractional-order controllers.

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“…Meanwhile, fractional-order systems can describe the dynamic characteristics of real-world systems better than can integer-order systems, owing to the property of memory (Ullah et al, 2017). The controller design becomes flexible with the introduction of fractional-order operators, such as fractional-order sliding-mode controllers (Pashaei and Badamchizadeh, 2016; Zhong et al, 2016), fractional-order iterative learning controllers and fractional-order P I λ D μ controllers (Bettayeb et al, 2017; Lamba et al, 2017; Mandic et al, 2017; Pan et al, 2016). With the development of physics and technology, many researchers have found that fractional-order systems can reveal the dynamic characteristics of many physical systems (Liu et al, 2017; Lü et al, 2017; Luo, 2015; Sedraoui et al, 2016; Wei et al, 2017).…”

Section: Introductionmentioning

confidence: 99%

Fractional-order Kalman filters for continuous-time fractional-order systems involving correlated and uncorrelated process and measurement noises

Liu

Gao

Yang

et al. 2018

Transactions of the Institute of Measurement and Control

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This paper presents fractional-order Kalman filters using the fractional-order average derivative method for linear fractional-order systems involving process and measurement noises. By using the fractional-order average derivative method, a difference equation model is obtained by discretizing the investigated continuous-time fractional-order system, and the accuracy of state estimation is improved. Meanwhile, compared with the Tustin generating function, the fractional-order average derivative method proposed in this paper can reduce computation load and save calculation time. Two kinds of fractional-order Kalman filters are given, for the correlated and uncorrelated cases, in terms of the process and measurement noises for linear fractional-order systems, respectively. Finally, simulation results are illustrated to verify the effectiveness of the proposed Kalman filters using the fractional-order average derivative method.

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Dominant pole placement with fractional order PID controllers: D-decomposition approach

Cited by 56 publications

References 28 publications

Using the Bayesian Framework for Inference in Fractional Advection-Diffusion Transport System

Using the Bayesian Framework for Inference in Fractional Advection-Diffusion Transport System

Particle Swarm Optimization of PID Controller under Constraints on Performance and Robustness

Fractional-order Kalman filters for continuous-time fractional-order systems involving correlated and uncorrelated process and measurement noises

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