A low-order approximation method for fractional order PID controllers

Birs, Isabela; Muresan, Cristina I.; Ghita, Maria; Ionescu, Clara M.; Keyser, Robin De

doi:10.1109/cdc51059.2022.9992458

Cited by 1 publication

(4 citation statements)

References 29 publications

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“…A low order approximation technique of a FO controller using a metaheuristic approach is developed in [15]. Another reduced-order representation of FO-PIDs starting from ORA approximation is designed in [16]. In terms of numerical implementation, a discrete-time and low-order approximation method for FO-PID controllers is presented in [17].…”

Section: A Literature Reviewmentioning

confidence: 99%

“…2 Solve the optimization problem (17) using the D-K iteration approach [8]. 3 Starting from the initial approximation order N , find N ⋆ by solving (16). 4 Use N ⋆ to find the initial feasible point K N ⋆ .…”

Section: A Example Imentioning

confidence: 99%

“…The initial ORA approximation of the FO-PID controller ( 22) is of order 12. After solving the optimization problem (16), the value of N cannot further decrease, as a further reduction of N leads to an upper SSV bound of 1.4176 and, as such, RS and RP will not be guaranteed anymore. Therefore, the input for Algorithm 1 becomes the initially designed ORA approximation of order 12.…”

Section: A Example Imentioning

confidence: 99%

“…The considered controller family K is: The initial ORA approximation K ORA (s) of the FO-PID controller (28) is of order 14. After solving the optimization problem (16), the optimal value of the order of approximation is N ⋆ = 4, resulting a controller K N ⋆ (s) having order 10, which is also input for the Algorithm 1. After applying this algorithm, the FO-PID controller's representation K red is reduce to a 4th order controller, obtaining an upper bound of the SSV of 0.9549 < 1.…”

Section: B Example IImentioning

confidence: 99%

See 3 more Smart Citations

Reduced-Order Approximation of Fractional-Order Controllers by keeping Robust Stability and Robust Performance

Mihaly

Şuşcă

Birs

et al. 2023

2023 American Control Conference (ACC)

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Recently, the fractional-order element has been integrated into the Robust Control Framework considering the Oustaloup method. As such, the resulting infinite impulse response approximation manages to satisfy the robust stability and the robust performance criteria according to a given uncertainty block. However, the recommended approximation order for each fractional-order element is the number of decades of the frequency range where the approximation is valid, which can lead to a high-order controller. The current paper describes an optimization-based technique to find a loworder approximation of a fractional-order controller such that the resulting controller maintains the robust stability and robust performance as well. A set of numerical experiments have also been performed in order to illustrate the proposed method.

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Section: A Literature Reviewmentioning

confidence: 99%