Robust Design of Tilted Integral Derivative Controller for Non-integer Order Processes with Time Delay

Gnaneshwar, Kurnam; Padhy, Prabin Kumar

doi:10.1080/03772063.2021.2004462

Cited by 7 publications

(10 citation statements)

References 37 publications

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“…Remark 1. Some examples of identified physical systems as Equation ( 1) are a coupled-tanks apparatus [28], a heat flow equipment [29], DC-servo systems [30] and laboratory temperature control setups [31].…”

Section: Preliminariesmentioning

confidence: 99%

“…, n ∈ ℕ, the characteristic function of the closed-loop control system can be obtained as (31) We will present a useful definition (Definition 4) used in analyzing the robust stability of the system.…”

Section: Case Ofmentioning

confidence: 99%

“…

\begin{equation} \begin{aligned} &C(s) =\frac{N_c(s)}{s^{\lambda }}=\frac{k_p s^{\lambda } + k_i + k_d s^{\mu +\lambda }}{s^\lambda },\\ & 0&lt;\lambda , \mu &lt;2, \alpha _n &gt; \mu . \end{aligned} \end{equation}

Remark Some examples of identified physical systems as Equation (1) are a coupled‐tanks apparatus [28], a heat flow equipment [29], DC‐ servo systems [30] and laboratory temperature control setups [31]. …”

Section: Preliminariesmentioning

confidence: 99%

“…Despite the extensive study concerning the problem of robustly calculating the stabilizing region of FOPID controllers for fractional-order systems having time delay [21][22][23][24][25][26], a valid mathematical proof of calculating the value set for these systems seems to be elusive. It should be noted that, for the interval fractional-order plants with an interval time delay, the study of the stabilizing region of FOPID controllers has not been well elaborated and it is a renewed research area.…”

Section: Introductionmentioning

confidence: 99%

“…The method proposed in this paper can investigate such characteristic functions having interval plant with an interval time delay.Example 3. In[31], the following fractional-order plant has been identified for an laboratory temperature control setup. P (s) = 0.63705 72.995 s 0.81166 + 1 e −15.513s .…”

mentioning

confidence: 99%

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Robust stabilization of interval fractional‐order plants with an interval time delay by fractional‐order proportional integral derivative controllers

Ghorbani,

Tepljakov,

Petlenkov

2023

IET Control Theory & Appl

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This paper concentrates on presenting a reliable procedure to compute the stabilizing region of fractional‐order proportional integral derivative (FOPID) controllers for interval fractional‐order plants having an interval time delay. An interval fractional‐order plant is defined as a fractional‐order transfer function whose denominator and numerator coefficients are all uncertain and lie in specified intervals. Also, an interval time delay points to a delay term whose value varies in a specific interval. The D‐decomposition technique and the value set concept are employed to determine the stabilizing region of FOPID controllers. In this study, first, a theorem is presented to compute the boundary of the value sets of systems having interval time day. Then, a lemma is provided for robust stability analysis of the given closed‐loop control system. For a convenient use of the paper results, an algorithm is proposed to solve the problem of robustly stabilizing interval fractional‐order plants with an interval time delay using FOPID controllers. Finally, four examples are provided to illustrate the proposed procedure.

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Section: Preliminariesmentioning

confidence: 99%

Section: Case Ofmentioning

confidence: 99%

“…

\begin{equation} \begin{aligned} &C(s) =\frac{N_c(s)}{s^{\lambda }}=\frac{k_p s^{\lambda } + k_i + k_d s^{\mu +\lambda }}{s^\lambda },\\ & 0&lt;\lambda , \mu &lt;2, \alpha _n &gt; \mu . \end{aligned} \end{equation}

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Robust stabilization of interval fractional‐order plants with an interval time delay by fractional‐order proportional integral derivative controllers

Ghorbani,

Tepljakov,

Petlenkov

2023

IET Control Theory & Appl

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Non-parametric fractional-order controller design for stable process based on modified relay

Gnaneshwar,

Kumar,

Sharma

et al. 2024

Journal of Control and Decision

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Fractional Dual-Tilt Control Scheme for Integrating Time Delay Processes: Studied on a Two-Tank Level System

Das,

Chakraborty,

Mehta

et al. 2024

IEEE Access

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Industrial processes of time delayed integrating type require sophisticated control methods because of their non-self-regulating nature. Literature presents fractional order controllers as possible solution to this problem and there is scope for further enhancing the performance of the existing solutions. Though fractional order controllers are capable of outperforming their integer order counterparts, it is evident in literature that the former controller designs are complex and hence analytical tuning procedures for the same are scarce. Hence, this paper presents a novel predictive strategy for time-delayed integrating processes based on two fractional-order tilt-derivative (FOT α D 1−α ) controllers. These controllers are analytically designed with only two tunable parameters. These tuneables are computed using gain-and phase-margin specifications. In contrast to the previous methods, the presented scheme is more capable of eliminating input-load disturbances without adding complexity in terms of tunable parameters. In addition to the investigations carried out using three difficult benchmark plant models, the present design is also experimentally validated using a two-tank level control system to vindicate its efficacy. Through robust stability analysis, it is shown that the suggested strategy is capable of achieving stable closed-loop responses amid upto 50% perturbation in plant parameters.

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Robust Design of Tilted Integral Derivative Controller for Non-integer Order Processes with Time Delay

Cited by 7 publications

References 37 publications

Robust stabilization of interval fractional‐order plants with an interval time delay by fractional‐order proportional integral derivative controllers

Robust stabilization of interval fractional‐order plants with an interval time delay by fractional‐order proportional integral derivative controllers

Non-parametric fractional-order controller design for stable process based on modified relay

Fractional Dual-Tilt Control Scheme for Integrating Time Delay Processes: Studied on a Two-Tank Level System

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