Indirect iterative learning control design based on 2DOF IMC for batch processes with input delay

Cui, Jiyao; Wang, Zhihong; Chen, Yueling; Liu, Tao

doi:10.23919/chicc.2017.8027915

Cited by 5 publications

(11 citation statements)

References 20 publications

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“…Note that, in the frequency domain, the delay time in (1) can represent the input delay or the output response delay [27,29,30]. Remark 1.…”

Section: Problem Formulationmentioning

confidence: 99%

“…In the ILC literature, from an input‐output viewpoint, the tracking error of an iteration‐varying reference trajectory

r_{k} false(t false)

for a delay‐free system is given by

e_{a k} false(t false) = r_{k} false(t false) - y_{k} false(t false), \forall k \in Z

[50, 51]. The tracking error of a fixed reference trajectory

r (t)

for a time‐delay system in the presence of uncertainty in input delay

θ

is described by

e_{b k} false(t false) = r false(t - \hat{θ} false) - y_{k} false(t false), \forall k \in Z

, where

\overset{θ}{true}

is an estimate of

θ

[28–30]. Now, according to this discussion, we introduce the following definition.Definition Let us define the tracking error of an iteration‐varying reference trajectory

r_{k} false(t false)

for a time‐delay system in the presence of uncertainty in input delay

θ

as follows:

e_{k} (t) = r_{k} (t - \hat{θ}) - y_{k} (t), \forall k \in Z .

From there, the tracking error

e_{k} false(t false), \forall k \in Z

in frequency‐domain is given by

E_{k}

…”

Section: Problem Formulationmentioning

confidence: 99%

“…In the ILC literature, from an input-output viewpoint, the tracking error of an iteration-varying reference trajectory r k (t ) for a delay-free system is given by e ak (t ) = r k (t ) − y k (t ), ∀k ∈ ℤ [50,51]. The tracking error of a fixed reference trajectory r (t ) for a time-delay system in the presence of uncertainty in input delay 𝜃 is described by e bk (t ) = r (t − θ) − y k (t ), ∀k ∈ ℤ, where θ is an estimate of 𝜃 [28][29][30]. Now, according to this discussion, we introduce the following definition.…”

Section: Problem Formulationmentioning

confidence: 99%

“…By choosing an appropriate W b , one can design the controller C satisfying convergence conditions ℘ 1 , ℘ 2 and ℘ 4 using, for example, the 𝜇 -synthesis approach [53] or population-based methods [54]. However, since the proposed ILC scheme in this study is based on IMC structure, similar to other related works reported in [29,30], we are also interested in using a unified controller derived from IMC theory. To this end, we consider the controller given in [29] as follows:…”

Section: Theorem 2 a Sufficient Condition For Satisfying Conditionmentioning

confidence: 99%

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Robust iterative learning control for uncertain continuous‐time system with input delay and random iteration‐varying uncertainties

Shokri-Ghaleh

Ganjefar

Shahri

2021

IET Control Theory & Appl

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This study deals with the problem of robust iterative learning control (ILC) for linear continuous-time systems with input delay subject to uncertainties in input delay, plant dynamic, reference trajectory, initial conditions and disturbances. Using the internal model control (IMC) structure in the frequency domain, an ILC scheme is proposed in which the IMC structure is responsible for coping with uncertainties in both delay time and plant dynamic. Sufficient conditions are derived to ensure that the tracking error expectation is bounded and converges monotonically to a small neighbourhood of zero (in the L 2 -norm sense) when uncertainties in reference trajectory, initial conditions and disturbances vary randomly from trial to trial. It is shown that the derived conditions are still valid to guarantee both boundedness and monotonic convergence of the tracking error variance (in the L 2 -norm sense). Illustrative examples are provided to demonstrate the effectiveness of the proposed method.

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“…Note that, in the frequency domain, the delay time in (1) can represent the input delay or the output response delay [27,29,30]. Remark 1.…”

Section: Problem Formulationmentioning

confidence: 99%

“…In the ILC literature, from an input‐output viewpoint, the tracking error of an iteration‐varying reference trajectory

r_{k} false(t false)

for a delay‐free system is given by

e_{a k} false(t false) = r_{k} false(t false) - y_{k} false(t false), \forall k \in Z

[50, 51]. The tracking error of a fixed reference trajectory

r (t)

for a time‐delay system in the presence of uncertainty in input delay

θ

is described by

e_{b k} false(t false) = r false(t - \hat{θ} false) - y_{k} false(t false), \forall k \in Z

, where

\overset{θ}{true}

is an estimate of

θ

[28–30]. Now, according to this discussion, we introduce the following definition.Definition Let us define the tracking error of an iteration‐varying reference trajectory

r_{k} false(t false)

for a time‐delay system in the presence of uncertainty in input delay

θ

as follows:

e_{k} (t) = r_{k} (t - \hat{θ}) - y_{k} (t), \forall k \in Z .

From there, the tracking error

e_{k} false(t false), \forall k \in Z

in frequency‐domain is given by

E_{k}

…”

Section: Problem Formulationmentioning

confidence: 99%

Section: Problem Formulationmentioning

confidence: 99%

Section: Theorem 2 a Sufficient Condition For Satisfying Conditionmentioning

confidence: 99%

See 2 more Smart Citations

Robust iterative learning control for uncertain continuous‐time system with input delay and random iteration‐varying uncertainties

Shokri-Ghaleh

Ganjefar

Shahri

2021

IET Control Theory & Appl

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show abstract

“…The introduction of the 2-degree-of-freedom (2DOF) IMC structure enables the control system to achieve good tracking performance and fast disturbance rejection simultaneously [7]. This feature has made 2DOF IMC widely used in modern control problems [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

A New Approach to Compensator Design Based on Multi-Loop Technique and Scalable Forward Model Complexity

Osypiuk

2021

Electronics

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Using a compensator in the structure is one of the simplest ways to achieve efficient control of a non-linear process. Unfortunately, accessing the inverse process model is not a trivial issue. Except for some special cases, it is much easier to determine the forward process model than the inverse one. For this reason, it would be interesting to propose an alternative solution to the well-known feedforward control method. In this paper, a simple multi-loop concept will be introduced. The main idea is based on the natural (but limited) robustness offered by a single PID loop and the ability to scale up the complexity of the forward process model. The proposed structure multiplies a single PID loop including forward models with increasing complexity to calculate the resultant non-linear control value. This new approach produces a comparable performance to the feedforward method but does not require access to the inverse properties of the process. The idea was evaluated in terms of stability and robustness to parameter changes. In addition, a simulation study was carried out using two coupled non-linear processes, i.e., the position control of a robot manipulator with force interaction. The selection of this process was no casual choice. On the one hand, it is extremely complex; however, on the other hand, it provides the possibility to determine both the inverse and the forward dynamic model. This capability was helpful to perform an effective comparison of the proposed solution with the known feedforward structure.

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Novel Hybrid Iterative Learning–Fractional Predicative PI Controller for Time-Delay Systems

Devan

Hussin

Ibrahim

et al. 2022

Studies in Infrastructure and Control

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Indirect iterative learning control design based on 2DOF IMC for batch processes with input delay

Cited by 5 publications

References 20 publications

Robust iterative learning control for uncertain continuous‐time system with input delay and random iteration‐varying uncertainties

Robust iterative learning control for uncertain continuous‐time system with input delay and random iteration‐varying uncertainties

A New Approach to Compensator Design Based on Multi-Loop Technique and Scalable Forward Model Complexity

Novel Hybrid Iterative Learning–Fractional Predicative PI Controller for Time-Delay Systems

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