Impulsive semilinear heat equation with delay in control and in state

Camacho, Oscar; Leiva, Hugo

doi:10.1002/asjc.2017

Cited by 37 publications

(16 citation statements)

References 51 publications

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“…However, a limited amount of work is also available on approximate controllability. Camacho and Leiva 30 proved the approximate controllability for semilinear impulsive heat equation:

({, \begin{matrix} array ζ^{'} (ℏ) = - A ζ (ℏ) + B_{ω} \tilde{v} (ℏ - γ_{1}) + f^{e} (ℏ, ζ_{ℏ} (- γ), \tilde{v} (ℏ)), ℏ \in [0, \tilde{r}], ℏ \neq ℏ_{k}, \\ array ζ (ℏ) = ϕ (ℏ), ℏ \in [- γ, 0], \\ array \tilde{v} (ℏ) = {\tilde{v}}_{0} (ℏ), ℏ \in [- γ_{1}, 0], \\ array ζ (ℏ_{k}^{+}) = ζ (ℏ_{k}^{-}) + ℑ_{k}^{e} (ℏ_{k}, ζ (ℏ_{k}), \tilde{v} (ℏ_{k})), k = 1,2, 3, \dots, p, \end{matrix})

where

\overset{v}{true} \in frakturC false(false[0, \overset{r}{true} false]; {frakturℜ}^{m} false), ϕ \in frakturC, <...>

…”

Section: Introductionmentioning

confidence: 99%

Controllability and stability analysis of an oscillating system with two delays

Shah

Zada

2021

Math Methods in App Sciences

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In the current article, controllability and stability analysis of a system of differential equations is investigated. The system is governed by semilinear impulsive differential equations of second order with two delays. Controllability is studied using Rothe's fixed point theory while stability analysis is carried out with the help of Grönwall inequality and some other conditions. Fixed point approach is incorporated in determination of uniqueness of solution.

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“…However, a limited amount of work is also available on approximate controllability. Camacho and Leiva 30 proved the approximate controllability for semilinear impulsive heat equation:

({, \begin{matrix} array ζ^{'} (ℏ) = - A ζ (ℏ) + B_{ω} \tilde{v} (ℏ - γ_{1}) + f^{e} (ℏ, ζ_{ℏ} (- γ), \tilde{v} (ℏ)), ℏ \in [0, \tilde{r}], ℏ \neq ℏ_{k}, \\ array ζ (ℏ) = ϕ (ℏ), ℏ \in [- γ, 0], \\ array \tilde{v} (ℏ) = {\tilde{v}}_{0} (ℏ), ℏ \in [- γ_{1}, 0], \\ array ζ (ℏ_{k}^{+}) = ζ (ℏ_{k}^{-}) + ℑ_{k}^{e} (ℏ_{k}, ζ (ℏ_{k}), \tilde{v} (ℏ_{k})), k = 1,2, 3, \dots, p, \end{matrix})

where

\overset{v}{true} \in frakturC false(false[0, \overset{r}{true} false]; {frakturℜ}^{m} false), ϕ \in frakturC, <...>

…”

Section: Introductionmentioning

confidence: 99%

Controllability and stability analysis of an oscillating system with two delays

Shah

Zada

2021

Math Methods in App Sciences

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“…The classical PID-type control techniques do not provide acceptable results when working with processes that present elevated delay [5] or inverse response processes [4]. It is well known that PID controllers are by far the most applied form of feedback in use.…”

Section: Introductionmentioning

confidence: 99%

A Comparison of Linear and Nonlinear PID Controllers Reset-Based for Nonlinear Chemical Processes with Variable Deadtime

Diaz

Camacho

2021

Communications in Computer and Information Science

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This work presents an analysis, design, and comparison of the PI (Proportional and Integral) controller and control schemes PI linear and nonlinear controllers reset-based. The parameters of these control schemes have been set by trial and error to finally be tested in a nonlinear process with variable dead time. Controller performance is measured using integral square error (ISE), integral time square error (ITSE), total variations of control efforts (TVU), maximum overshoot (M p ) and settling time (t s ). The results show that reset control systems overcome fundamental limitations coming from linear control systems.

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“…On the other hand, the PID controllers' accomplishment is bounded in complex systems [2], [3]. One of the most critical process control problems is time delays [7]. It could cause some low-performance errors, non-convenient controller complexity, and systems instability, also if the systems contain varying time delays, produced as mixing consequences, wireless data communication protocols, or measurement lines.…”

Section: Introductionmentioning

confidence: 99%

“…It could cause some low-performance errors, non-convenient controller complexity, and systems instability, also if the systems contain varying time delays, produced as mixing consequences, wireless data communication protocols, or measurement lines. Sometimes, it could lead to poor stability and performance, and classical control cannot control the process [7].…”

Section: Introductionmentioning

confidence: 99%

Regulation of Nonlinear Chemical Processes with Variable Dead Time: a Generalized Proportional Integral Controller Proposal

Chacón¹,

Vallejo²,

Herrera³

et al. 2021

International Journal on Advanced Science, Engineering and Information Technology

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This work shows the development and application of a Generalized Proportional Integral (GPI) Controller based on a FirstOrder Plus Dead Time (FOPDT) approximation for an industrial chemical process. GPI control is a relatively recent advancement in automatic control. Nowadays, several enhancements with the GPI technique come from integral reconstructions of the system states. Chemical engineering processes present numerous challenging control problems, including nonlinear dynamic behavior. GPI can become a new option to consider in industrial applications since, along with the arrival of Industry 4.0, there are many improvements in computers and automation architecture to implement controller algorithms. The new controller's functionality shows significant accessibility of mathematical and logical potential. A comparison between the GPI and a PID controller is made under the same conditions to evaluate their performance. After carrying out some tests, the GPI shows better performance and a smoother controller action when applied to the mixing tank with a variable delay than the PID. Performance indexes as Integral Square Error (ISE) for evaluating the Output Variable and Control Effort Total Variation (TVu) for evaluating the control action are used to measure performance. Finally, designing an appropriate controller like the GPI that recognizes and incorporates nonlinearities is required for chemical processes. Simulations were developed using Simulink-MATLAB.

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Impulsive semilinear heat equation with delay in control and in state

Cited by 37 publications

References 51 publications

Controllability and stability analysis of an oscillating system with two delays

Controllability and stability analysis of an oscillating system with two delays

A Comparison of Linear and Nonlinear PID Controllers Reset-Based for Nonlinear Chemical Processes with Variable Deadtime

Regulation of Nonlinear Chemical Processes with Variable Dead Time: a Generalized Proportional Integral Controller Proposal

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