Trajectory Tracking Control for Reaction–Diffusion System with Time Delay Using P-Type Iterative Learning Method
Round 1
Reviewer 1 Report
The paper “Trajectory tracking control for reaction-diffusion system with time delay using P-type iterative learning method” proposes new algorithm for tracking required trajectory for a system described by partial differential equation. The paper is well-written, clear from mathematical point of view and it is scientifically sound. The paper can be accepted for publication after the authors address a few questions and suggestions to improve the clarity of the text.
Usually Lyapunov-Krasovsky based control implies a certain Lyapunov function, not a ‘functional’.
Page 2, line 65. If ‘A’ is a symmetric matrix, then ‘AT’ is the same matrix. Please, clarify the meaning of the notation.
In eq. (1) the meaning of first term z_x_x(x,t)_x_x is not clear. Is it a typo?
It will add the clarity to the text of the authors will add some example of the control actuators that work according to eq. (7) and Fig. 1. How does it work from an engineering point of view? Is it necessary that g(x)=c(x) as in the eq. (7), i.e. the sensor and actuators distribution are the same?
In eq. (20) the control at (k+1)-step is calculated using the output error at the same (k+1)-step. How the error could be known before the control implementation?
The figures 2, 4, 5 and 6 should be zoomed to increase the readability.
The comparison analysis of the figures 4 and 6 should be added in the text. Why does the closed-loop control have the worse performance, its output errors are greater than that for the open-loop control?
Author Response
Please see the attachment.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The current paper proposes to deal with a tracking control problem for a class of unstable reaction diffusion system with time delay by using iterative learning algorithms to make the infinite dimensional repetitive motion system track the desired trajectory. The theory was validated using simulations.
Comments to author:
- Please review correct the paper since there are many spelling mistakes.
- Please add more details of how the theory from the previous sections is applied is applied in the results section.
- Please specify the sampling time.
- Please specify the controller parameters and how the parameters were obtained.
- Please add the units of measurement both abscissa and orderly in all figures.
- The authors could add a paragraph with the advantages and the disadvantages of the proposed method.
- The state of the art could be improved using some control techniques that can be used on this process:
o Hybrid Data-Driven Fuzzy Active Disturbance Rejection Control for Tower Crane Systems, European Journal of Control, vol. 58, pp. 373-387, 2021.
o Multi-Agent-Based Data-Driven Distributed Adaptive Cooperative Control in Urban Traffic Signal Timing, Energies, vol. 12, no. 7, pp. 1–19, 2019.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
The current paper has been seriously improved. The authors answered to all my concerns with explicit answers and from my point of view the paper deserves to be published in Actuators journal.
