Tuning of Model Predictive Controllers Based on Hybrid Optimizationâ€
Round 1
Reviewer 1 Report
i am grateful for the opportunity to review your manuscript.
i acknowledge and appreciate the effort that has gone in to elaborating upon and updating your earlier work from 2019.
i note that you have included recent bibliographic references, and that you have refined your original design shared during the 2019 symposium (eg, executing GAM before VNS, and the removal of the optimisation stage (with adequate justification)).
i am satisfied with the manuscript, and i draw your attention only to a typographical error in the MPCT in Figure 5, where 'hybrid' is misspelt.
Author Response
We thank the reviewer for the comments and contributions, and we are pleased that you liked our work. We have corrected the typographical error in Figure 5.
Reviewer 2 Report
This paper proposes a tuning method for MPC based on hybrid optimization. The motivation of the study is convincing, and simulation results well supported the effectiveness of the proposed method. However, I think the following issues should be addressed to clarify the contributions of this paper.
- Please clarify the intended function of the first term in eq. (7). Is it for assuring robustness again model uncertainties?
- It would be nice if the authors could explain what makes the MPC tuned by the proposed method robust to modeling errors (in Fig. 9-16).
- The authors refer to the open-loop response as the optimized trajectory. In my opinion, this is not very clear because the optimized trajectory implies the ideal one but the open-loop trajectory is not ideal (as shown in Fig. 6).
- The authors claim that the proposed method has a low computational cost and satisfactory responses. Can this performance be presented quantitatively compared to the existing method?
- The proposed method is based on sequential optimization. Can the sequential optimization ensure convergence to the optimum? In addition, Section 3.1 only explains several possibilities of the proposed method to be a robust method but does not include an analytic approach. Is it possible to handle the convergence issue more rigorously?
- On p.14, line 392, the authors mention that the selected prediction and control horizons are the minimum value. How can you guarantee this?
- What if the VNS fails to find the solution even with the third-order search?
- The authors explain that the GAM is solved by sequential quadratic programming (SQP). I think the tuning of the SQP is also a difficult task to guarantee convergence for a complex optimization problem. If another tuning is required for MPC tuning, can we say that the proposed scheme is useful?
Author Response
Reviewer: This paper proposes a tuning method for MPC based on hybrid optimization. The motivation of the study is convincing, and simulation results well supported the effectiveness of the proposed method. However, I think the following issues should be addressed to clarify the contributions of this paper.
Answer: We thank the reviewer for the valuable comments and contributions.
Reviewer: Please clarify the intended function of the first term in eq. (7). Is it for assuring robustness again model uncertainties?
Answer: We have added a note in Equation (7) to clarify the function fulfilled by the first term of the equation. This first term is used to establish the performance criteria desired by the user. In turn, this term ensures the robustness of the controller against model uncertainties, as detailed by the reviewer.
Reviewer: It would be nice if the authors could explain what makes the MPC tuned by the proposed method robust to modeling errors (in Fig. 9-16).
Answer: We have added an explanation of how the MPCT manages to maintain the robustness of the control system. The controller is robust in the presence of modeling errors in case 2. In this case, the user establishes a conservative dynamic for the algorithm, which allows the MPCT to calculate the weighting matrices of the objective function in order to establish a moderate control action, avoiding entering sudden changes on the system that takes it to the instability zone.
Reviewer: The authors refer to the open-loop response as the optimized trajectory. In my opinion, this is not very clear because the optimized trajectory implies the ideal one but the open-loop trajectory is not ideal (as shown in Fig. 6).
Answer: We have modified the term "optimized trajectory" by the word "output trajectory at the first optimization, y_o(k|1)" to avoid confusion and adequately reference open-loop dynamics.
Reviewer: The authors claim that the proposed method has a low computational cost and satisfactory responses. Can this performance be presented quantitatively compared to the existing method?
Answer: We have added a paragraph on page 14 where we quantitatively compare the computational cost of our proposal against other proposals reported in the literature for the Shell Heavy Oil Fractionator case study.
Reviewer: The proposed method is based on sequential optimization. Can the sequential optimization ensure convergence to the optimum? In addition, Section 3.1 only explains several possibilities of the proposed method to be a robust method but does not include an analytic approach. Is it possible to handle the convergence issue more rigorously?
Answer: The objective of using sequential optimization is to find the most suitable parameters for the MPC controller using a less complex optimization strategy than a mixed-integer optimization. These parameters will largely depend on the dynamics desired by the user. In this proposal, the VNS method tries to find the most suitable length for the horizons with the objective that, from the first optimization, the controller finds the most suitable trajectory for the process. The GAM method tries to find the weighting matrices to adjust the dynamics to the desired trajectory by the user. However, since the GAM algorithm is a multi-objective method that gives information about handling trade-offs between different criteria, there is no unique optimum. The proposed method helps trade-offs with loop sensitivity, performance speeds, and system robustness by sequentially employing these two optimization methods to approximate an effective solution.
Reviewer: On p.14, line 392, the authors mention that the selected prediction and control horizons are the minimum value. How can you guarantee this?
Answer: The reviewer is correct. We have removed the claim that the VNS found the minimum values of the horizons. In this case, the VNS algorithm finds appropriate lengths to have similar trajectories between the first optimization and the closed-loop control with small values for both horizons, based on its search strategy, taking as reference the internal model of the controller.
Reviewer: What if the VNS fails to find the solution even with the third-order search?
Answer: If the third-order search is executed and the algorithm does not find another solution, then the VNS method selects the horizons with the lowest cost found in its search. We add this note on page 9.
Reviewer: The authors explain that the GAM is solved by sequential quadratic programming (SQP). I think the tuning of the SQP is also a difficult task to guarantee convergence for a complex optimization problem. If another tuning is required for MPC tuning, can we say that the proposed scheme is useful?
Answer: We have used the Matlab routine fgoalattain to solve GAM, which employs a well-tuned SQP algorithm. This algorithm has a modified merit function in the line search and a modified Hessian, which takes advantage of the special structure of this problem. However, any other NLP algorithm could be used to solve GAM in order to circumvent the eventual convergence problem. The objective function formulation of the MPC controller is a weighted multi-objective problem with competitive objectives. Depending on the importance of these objectives within the control problem, the weights are established for each objective. For example, in the case studies, different tunes were established where the behavior of the variables was analyzed in face of the MPC parameters found. Thus, if another tuning is required, the desired dynamics and constraints must be specified in the MPCT. In this context, the proposed tuning scheme is helpful because, despite the complexity of the problem, it manages to provide a solution according to the user's needs. Note that this algorithm is initially intended to find controller parameters offline.
Round 2
Reviewer 2 Report
This version is acceptable for publication.
