이동블록 및 잔류편차 제거 모델예측제어 기법의 최적성 향상

학위논문(박사)--서울대학교 대학원 :공과대학 화학생물공학부,2020. 2. 이종민.Model predictive control (MPC) is a receding horizon control which derives finite-horizon optimal solution for current state on-line by solving an optimal control problem. MPC has had a tremendous impact on both industrial and control research areas. There are several outstanding issues in MPC. MPC has to solve the optimization problem within a sampling period so that the reduction of on-line computational complexity is a one of the main research subject in MPC. Another major issue is model-plant mismatch due to the model based predictive approach so that offset-free tracking schemes by compensating model-plant mismatch or unmeasured disturbance has been developed. In this thesis, we focused on the optimality performance of move blocking which fixes the decision variables over arbitrary time intervals to reduce computational load for on-line optimization in MPC and disturbance estimator approach based offset-free MPC which is the most standardly used method to accomplish offset-free tracking in MPC. We improve the optimality performance of move blocked MPC in two ways. The first scheme provides a superior base sequence by linearly interpolating complementary base sequences, and the second scheme provides a proper time-varying blocking structure with semi-explicit approach. Moreover, we improve the optimality performance of offset-free MPC by exploiting learned model-plant mismatch compensating signal from estimated disturbance data. With the proposed schemes, we efficiently improve the optimality performance while guaranteeing the recursive feasibility and closed-loop stability.모델예측제어는 현재 시스템 상태에 대한 유한 구간 최적해를 도출하는 온라인 이동 구간 제어 방식이다. 모델예측제어는 피드백을 통한 공정 동특성과 제약 조건을 효과적으로 반영하는 장점으로 인해 산업 및 제어 연구 분야에 큰 영향을 미쳤다. 이러한 모델예측제어에는 몇 가지 해결되어야 할 문제가 있다. 모델예측제어에서는 샘플링 기간 내에 최적화 문제를 풀어내야 하기 때문에, 온라인 계산 복잡성의 감소가 주요 연구 주제 중 하나로 활발히 연구되고 있다. 또 다른 주요 문제는 모델에 기반한 예측을 이용하는 접근 방식으로 인해 모델-플랜트 불일치로 인한 오차를 해결해야 한다는 점이며, 모델 플랜트 불일치 또는 측정되지 않은 외란을 보상하여 잔류편차 없이 참조신호를 추적하는 연구가 활발히 이루어지고 있다. 이 논문에서는 모델예측제어에서의 온라인 최적화를 위한 계산 부하를 줄이기 위해 임의의 시간 간격에 걸쳐 결정 변수를 고정시키는 이동 블록 전략의 최적성 향상에 중점을 두었으며, 또한 잔류편차를 제거하기 위해 가장 표준적으로 사용되는 외란 추정기를 이용한 잔류편차-제거 모델예측제어 기법의 최적성 향상에 중점을 두었다. 이 논문에서는 이동 블록 모델예측제어의 최적 성능을 향상시키기 위한 두 가지 전략을 제시한다. 첫 번째 전략은 이동 블록 전략에서 일반적으로 고정된 채로 사용되는 기반 시퀀스를 상호 보완적인 두 기반 시퀀스의 선형 보간으로 대체함으로써 보다 우수한 기반 시퀀스를 제공하며, 두 번째 전략은 준-명시적 접근법을 활용하여 현재 시스템 상태에 적절한 시변 블록 구조를 온라인에서 제공한다. 또한, 잔류편차-제거 모델예측제어 기법의 최적 성능을 향상시키기 위해 추정 외란 데이터로부터 학습된 모델-플랜트 불일치 보상 신호를 온라인에서 이용하는 전략을 제안하였다. 제안된 세 가지 기법을 통해 모델예측제어의 반복적 실현가능성과 폐쇄-루프 안정성을 보장하면서 최적 성능을 효율적으로 개선 하였다.1. Introduction 1 2. Move-blocked model predictive control with linear interpolation of base sequences 5 2.1 Introduction 5 2.2 Preliminaries 9 2.2.1 MPC formulation 9 2.2.2 Move blocking 12 2.2.3 Move blocked MPC (MBMPC) 15 2.3 Move blocking schemes 16 2.3.1 Previous solution based offset blocking 17 2.3.2 LQR solution based offset blocking 18 2.4 Interpolated solution based move blocking 20 2.4.1 Interpolated solution based MBMPC 20 2.4.2 QP formulation 26 2.5 Numerical examples 29 2.5.1 Example 1 (Feasible region) 30 2.5.2 Example 2 (Performance in regulation problem) 33 2.5.3 Example 3 (Performance in tracking problem) 36 3. Move-blocked model predictive control with time-varying blocking structure by semi-explicit approach 43 3.1 Introduction 43 3.2 Problem formulation 46 3.3 Move blocked MPC 48 3.3.1 Move blocking scheme 48 3.3.2 Implementation of move blocking 51 3.4 Semi-explicit approach for move blocked MPC 53 3.4.1 Off-line generation of critical region 56 3.4.2 On-line MPC scheme with critical region search 60 3.4.3 Property of semi-explicit move blocked MPC 62 3.5 Numerical examples 70 3.5.1 Example 1 (Regulation problem) 71 3.5.2 Example 2 (Tracking problem) 77 4. Model-plant mismatch learning offset-free model predictive control 83 4.1 Introduction 83 4.2 Offset-free MPC: Disturbance estimator approach 86 4.2.1 Preliminaries 86 4.2.2 Disturbance estimator and controller design 87 4.2.3 Offset-free tracking condition 89 4.3 Model-plant mismatch learning offset-free MPC 91 4.3.1 Model-plant mismatch learning 92 4.3.2 Application of learned model-plant mismatch 97 4.3.3 Robust asymptotic stability of model-plant mismatch learning offset-free MPC 102 4.4 Numerical example 117 4.4.1 System with random set-point 120 4.4.2 Transformed system 125 4.4.3 System with multiple random set-points 128 5. Concluding remarks 134 5.1 Move-blocked model predictive control with linear interpolation of base sequences 134 5.2 Move-blocked model predictive control with time-varying blocking structure by semi-explicit approach 135 5.3 Model-plant mismatch learning offset-free model predictive control 136 5.4 Conclusions 138 5.5 Future work 139 Bibliography 145Docto

회분식 고분자 세척공정의 기초적 모델링 및 실험적 연구

학위논문 (석사)-- 서울대학교 대학원 : 화학생물공학부, 2016. 2. 이종민.After polymerization reaction, impurities composed of adduct, used solvent and catalyst remain inside the formed polymers. These impurities should be removed by washing to improve the purity of the polymers. In this process, the model of the polymer washing process is essential to optimize the energy, resources and operating time. This work proposes a fundamental model of polymer washing process to provide theoretical basis for optimization. The model describes the impurity distribution inside the polymers using pseudo steady state approximation with the concept of moving boundary of diffusion. Also, the impurity diffusion at polymer surface is described with Fick's law. In addition, this work reports an experimental investigation of polymer washing process using SPAEK (sulfonated poly(aryl ether ketone)) samples. In the investigation, impurity diffusion coefficient at polymer surface of the experiment is computed from the pH data. The computed D have different values for each operation, as a lumped parameter. However these values show the same trajectory with the introduction of a dimensionless number Co for each operation. This means other impurity diffusion factors, not included in the model, embraced in D are only affected by Co, even if the initial impurity concentrations inside the polymers are different for each operation. Finally, we predict the pH changes in a different experimental condition, and validate the prediction performance of the model.Chapter 1. Introduction 1 Chapter 2. Modeling 4 2.1 Pseudo steady state approximation of impurity distribution inside the polymer 6 2.2 Mole balance of impurities inside the polymer and in batch 8 2.3 Impurity diffusion rate at polymer surface 9 Chapter 3. Experimental Investigation 11 3.1 Relationship between hydroxide ion concentration and impurity concentration 12 3.2 Impurity diffusion coefficient at polymer surface 15 3.3 Numerical simulation for the radius of the diffusion boundary 20 Chapter 4. Model Validation 22 4.1 Estimation of impurity diffusion coefficient at polymer surface 23 4.2 Numerical simulation for pH changes and model validation 23 Chapter 5. Conclusion 29 References 31 초 록 34Maste