Optimizing Membership Function Tuning for Fuzzy Control of Robotic Manipulators Using PID-Driven Data Techniques

In this study, a method for optimizing membership function tuning for fuzzy control of robotic manipulators using PID-driven data techniques is presented. Traditional approaches for designing membership functions in fuzzy control systems often rely on the experience and knowledge of the system designer, which can lead to suboptimal performance. By utilizing data collected from a PID control system, the proposed method aims to enhance the precision and controllability of robotic manipulators through improved fuzzy logic control. A Mamdani-type fuzzy logic controller was developed and its performance was simulated in Simulink, demonstrating the effectiveness of the proposed optimization technique. The results indicate that the method can outperform conventional P control systems in terms of overshoot reduction while maintaining comparable transient response specifications. This research highlights the potential of the PID-driven data-based approach for optimizing membership function tuning in fuzzy control systems and offers valuable insights for the development and evaluation of fuzzy logic control in robotic manipulators. Future work may focus on further optimization of the tuning process, evaluation of system robustness under various operating conditions, and exploring the integration of other artificial intelligence techniques for improved control performance

특정 점의 추적을 위한 모델예측제어가 결합된 새로운 반복학습제어 기법

학위논문 (박사)-- 서울대학교 대학원 : 화학생물공학부, 2017. 2. 이종민.본 논문에서는 제약조건이 있는 다변수 회분식 공정의 제어를 위해 반복학습제어(Iterative learning control, ILC)와 모델예측제어(Model predictive control, MPC)를 결합한 반복학습 모델예측제어(Iterative learning model predictive control, ILMPC)를 다룬다. 일반적인 ILC는 모델의 불확실성이 있더라도 이전 회분의 정보를 이용해 학습하기 때문에 출력을 기준궤적에 수렴시킬 수 있다. 하지만 기본적으로 개루프 제어이기 때문에 실시간 외란을 제거할 수 없다. MPC는 이전 회분의 정보를 이용하지 않기 때문에 모든 회분에서 동일한 성능을 보이며 모델의 정확도에 크게 의존한다. 본 논문에서 ILC와 MPC의 모든 장점을 포함하는 ILMPC를 제안한다. 많은 회분식 또는 반복 공정에서 출력은 모든 시간에서의 기준궤적을 추적할 필요가 없다. 따라서 본 논문에서는 원하는 점에만 수렴할 수 있는 새로운 ILMPC 기법을 제안한다. 제안한 기법을 사용할 경우 원하는 점을 지나는 기준궤적을 만드는 과정이 필요 없게 된다. 또한 본 논문은 점대점 추적, 반복 학습, 제약조건, 실시간 외란 제거 등의 성능을 보이기 위한 다양한 예제를 제공한다.In this thesis, we study an iterative learning control (ILC) technique combined with model predictive control (MPC), called the iterative learning model predictive control (ILMPC), for constrained multivariable control of batch processes. Although the general ILC makes the outputs converge to reference trajectories under model uncertainty, it uses open-loop control within a batchthus, it cannot reject real-time disturbances. The MPC algorithm shows identical performance for all batches, and it highly depends on model quality because it does not use previous batch information. We integrate the advantages of the two algorithms. In many batch or repetitive processes, the output does not need to track all points of a reference trajectory. We propose a novel ILMPC method which can only consider the desired reference points, not an entire reference trajectory. It does not require to generate a reference trajectory which passes through the specific desired points. Numerical examples are provided to demonstrate the performances of the suggested approach on point-to-point tracking, iterative learning, constraints handling, and real-time disturbance rejection.1. Introduction 1 1.1 Background and Motivation 1 1.2 Literature Review 4 1.2.1 Iterative Learning Control 4 1.2.2 Iterative Learning Control Combined with Model Predictive Control 15 1.2.3 Iterative Learning Control for Point-to-Point Tracking 17 1.3 Major Contributions of This Thesis 18 1.4 Outline of This Thesis 19 2. Iterative Learning Control Combined with Model Predictive Control 22 2.1 Introduction 22 2.2 Prediction Model for Iterative Learning Model Predictive Control 25 2.2.1 Incremental State-Space Model 25 2.2.2 Prediction Model 30 2.3 Iterative Learning Model Predictive Controller 34 2.3.1 Unconstrained ILMPC 34 2.3.2 Constrained ILMPC 35 2.3.3 Convergence Property 37 2.3.4 Extension for Disturbance Model 42 2.4 Numerical Illustrations 44 2.4.1 (Case 1) Unconstrained and Constrained Linear SISO System 45 2.4.2 (Case 2) Constrained Linear MIMO System 49 2.4.3 (Case 3) Nonlinear Batch Reactor 53 2.5 Conclusion 59 3. Iterative Learning Control Combined with Model Predictive Control for Non-Zero Convergence 60 3.1 Iterative Learning Model Predictive Controller for Nonzero Convergence 60 3.2 Convergence Analysis 63 3.2.1 Convergence Analysis for an Input Trajectory 63 3.2.2 Convergence Analysis for an Output Error 65 3.3 Illustrative Example 71 3.4 Conclusions 75 4. Iterative Learning Control Combined with Model Predictive Control for Tracking Specific Points 77 4.1 Introduction 77 4.2 Point-to-Point Iterative Learning Model Predictive Control 79 4.2.1 Extraction Matrix Formulation 79 4.2.2 Constrained PTP ILMPC 82 4.2.3 Iterative Learning Observer 86 4.3 Convergence Analysis 89 4.3.1 Convergence of Input Trajectory 89 4.3.2 Convergence of Error 95 4.4 Numerical Examples 98 4.4.1 Example 1 (Linear SISO System with Disturbance) 98 4.4.2 Example 2 (Linear SISO System) 104 4.4.3 Example 3 (Comparison between the Proposed PTP ILMPC and PTP ILC) 107 4.4.4 Example 4 (Nonlinear Semi-Batch Reactor) 113 4.5 Conclusion 119 5. Stochastic Iterative Learning Control for Batch-varying Reference Trajectory 120 5.1 Introduction 121 5.2 ILC for Batch-Varying Reference Trajectories 123 5.2.1 Convergence Property for ILC with Batch-Varying Reference Trajectories 123 5.2.2 Iterative Learning Identification 126 5.2.3 Deterministic ILC Controller for Batch-Varying Reference Trajectories 129 5.3 ILC for LTI Stochastic System with Batch-Varying Reference Trajectories 132 5.3.1 Approach1: Batch-Domain Kalman Filter-Based Approach 133 5.3.2 Approach2: Time-Domain Kalman Filter-Based Approach 137 5.4 Numerical Examples 141 5.4.1 Example 1 (Random Reference Trajectories 141 5.4.2 Example 2 (Particular Types of Reference Trajectories 149 5.5 Conclusion 151 6. Conclusions and Future Works 156 6.1 Conclusions 156 6.2 Future work 157 Bibliography 158 초록 170Docto

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