[연세대학교] 제어 및 지능형 시스템의 해석 및 설계

[연세대학교] 제어 및 지능형 시스템의 해석 및 설계 - 최종 보고서 (Model Predictive Control)

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1. Model Predictive Control

Model Predictive Control (MPC)는 제어 공학 분야에서 오랜 역사를 가지고 있습니다. 이 방법은 동적 시스템의 수학적 모델을 사용하여 미래 동작을 예측하고 제어합니다. 이 연구에서는 카트 위의 역진자 예를 사용하여 그 효과를 입증합니다. 동적 최적화를 위한 Python 패키지인 GEKKO를 사용하여 전체 분석 및 설계 절차를 시뮬레이션합니다.
2. Inverted Pendulum

역진자 시스템은 불안정하고 비선형적이어서 많은 제어 이론의 응용 분야에서 인기 있는 프로세스입니다. 카트 위의 역진자 시스템의 운동 방정식은 Lagrangian을 사용하여 얻어졌으며, 불안정한 평형점 주변에서 선형화되었습니다.
3. Linearization

선형화된 상태 공간 방정식을 기반으로 카트가 기준 신호를 따르고 진자가 수직 위치를 유지할 수 있는 최소 플랜트 입력을 생성하는 제어기가 설계되었습니다.
4. GEKKO

제어 절차는 최적화 라이브러리 GEKKO를 사용하는 Python으로 시뮬레이션되었습니다.

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1. Model Predictive Control

Model Predictive Control (MPC) is a powerful optimization-based control technique that has gained significant attention in various industries due to its ability to handle complex systems with constraints. MPC is particularly useful in applications where the system dynamics are well-understood, and the control objectives and constraints can be explicitly formulated. The key advantage of MPC is its ability to anticipate future system behavior and proactively adjust the control inputs to optimize a given performance criterion, such as minimizing energy consumption or tracking a desired reference trajectory. MPC's flexibility in handling multivariable systems, nonlinearities, and constraints makes it a versatile tool for a wide range of applications, including process control, robotics, automotive systems, and energy management. However, the implementation of MPC can be computationally intensive, especially for systems with fast dynamics or a large number of variables. Ongoing research in areas such as efficient optimization algorithms, model reduction techniques, and distributed MPC architectures aims to address these challenges and further expand the applicability of MPC in real-world scenarios.
2. Inverted Pendulum

The inverted pendulum is a classic control problem that has been extensively studied in the field of control theory and robotics. It represents a challenging nonlinear, unstable system that requires precise control to maintain the pendulum in an upright position. The inverted pendulum serves as a benchmark for evaluating the performance and capabilities of various control strategies, including classical control techniques, modern control methods, and machine learning-based approaches. Solving the inverted pendulum problem has important implications for the development of advanced control systems, such as those used in bipedal robots, self-balancing vehicles, and other dynamic systems that require rapid and accurate stabilization. The complexity of the inverted pendulum problem, with its inherent instability and sensitivity to disturbances, makes it an excellent testbed for exploring innovative control algorithms, state estimation techniques, and real-time optimization methods. Continued research on the inverted pendulum problem contributes to the advancement of control theory and the practical implementation of sophisticated control systems in various engineering applications.
3. Linearization

Linearization is a fundamental technique in control theory and system analysis, which involves approximating a nonlinear system around a specific operating point using a linear model. This approach is particularly useful when dealing with complex, nonlinear systems, as it allows for the application of well-established linear control methods and analysis tools. Linearization enables the use of linear system theory, including techniques such as pole placement, optimal control, and Kalman filtering, which can provide valuable insights and facilitate the design of effective control strategies. However, it is important to note that the accuracy of the linearized model is limited to a small region around the chosen operating point, and the performance of the control system may degrade as the system moves away from this point. Consequently, the choice of the operating point and the range of validity of the linearized model are crucial considerations in the design process. Ongoing research in this area focuses on developing more sophisticated linearization techniques, such as gain-scheduling, multiple-model approaches, and nonlinear model predictive control, to extend the applicability of linearization and improve the performance of control systems in a wider range of operating conditions.
4. GEKKO

GEKKO is a powerful open-source optimization suite that has gained significant attention in the field of process control and systems engineering. It provides a comprehensive framework for solving a wide range of optimization problems, including dynamic optimization, parameter estimation, and model predictive control. The key strengths of GEKKO lie in its ability to handle complex, nonlinear systems with constraints, its flexibility in accommodating different problem formulations, and its efficient numerical solvers. GEKKO's modular design and user-friendly interface make it accessible to researchers and practitioners from various backgrounds, enabling them to quickly prototype and deploy advanced optimization-based control solutions. The versatility of GEKKO allows it to be applied to a diverse range of applications, such as chemical process control, energy systems optimization, robotics, and aerospace engineering. Ongoing developments in GEKKO, including improvements in solver performance, integration with machine learning techniques, and support for distributed and cloud-based optimization, further enhance its capabilities and expand its reach in the control and optimization community. As a robust and versatile optimization tool, GEKKO continues to play a crucial role in advancing the state-of-the-art in control systems and decision-making processes across various industries and research domains.