• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.42 no.3
• /
• pp.243-253
• /
• 2014

This paper deals with the Quantitative Feedback Thoery(QFT) guaranteeing robustness in spite of the plant parametric uncertainty. In the frequency domain, the QFT guarantees the robustness of the design specification on the uncertainty of plant parameters and disturbance. In order to use the QFT, a selected plant is a Quad Rotor Vehicle(QRV) which has excellent maneuverability and possibility of vertical take-off and landing like the helicopter. And attitude control is examined the possibility satisfied the requirement specification under the setting parametric uncertainty of motors driving 4-blades. Additionally, in an attitude control, the pre-filter considering parameter range and operating range of a QRV was used. For these purpose, in this paper, by using QFTCT, that is the QFT Control Toolbox designing the controller in MATLAB by the QFT, each design phases are introduced.

• Communications of Mathematical Education
• /
• v.37 no.1
• /
• pp.65-84
• /
• 2023

The method of Lagrange multipliers, one of the most fundamental algorithms for solving equality constrained optimization problems, has been widely used in basic mathematics for artificial intelligence (AI), linear algebra, optimization theory, and control theory. This method is an important tool that connects calculus and linear algebra. It is actively used in artificial intelligence algorithms including principal component analysis (PCA). Therefore, it is desired that instructors motivate students who first encounter this method in college calculus. In this paper, we provide an integrated perspective for instructors to teach the method of Lagrange multipliers effectively. First, we provide visualization materials and Python-based code, helping to understand the principle of this method. Second, we give a full explanation on the relation between Lagrange multiplier and eigenvalues of a matrix. Third, we give the proof of the first-order optimality condition, which is a fundamental of the method of Lagrange multipliers, and briefly introduce the generalized version of it in optimization. Finally, we give an example of PCA analysis on a real data. These materials can be utilized in class for teaching of the method of Lagrange multipliers.