AFC – Chapter 2. Mathematical modeling of dynamical systems.

Learning Purposes

1. Define the concepts of a physical model and a mathematical model.
2. Identify the stages of a physical system’s physical modeling and mathematical modeling process.
3. Recognize the different ways of expressing the mathematical model of a physical system: in differential equations, transfer function, and state space.
4. Define the fundamental concepts related to model systems in state space: state, state space, system order, state vector, state variables, input vector, and output vector.
5. Formulate the mathematical model of several types of systems in state space and recognize the non-uniqueness of the model of a system in state space.
6. Recognize the need to linearize nonlinear mathematical models to facilitate their analysis.
7. Identify the steps of the linearization procedure for univariate and multivariable systems with smooth nonlinearities: determination of the operating point or equilibrium point, definition of deviations, and approximation using the first terms of the Taylor series to obtain the linearized mathematical model.
8. Calculate the linearized mathematical model for various nonlinear mathematical models.
9. Calculate the linearized mathematical model for a fixed-wing aircraft.

Learning Activities

• Watch the video. Lecture 3. Physical modeling and mathematical modeling of a system. Examples of fluidic systems / mechanical systems. 
• Watch the video. Lecture 4. Mathematical models of physical systems examples: mechanical systems / electrical systems.
• Watch the video. Lecture 5. Mathematical models of physical systems examples. Electrical systems / electromechanical systems.
• Watch the video. Lecture 6. Mathematical models of physical systems examples. Thermal systems / fixed wing aircraft.
• Watch the video. Lecture 7. Linearization of nonlinear mathematical models. The concept of linearization.
• Watch the video. Lecture 8 – Part 1. Examples of linearization of MIMO systems.
• Watch the video. Lecture 8 – Part 2. Linearization of fixed wing aircraft model case of study.
• Work on the problem set 2.
• Participate in synchronous meetings of attention to students and solutions to concerns.

Resources for chapter 2

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