Introducción a Modelado de Sistemas Físicos

Introduction to Physical System Modeling

Overview of the Course

• José Luis Mendoza Soto introduces a new course on modeling physical systems, focusing on mathematical models for various mechanical, electrical, hydraulic, and thermal systems.

• The material presented is intended as supplementary support for university students and aims to grow his YouTube channel.

Understanding Systems

• A system is defined as a set of elements interacting to perform a specific function.

• Systems are often represented using block diagrams with arrows indicating input (excitation signals) and output (response signals).

• Input signals affect the system's behavior, while output signals represent the system's response to these inputs.

Block Diagram Representation

• Within block diagrams, mathematical models like transfer functions in frequency domain are typically included.

• Input examples vary by system type: voltage/current for electrical systems; force/position for mechanical systems; heat for thermal systems.

Analyzing Electrical Circuits

Circuit Behavior

• The output signal of interest can be voltage or current at specific points in an electrical circuit.

• An RC circuit example illustrates how applying voltage modifies variables like capacitor voltage and current through components.

Mathematical Modeling

• The mathematical model allows analysis of variable behaviors within the system based on input changes.

• For an RC circuit, differential equations serve as mathematical models that describe how output variables respond over time.

Practical Applications of Models

Step Response Analysis

• Applying a constant DC voltage acts as a step input signal; analyzing this helps understand capacitor behavior over time.

• Solving differential equations provides insights into how voltages change across different time intervals.

Example from UAV Control Systems

Understanding Control Systems for Flight Stabilization

Mathematical Models in Control Systems

• The discussion begins with the importance of mathematical models in designing control systems for flight stabilization of devices, particularly drones.

• A synthesized model is introduced, focusing on angular velocity (omega) around three axes, which are represented as vectors with three components.

• Key variables include translational position and thrust generated by motors; understanding these helps determine motor speeds necessary for specific movements.

• An example illustrates that if two motors spin in one direction and two in the opposite, the drone can remain static at a certain altitude. Adjusting motor speed leads to translational movement.

• The behavior of the drone can be simulated using mathematical models and differential equations to visualize its motion across different axes.

Defining Mathematical Models

• The session transitions into defining what constitutes a mathematical model, emphasizing its role in applying experiments to answer questions about specific systems.

• Various types of models are discussed: descriptive models provide verbal statements about behaviors (e.g., reliability), while physical models mimic real system properties (e.g., architectural scale models).

• Physical modeling examples include fashion runway displays where clothing is showcased on models to predict aesthetic outcomes.

Types of Mathematical Models Relevant to Electrical Engineering

• In electrical engineering, mathematical models describe relationships between measurable variables within a system using mathematical expressions.

• Variables can encompass a wide range including voltage, current, speed, force, pressure, temperature etc., applicable not only in physics but also in economics and chemistry contexts.

Classification of Systems

• A review of system classifications highlights various characteristics such as dynamic vs. static systems and stochastic vs. deterministic systems.

• Other distinctions include linear vs. nonlinear systems and continuous vs. discrete systems; understanding these classifications aids in identifying the type of system being studied.

Focus on Dynamic Systems

• The course will primarily focus on dynamic systems relevant to automatic control design and their application across various fields for estimating behaviors effectively.

Introduction to Deterministic Systems

Overview of System Types

• The discussion focuses on deterministic systems, indicating that the course will not delve into punishment systems unless further extensions are provided later.

• Various models will be explored, including concentrated parameter models, linear systems, and potentially some nonlinear systems.

• The course will cover continuous and discrete systems as well as time-variant characteristics, emphasizing the importance of time invariance in system analysis.

Linear Systems and Frequency Domain Techniques

• Linear systems allow for the application of techniques such as the Laplace transform to transition system representation into the frequency domain.

• A more detailed classification of these systems will be addressed in a subsequent video segment.