Introduction to Control Systems - Part 1

Summary

This lecture introduces the scope and basic approach of an undergraduate course in classical control systems. It defines the systems the course will study and explains what “control” means in this context.

What Is a Dynamic System?

A system—also called a plant or process—is an entity that receives an input (u(t)) and produces an output (y(t)). In a dynamic system, these quantities vary with time. Mathematically, the system can be viewed as a mapping (S) from input to output:

[ y(t) = S{u(t)}. ]

System Classes Covered in the Course

The course focuses on single-input, single-output (SISO), linear, time-invariant, causal dynamic systems.

• SISO: The system has one scalar input and one scalar output. By contrast, a multiple-input, multiple-output (MIMO) system has vector-valued inputs and outputs.
• Linear: A system is linear if it satisfies additivity and homogeneity. Equivalently, it obeys the principle of superposition: a linear combination of inputs produces the same linear combination of their corresponding outputs.
• Time-invariant: The system’s response does not depend on when an input is applied. If an input is shifted in time, its output is shifted by the same amount. In practice, this is an approximation: a system’s properties may change over longer periods because of wear or other effects. Whether the approximation is appropriate depends on the timescale of interest.
• Causal: The output at any time depends only on current and past inputs, not on future inputs. Causal systems are therefore non-anticipatory.

Many real systems are nonlinear or change over time, but linear time-invariant models are often useful approximations for practical analysis and design.

What Does Control Mean?

In this course, control means making a system behave as desired. For example, a DC motor can be treated as a system whose input is armature voltage and whose output is shaft speed. If a particular speed is desired, the control problem is to determine what voltage should be applied to achieve it.

Broad Methodology for Control Design

The course’s overall approach has three main steps:

1. Develop a mathematical model of the system—a representation of the input–output relationship.
   • The course will primarily use physics-based models.
   • Models can also be data-driven or empirical, based on observed behavior.
   • A model may combine physical laws with experimental data.
2. Analyze the system’s response using the mathematical model.
3. Design a controller to make the system produce the desired output.

The goal is to learn how to design controllers for practical systems that can be represented, at least approximately, by the system classes covered in the course.

Speakers or Sources Featured

• Lecturer: An unnamed instructor presenting the course material.
• Other speakers or sources: None identified in the subtitles.