Defining The Order Of A System: A Comprehensive Guide

How can one ascertain both the order and type of a system? To determine the order of a system, you count the total number of poles present in the closed-loop system. In parallel, to identify the type of the system, you look for the number of poles specifically situated at the origin, where s equals zero, within the open-loop transfer function. This method enables you to categorize and understand the system’s characteristics. Please note that the information provided here is accurate as of July 3, 2023.

A first-order system can be defined as a type of dynamic system characterized by a transfer function in which the denominator has a first-order polynomial, meaning the highest power of “s” is 1. To provide more context, let’s recall a previous tutorial on transfer functions. In the context of transfer functions, first-order systems can be identified by the presence of just one pole in their transfer function. This means that the system’s response to changes in input or disturbances exhibits a characteristic behavior where the influence of the pole dominates. This basic concept of first-order systems was discussed on January 17, 2021, to help clarify the fundamental principles underlying these systems.

“What is meant by the ‘order’ of a control system? The order of a control system is a crucial concept that provides insight into the system’s complexity and behavior. It is determined by the highest power of ‘s’ present in the denominator of the closed-loop transfer function, denoted as G(s), within a unity feedback system. In simpler terms, it represents the highest exponent of ‘s’ in the equation that describes the system’s response. Understanding the order of a control system helps engineers and researchers analyze and design control systems more effectively. This concept is fundamental to the field of control theory, as it informs the stability, performance, and overall characteristics of the system.”