In control systems engineering, an analogous system refers to a system that behaves in a similar way to another system, especially in terms of its dynamic response to input signals. Analogous systems are often used to model and analyze the behavior of complex systems by comparing them to simpler, well-understood systems.
The concept of analogous systems is based on the idea that systems with similar mathematical equations governing their behavior will exhibit similar responses to similar inputs. This allows engineers to leverage their knowledge of a simpler system to understand and predict the behavior of a more complex system.
There are two main types of analogous systems: electrical and mechanical. These are described below:
Electrical Analogous System: This involves representing a physical system using electrical components and circuits that share similar mathematical relationships. The variables of the original system, such as force, velocity, or pressure, are mapped onto corresponding electrical variables like voltage, current, and resistance. This approach is particularly useful for systems that exhibit linear behavior, where the output is directly proportional to the input.
An example of an electrical analogous system is modeling a mechanical spring-mass-damper system using an electrical circuit with resistors, capacitors, and inductors. The relationships between the components' parameters are analogous to the relationships between the mechanical system's parameters.
Mechanical Analogous System: This involves representing an electrical or other physical system using mechanical components and principles. Similar to electrical analogies, this approach is used to find equivalent mechanical systems that behave similarly to the original systems. This is particularly useful when dealing with mechanical systems.
For instance, a mechanical spring-mass-damper system can be analogous to an electrical RLC circuit with a resistor, inductor, and capacitor. The way these elements interact in the circuit resembles the behavior of the mechanical system.
Analogous systems are helpful for analysis, design, and control purposes. They simplify complex systems into more understandable and manageable forms. Engineers can apply known control theory and techniques to the analogous system to gain insights that can then be translated back to the original system. However, it's important to note that while analogous systems provide a valuable tool for understanding and approximating complex systems, they are approximations and might not capture all the nuances of the real system's behavior.