Linear Control System

When we talk about a linear control system it is all about how it responds to inputs. Picture it this way imagine you have a magical machine called ‘System S’ that does stuff based on what you give it. Now this machine follows two important rules:

Homogeneity: If you give it something to do say a task or an instruction & you make that instruction bigger or smaller by a certain amount the result from the machine gets bigger or smaller by the same amount. It is like when you increase the work you ask it to do the result also increases by the same factor.

Additivity: Now, if you give this machine two different tasks separately, it gives you two results, right?. Now, here is the interesting part. If you combine these two tasks and give them to the machine as one big task (adding the two smaller tasks together), the result you get is the same as if you added the results of the two smaller tasks separately. It is like the machine does not care if you give it two jobs or one big combined job, the result is the sum of the individual results.

When we talk about linear control systems, we are talking about systems that play by these rules. They were the types of systems that follow these two principles that is they respond predictably when you make the task bigger or smaller & their response to combined tasks is just the sum of their responses to the individual tasks.

Example of Linear Control System

Think of a simple circuit with just resistors and a battery that gives a steady flow of electricity. In this circuit, if you change the voltage from the battery that’s make it stronger or weaker the resulting current in the circuit changes by the same factor. That’s the homogeneity part – change one thing & the other changes in sync. Now if you have a bunch of resistors connected in different ways and you measure the voltage and current at different points you will find that if you sum up the voltages or currents separately it’s the same as if you add them all together at once. In other words the total effect is just the sum of all the individual effects. This behavior makes it a linear control system.

So, this circuit when we ignore any funky side effects and assume everything working perfectly shows a linear relationship between voltage and current. It is a good example of a linear control system because it plays by the rules of homogeneity and additivity.

A control system is like a manager for machines. It tells them what to do so they work the way we want. There are different kinds of control systems, like ones that follow a straight line and others that don’t. They’re all about making sure things work the way we need them to. In this, we will discuss Linear Control Systems and Non-linear Control Systems With Tabular Comparison and a Block Diagram.