The Basics of Controls and State Space Behavior

Hey Guys.. I will try to share some tools that I learnt during the course of my Masters and in the industry. In my last post I mentioned a few things related to controls that you will learn during your 3^rd or 4^th year. Today I will discuss a few things that are important and always needed in industry. These may or may not be covered in the class and hence I felt I could share these.

In this field you will be given a task of modeling a particular system and then designing a controller for it which will help you attain desired behavior. If you consider a black box model your entire work could be represented by the block diagram shown below. Let’s discuss the parts of this which will result as a perfect segway into state space (the most important tool to design systems).

Block Diagram

1. The block “A” is called the plant. This is defined by the laws of physics and is the guy that we  have to control. E.g. This could be a car going uphill at constant speed, a tap filling water in a tank, a line follower robot, a hydro electric power plant etc. All you need to remember is.. the behavior of this plant is defined by physical laws and is constant. You don’t have any control over its definition.
2. The block “B” is your controller. You design this so that you can control “A” as you want. E.g You will have a flexibility to design a controller “B” that will maintain the speed of your car going uphill at 50Km/Hr or maintain the robot on the black line all the time. 
3. The block “C” is your output that you can measure or observe and then use it in your controller. E.g It can be the speed of the car or velocity of the line follower. 
4. The signal “u” is the control. This is the signal that is generated from your controller which is fed to the plant to control it as you want. 
5. And finally, this controller will be responsible to control a particular “state” of your system. Your system can have many states. One of these many states is your “output” that you observe/ measure with the help of block “C”.

So, the ingredients of the any damn system are: the Plant (A), the Controller (B),the control input (u), the state (x) and the output that you measure (y). And mathematically, any damn system can be represented as

Believe me, with this representation, it becomes super easy to analyze the system compared to writing huge differential equations by drawing free  body diagrams as we all learn in Math 3 and Physics! This representation is called state space and next time we will  see how we generate this state space from any given damn system.

State Space should be your friend and  you should be comfortable in playing with it!