DAVID SMITH - Control Systems for Complete Idiots (Electrical Engineering for Complete Idiots)

1.1 INTRODUCTION

In this day and age everything around us is automatic and our desire to automate more stuff is only increasing. Control systems finds its applications in everything you can possibly think of. The concept of Control system plays an important role in the working of, everything from home appliances to guided missiles to self-driving cars. These are just the examples of Control systems we create. Control systems also exist in nature. Within our own body, there are numerous control systems, such as the pancreas, which regulate our blood sugar. In the most abstract sense it is possible to consider every physical object a control system. Hence from an engineering perspective, it is absolutely crucial to be familiar with the analysis and designing methods of such Control systems.

1.2 TERMS

So far we have used the term Control system many a times. To understand the meaning of the word Control system, first we will define the word system and then we will define a Control system.

A system is nothing but an arrangement of physical components which act together as a unit to achieve a certain objective. A room with furniture, fans, lighting etc. is an example of a system. To control means to regulate or direct. Hence a Control system is an arrangement of physical components connected in such a manner to direct or regulate itself or another system. For example, if a lamp is switched ON or OFF using a switch, the entire system can be called a Control system. In short, a Control system is in the broadest sense, an interconnection of physical components to provide a desired function, involving some kind of controlling action in it.

For each system, there is an excitation and a response or to simply put it, an input and an output. The Input is the stimulus, excitation or command applied to a Control system to produce a specific response and the Output is the actual response obtained from the Control system. It may or may not be equal to the response we intended to produce from the input provided (Thats whole other story). Now consider an example, when you clap your hands, it makes sound, this is a system. So what are the input and output of this system?? Is the input, the motion of your hands?? Or Is it the trigger from your brain or something else. Similarly, what is the output of the system?? The sound?? Or the vibrations generated?? For a system, the inputs and outputs can have many different forms. In fact, its completely up to us to decide what a systems input and output parameters should be, based on the application and most times, Control systems have more than one input or output.

The purpose of the control system usually identifies or defines the output and input. If the output and input are given, it is possible to identify and define the nature of the system components. Fortunately for us, more often than not, all inputs and outputs are well defined by the system description. Sometimes they are not, like noises or disturbances in the output. Disturbance is any signal that adversely effects the output of a system. Some of these disturbances are internally generated, others from outside the system.

1.3 CLASSIFICATION OF CONTROL SYSTEMS

There are a lot of ways to classify Control systems, Natural-Manmade, Single input single output -Single input multiple output etc., but we will focus on some of the important classifications:

1.3.1 Time Varying and Time Invariant Systems

Time Invariant Control systems are those in which the system parameters are independent of time. In other words, the system behavior doesn't change with time. For example, consider an electrical network, say your mobile charger, consisting of resistors and capacitors. It produces an output of 5V when connected to a 230V AC supply. This system is a time invariant one, because it is expected to behave exactly the same way, whether its used at 6 pm or 11 pm or any other time.

On the other hand, Systems whose parameters are functions of time are called Time varying systems. The behavior of such systems not only depends on the input, but also the time at which the input is applied. The complexity of design increases considerably for such type of Control systems.

1.3.2 Linear and Non-Linear Systems

A Linear system is one that obeys the Superposition property. Superposition property is a basically a combination of 2 system properties:

1. Additivity property : A system is said to be additive if the response of a system when 2 or more inputs are applied together is equal to the sum of responses when the signals are applied individually. Suppose we provide an input ( x ) to a system and we measure its response. Next, we provide a second input ( x ) and measure its response. Then, we provide the sum of the two inputs x + x . If the system is linear, then the measured response will be just the sum of the responses, we noted down while providing the two inputs separately.