# How to Study Control Systems?

Hi Guys,

Control Systems is one of the most important subjects for both Electrical as well as Communication engineers from GATE point of view. The weight-age of Control Systems has been consistent over the years at around 8-10 marks surpassing many core subjects of both branches itself. The problems that appear in GATE from this topic are based on the application of concepts instead of directly asking a theoretical concept. So, while preparing Control Systems, the focus must be on solving a lot of problems.

Also, there are numerous interesting real-life applications of Control Systems which make this topic all the more wonderful. Around us we see many systems operating in our everyday life and we can treat every system as a control system though it may be manual or automatic. Even our human body itself can be treated as a control system with brain acting as controller or processor and co-coordinating the actions of different body parts based on response delivered to the brain by different senses.

Thus by seeing the practical applications of this subject you can be much more involved and can easily generate interest which you may otherwise lack. So the key to this kind of subject is to learn practical applications side by side or else these subjects can become very monotonous.

The standard book that you can follow for this subject is Automatic Control Systems by B.C. Kuo. It has been well written with numerous practical application of concepts given.

The standard book that you can follow for this subject is Automatic Control Systems by B.C. Kuo. It has been well written with numerous practical application of concepts given.

Now I will treat this subject topic by topic and will try to highlight the relevant and irrelevant portions in each topic so that you can concentrate more on relevant topics instead of getting lost in the vastness of standard books. The following topics are included in GATE curriculum:

## • **Transfer Functions**

Basically, in this topic we need to learn about Block Diagram Reduction Technique and simple equivalent Transfer Functions for both positive and negative feedback. This topic is very basic and very much necessary as foundations of all advanced topics are laid here and strong foundations are the core of every successful student. Next thing that comes in this topic is Signal Flow Graphs and Mason’s Gain Formula as these concepts may sometimes simplify the effort if you have to calculate equivalent transfer function as block diagram technique may sometimes be very lengthy. Almost every year one question from SFG is guaranteed so do prepare this topic well.

## • **Mathematical Modeling of Control Systems**

This topic was recently introduced in GATE syllabus and under this topic, you have to study about modeling of Mechanical Systems and how we can draw equivalent electrical circuits for mechanical systems. You also have to study about nodal diagram and how to derive the differential equations for mechanical systems.

## •** Time Domain Analysis**

This topic is basically very easy and mostly formula based as we need to learn the formulas for various time domain parameters like Rise Time, Maximum Overshoot, Settling Time, Peak Time and also various error coefficients like Position Error Coefficient, Velocity Error Coefficient and Acceleration Error Coefficient but remember as per GATE we are asked to compute the actuating error instead of error between output and input. So, error coefficients can be used directly for non-unity feedback systems as well.

## • Stability

This topic is very simple and the only concept that needs to be studied here is the Routh Stability Criterion and also keep in mind the special cases for Routh Criterion. The special cases include when the entire row goes to zero or the first element of the row is zero. The questions from this topic are very rare but an understanding of stability criteria is must to have a general understanding. As these basic concepts can help you understand the behavior of many systems.

## • Root-Locus Technique

In this topic, we need to learn about drawing root-locus and general properties associated with it like the number of asymptotes, the angle of asymptotes, centroid, break-away and break-in points. The one most important point to remember is the change in root-locus properties when positive feedback is applied instead of negative feedback there we have to understand about the Complimentary Root Locus. From past 3-4 years every year a question from this topic is being asked.

## • Frequency Domain Analysis

In this topic many small formulas like Resonant Frequency, Resonant Peak and Bandwidth are important. Apart from that the concept of Nyquist Criterion is important and here we need to learn small Nyquist Plots for a simple function and how do they change once you add zeroes and poles. If you can draw Nyquist Plot you may directly be able to judge the stability of the system. The other concepts that can be frequently seen in GATE exam from this topic is Gain and Phase Margin. In Gain and Phase Margin you have to practice as many problems as possible and there is not much theory involved in it. The last topic that is covered here and is most relevant for GATE exam is Bode Plots and here you need to learn how to draw asymptotic Bode Plots and slope of each asymptote. Also, you need to practice finding transfer functions from a given Bode Plot.

## • State-Space Analysis

This topic mostly contains concepts that we study in Linear Algebra but we need to learn about two parts mainly that is deriving state model from Differential Equation, Signal Flow Graph and Transfer Function using Controllable Canonical Form, Observable Canonical form, Diagonal Canonical Form and Jordan Canonical Form. The second part involves analysis of State Model that is finding Transfer Function and Statbolity from State Space Model and State Transition Matrix and its relation with Transfer Function and also the solution of State Space Equation by the use of State Transition Matrix. The concepts of Controllability and Observability are also very important and you must judge these aspects of a Control System by the use of Controllability and Observability Matrices. You can expect a question from this topic every year in GATE exam.

## • Compensators and Controllers

Here we just need to learn the condition for maximum phase shift for both Lead and Lag Compensators and also electrical circuit implementation of both. In Controllers, you need to study about basic controllers such as Proportional, Derivative and Integral Controller and their combination such as PD and PI Controller. Just study about differences in these controller and their properties.

So, these are the topics that I feel are relevant for GATE in Control Systems and if you feel that I have missed something you can mention it in the comments.

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