##### About the course

In this course, you will be introduced to the fundamentals of modeling and control of linear time-invariant systems; primarily from the classical viewpoint of Laplace transforms and a brief emphasis on the state space formulation as well. This course also includes a detailed application of filter design in the field of navigation and human movement (gait).

##### Learning Outcomes

After completing this course, you will be able to:

- Apply Laplace transform and state space techniques to model dynamic systems, and convert between these formulations.
- Analytically quantify the time and frequency domain behavior of dynamic systems.
- Specify steady state control system requirements.
- Select prototype controller structures to achieve these requirements.
- Formulate dynamic feedback controller design specifications in the frequency domain.
- Synthesize feedback controllers using root locus, Nyquist, and Bode techniques.
- Design their very own basic navigational system using inertial sensors and microcontrollers.
- Boost your hireability through innovative and independent learning.
- Get a certificate on successful completion of the course.

##### Target Audience

The course can be taken by:

**Students:** All students who are pursuing any technical/professional courses in electrical/electronic engineering.

**Teachers/Faculties:** All teachers/faculties who wish to acquire new skills or improve their efficiency in Control Engineering.

**Professionals:** All working professionals, who wish to enhance their skills by learning control engineering.

##### Why Learn Control Engineering?

Control Engineering is involved in a very vast area of technology. Control Engineering has applications even outside the Engineering domain. It is used in Financial Management and Science. Control Engineering has gained importance due to the fact that it is a part of a wide range of machines like Washing machines to Fighter aircraft. As technology becomes more readily available, cheaper and infinitely more powerful, there is an increasing incentive to take advantage of robotics and control systems engineers. According to the Bureau of Labor Statistics, the median annual wage for Control engineers was $94,250 ($45.31 per hour) in 2013. According to data from 2012, the growth rate for jobs was about 4%, which is slower than average. As automation and feedback-driven controls expand into more industries, we expect this to improve.

##### Course Features

**24X7 Access:**You can view lectures as per your own convenience.**Online lectures:**35 hours of online lectures with high-quality videos.**Updated Quality content:**Content is latest and gets updated regularly to meet the current industry demands.

##### Test Evaluation

Each lecture will have a quiz containing a set of multiple choice questions. Apart from that, there will be a final test based on multiple choice questions.

Your evaluation will include the overall scores achieved in each lecture quiz and the final test.

##### Certification

Certification requires you to complete all the lectures, quizzes, and the final test. Your certificate will be generated online after successful completion of course.

##### Topics to be covered

**Introduction to Systems and Control**- What is a System, its examples and different notations?
- How is the system classified and described?
- What is a Control System, what are disturbances and feedback in it and its example?

**Modeling of Systems**- What is the Model and what are the various types of Mathematical Models?
- How is a System modeled?

**Elements of Modelling**- How a Physical and Electrical System is classified and what are its elements?
- How to do an analysis of Electrical Systems and its example?
- How a Mechanical System are classified and what are its basic elements?
- How to do an analysis of Mechanical Systems and its example?
- How to establish analogy b/w Electrical and Mechanical systems and Transformer differs from Gears?

**Examples of Modelling**- How to model Cruise Control for Car?
- What is Transformer and how it is modeled?
- How Is Pendulum modeled?
- What is a Predator-Prey Model and what are the assumptions for deriving this Model?
- How to model a Predator-Prey Model and what is the Variant of Predator-Prey Model?

**Solving Problems in Modelling of Systems.**- How to solve System modeling problems (Part-1)?
- How to solve System modeling problems (Part-2)?
- How to solve System modeling problems (Part-3)?
- How to solve System modeling problems (Part-4)?

**Laplace Transforms**- What is the difference between Time and Frequency Domain and its examples?
- What is Domain Transformation and its Advantages?
- What is the motivation behind Laplace Transform?
- What are the Laplace Transform and its examples?
- Why is Laplace Transform important?
- What are Initial and Final Value Theorems?

**Inverse Laplace Transforms**- What are the Inverse Laplace Transform and its properties?
- What is Convolution theorem, its example and what is Convolution in s-domain, its example?
- What are the advantages of the Laplace Transform and its example?

**Transfer Function of Modelling Block Diagram Representation**- What is a Transfer Functions?
- How to interpret Transfer Function as Impulse Response?
- How to find transfer Function, its examples?
- What are the Properties of Transfer Function?
- What are the General form of Transfer Function and its example?
- How the Block diagram of a System looks like and what are its components and different forms?
- What are the loading effects on transfer function, its example and how to represent a transfer function through block diagram?

**Solving Problems on Laplace Transforms and Transfer Functions**- How to calculate Laplace transform of Signal?
- How to solve non-homogenous differential equations?
- How to Transfer Function from a given circuit model?
- How to find the transfer function of the given electro-mechanical System?

**Block Diagram Reduction, Signal Flow Graphs**- How to reduce the block diagram and what are the basic rules for block diagram Simplification?
- What is the Signal Flow Graphs?
- What are Mason's Gain Formula and its example?

**Solving Problems on Block Diagram Reduction, Signal Flow Graphs**- How to find Transfer function and draw its signal flow graph (Part-1)?
- How to find Transfer function and draw its signal flow graph (Part-2)?
- How to find Transfer function and draw its signal flow graph (Part-3)?
- How to find Signal flow graphs from the network equation directly?

**Time Response Analysis of systems**- How to do Time Domain Analysis and what are the Standard Test Inputs?
- What are First-Order Systems and their responses on different inputs (Part-1)?
- What are First-Order Systems and their responses on different inputs (Part-2)?
- What are Second Order Systems and their Important Parameters?
- What are Second Order Systems and their responses on different inputs (Part-1)?
- What are Second Order Systems and their responses on different inputs (Part-2)?

**Time Response specifications**- What are the Time Response Specifications and what are the Time Responses of an Underdamped System?
- How to express Time Response for Second-order Underdamped System?
- What are the Applications Of Damped Systems?
- What is Steady State Error and what is a Steady State Error for Standard Inputs?
- What is the feature of Steady State Error and what is a Steady State Error for different Systems?

**Solving Problems on Time Response Analysis and specifications**- What is the example problem on time response & what are the specifications of time response (Part-1)?
- What is the example problem on time response & what are the specifications of time response (Part-2)?

**Stability**- What is Stability?
- What is BIBO Stability, its Mathematical form and how to illustrate Poles and Zeros using an example?
- How to attaining Stability in Frequency Domain?

**Routh Hurwitz Criterion**- What is Routh Hurwitz Criterion?
- What is RH Criterion (continued)?
- How to do Stability Analysis for different examples?
- What is an Auxiliary Polynomial and an Auxiliary Equation, its examples?
- What is the history of Routh Hurwitz Stability Criterion?

**Routh Hurwitz Criterion T 1**- How to determine the stability of the system?
- how to find the stability of the system using RH criterion?
- How is an auxiliary polynomial used for finding the roots and determining the stability of the system?
- How are RH criteria applied in feedback systems to determine the gain?
- How to find whether a system is stable or marginally stable or unstable?
- How to find the roots of the system to determine the stability of the system?
- How to find the range of parameter to determine the stability of the system using RH criterion?

**Closed-loop System and Stability**- What are closed and open loop system and their examples?
- What are the different problems on Closed and Open loop systems?
- How to do Error signal analysis, how to track Error and what are its conditions?
- What is Sensitivity, Disturbance rejection and Noise Attenuation?
- What is a Characteristic equation, its conditions and what is Improved Stability, its advantages/disadvantages?
- What is Relative Stability, its conditions and how to determine Relative stability by using RH criterion?

**Root Locus Technique**- Why Root locus Technique Comes?
- What is the Root Locus Technique, its conditions, example and its advantages?
- How are Pole locations related to the Performance?

**Root Locus Plots - Part 1**- What are Evan's Conditions?
- What are the Points on Root Locus and its conditions?
- How to draw Root Locus using Construction Rule 1 and Construction Rule 2?
- How to draw Root Locus using Construction Rule 3?

**Root Locus Plots - Part 2**- How to draw Root Locus using Construction Rule 4?
- How to draw Root Locus using Construction Rule 5?
- How to draw Root Locus using Construction Rule 6?
- How to draw Root Locus?

**Root Locus Plots - Part 3**- How to draw Root Locus using Construction Rule 7?
- How to draw Root Locus using Construction Rule 8 and 9?

**Root Locus Plots - Part 4**- How to draw Root locus, its example (Part-1)?
- How to draw Root locus, its example (Part-2)?
- How to draw Root locus, its example (Part-3)?
- How to draw Root locus, its example (Part-4)?

**Introduction to Frequency Response**- What are the Frequency response and its advantages?
- What is the Concept of Frequency Response and its various conditions?
- What is the Frequency Response of Closed loop systems and what are the Frequency domain specifications?
- What is Second Order Systems?

**Frequency Response Plots**- What are the Polar plots (Part-1)?
- What are the Polar plots (Part-2)?
- What is the Stability in the frequency domain (Part-1)?
- What is the Stability in the frequency domain (Part-2)?
- What is the Nyquist stability criterion (Part-1)?
- What is the Nyquist stability criterion (Part-2)?

**Relative Stability**- What are the Special cases of Nyquist Plots?
- How to plot Nyquist Plots for different examples?
- What is Relative Stability?
- What are Gain and Phase Margins (Part-1)?
- What are Gain and Phase Margins (Part-2)?

**Bode plots**- What is the Bode plot?
- How to plot the logarithm of the magnitude of a Sinusoidal transfer function (Part-1)?
- How to plot the logarithm of the magnitude of a Sinusoidal transfer function (Part-2)?
- How to plot the logarithm of the magnitude of a Sinusoidal transfer function (Part-3)?
- How to plot the logarithm of the magnitude of a Sinusoidal transfer function (Part-4)?
- What is the procedure of plotting the Bode plot?
- How to plot Bode plots?
- How to find Error constants from the Bode plots?

**Basics of Control design Proportional, Integral and Derivative Actions - Part 1**- What are the Closed loop system and its performance specification?
- What are Dominant poles of a System (part 1)?
- What are Dominant poles of a System (part 2)?
- What are the effects of adding poles and zeros to the open loop transfer function?
- What is Proportional control?

**Basics of Control design Proportional, Integral and Derivative Actions - Part 2**- What is Proportional control action?
- What is Integral control action and what is the effect of disturbance on using these kinds of controllers?
- What is the effect of Integral control with proportional control action?
- How to derivate control action and what is the effect of Proportional with Derivate control action?
- What is the effect of Integral plus Proportional plus Integral control action?

**Problems on PID Controllers**- What are the example problems on PID Controllers (Part-1)?
- What are the example problems on PID Controllers (Part-2)?
- What are the example problems on PID Controllers (Part-3)?
- What are the example problems on PID Controllers (Part-4)?

**Basics of Control design Proportional, Integral and Derivative Actions - Part 3**- Highlights
- Why Is Integral control used?
- What are the important points to observe while working with an integrator?
- What are the important points to observe while working with Proportional with Derivative controllers?
- How to compensate Lag and what is the effect of adding the lag compensator on the root locus?
- How to compensate Lead and what is the effect of adding the lead compensator on the root locus?
- What are the performance specifications in the time and frequency domains?

**Control design in the time domain and discusses the lead compensator**- How is lead compensator used to achieve desired pole location (Part-2)?
- How to achieve desired performance specifications using Root locus?
- What is the transient response and what are steady-state performance specifications?
- How to make use of root locus plot to design controllers?
- How is lead compensator used to achieve desired pole location (Part-1)?

**Improvement of the Transient Response using lead compensation**- How to construct lead compensator with help of basic circuit elements?
- How to improve the transient response using lead compensation (Part-1)?
- How to improve the transient response using lead compensation (Part-2)?
- How to improve the transient response using lead compensation (Part-3)?

**Design of control using lag compensators**- How to design Lag compensator for meeting the required steady state specifications?
- How Lag compensators helps in improving the steady state response?

**The design of Lead-Lag compensators using root locus**- What are Lead-Lag compensators?
- How Are Lead-Lag compensators realized?
- Why and how to Design of Lead-Lag compensators using root locus for given problem?

**Introduction design of control in the frequency domain**- What was the Root locus based approach to design and design in the Frequency domain?
- What is the performance specification in the time domain and frequency domain?
- What are the design specifications in the frequency domain?
- What is the typical performance specification for design in the frequency domain?
- What is the approach to the design of compensators in the frequency domain (part 1)?

**Design of Lead Compensator using Bode Plots - Part 1**- What is the approach to the design of compensators in the frequency domain (part 2)?
- What is a Lead compensator in the frequency domain and what is it frequency characteristics?
- Why design Lead compensator for given example?
- How to design of a lead compensator in the frequency domain for given example and check whether this compensator is helpful or not?

**Design of Lag Compensators using Bode Plots - Part 2**- What is a Lag Compensator in the frequency domain and its Frequency characteristics?
- How to design Lag compensators using Bode Plots (part 1)?
- How to design Lag compensators using Bode Plots (part 2)?

**Design of Lead-Lag Compensators using Bode plots**- What is a Lead-Lag compensator in the frequency domain and what are the frequency characteristics of a lead-lag compensator?
- What are the desired specifications of lead-lag compensation?
- What happens when lead and lag compensator is used to obtain the desired specification?
- How to design lag part as the partial compensator of Lead-leg compensator obtain the desired specification?
- How to design Lead part of Lead-leg compensator and an overall lead-leg compensator that provide desired specifications?

**Experimental Determination of Transfer Function**- What are Minimum and Non-Minimum Phase Systems, their conditions?
- How to determine Minimum and Non-minimum phase systems?
- What are the steps to determine Transfer function from Bode plots and what is its methodology?
- How to determine transfer function from Bode plots?

**Effect of Zeros on System Response**- What are the mathematical Zeros, Poles and Stability?
- How Zeros of a system are determined and what is the effect of zeros?
- What is Internal Stability, Robustness and what are the performance limitations?
- What are the different effects of Zeros(part-1)?
- What are the different effects of Zeros (part-2)?

**Navigation - Stories and Some Basics**- Why is Navigation important?
- What is Navigation?
- What are the various types of Navigation and What is Coastal Navigation?
- What is Dead Reckoning?
- What is Celestial Navigation and Dead Reckoning with Celestial Navigation?
- What is the history of the great adventures of Indian navigation and what is Modern navigational technique?

**Navigation - Dead Reckoning and Reference Frames**- What is Inertial navigation?
- What is the principle of Navigating using inertial sensors (an example of Accelerometer)?
- What is the principle of Navigating using inertial sensors (an example of Gyroscope)?
- What is the 3-axis sensor?
- What is Attitude in Navigation and what is the problem with Attitude and reference frame?
- How to transform one reference frame into another reference frame (part 1)?
- How to transform one reference frame into another reference frame (part 2)?
- What is some Standard reference frame used for navigation?

**Inertial Sensors and Their Characteristics**- Highlights Introduction
- What are the various types of Inertial sensors and what is the effect of sensor noise on dead reckoning computations?
- What is the effect of bias error in the computation of angular position?
- What is the effect of bias error in the computation of translation position?
- What is MEMS gyroscope?
- What is the different type of errors in gyroscope?
- What are an Accelerometer and its noise characteristic?
- What are the various issues in sensor and applications of inertial sensors?

**Filter Design to Attentuate Inertial Sensor Noise**- Highlights Introduction
- What is a Continous time First order high pass filter?
- What is the discrete time First order high pass filter?
- What is the Continous and Discrete-time version of First-order low pass filter?
- What is the Idea behind implementing Complementary filter?
- How to implement HP & LP filter in discrete time and what is a Complementary filter?

**Complementary Filter - Part 1**- What is Sensor fusion and why it is needed?
- Why Low and High pass filter are used?
- What are the design steps of the complementary filter and how Low and High pass filters are defined?
- How to represent Low and High pass filter in Matlab and how to calculate angle?
- How to express Complementary filter in Mathematical form?
- How to design the complementary filter for the given problem (part-1)?
- How to design the complementary filter for the given problem (part-2)?

**Complementary Filter - Part 2**- What is a Sensor fusion Complementary Filter its equation?
- How to implement the use of High and Low pass filters in MATLAB (part 1)?
- How to implement the use of High and Low pass filters in MATLAB (part 2)?

**Introduction to State Space Systems**- What are the advantages and drawbacks of transfer function modeling approach?
- What is a state space system and general procedure to obtain it?
- How to obtain state space model of Mass spring damper system (MSD)?
- How to simulate MSD and What is the state of a system?
- What is the general form of a linear time-invariant state space model?
- How to obtain state space equation from the differential equation?
- How to drive desire state space model?
- How to obtain state space equation from the differential equation?
- How state space is related to the transfer function and how to obtain transfer function in state space model?

**Linearization of State Space Dynamics - Part 1**- What are linear and non-linear system and its example?
- What is Linearization?
- What is the General form of a Non-linear system, what are equilibrium points and why we linearize around an equilibrium point?
- How to compute equilibrium points and linearize around equilibrium point?
- How to go from the Jacobean to the linearized state-space system?

**Linearization of State Space Dynamics - Part 2**- How Is Predator-Prey model explained with an example?
- What are the important modeling assumptions?
- How to compute equilibrium points and linearize around it using Predator-Prey equations?
- How to simulate the Predator-Prey Model in MATLAB?
- What is the Model of the Van der Pol Oscillator?
- How to simulate Model of the Van der Pol Oscillator in MATLAB?

**State space canonical forms**- What is the standard form of state space model and what are the different canonical forms of state space model?
- Why is it called the controllable canonical form of state space model?
- What is the Observable and Diagonal canonical form?
- How are canonical forms derived for an example problem?

**State space solution and Matrix exponential**- How to derive matrix exponential and what are the various methods to solve matrix exponential?
- How to solve Matrix exponential?

**Controllability and Pole Placement**- What is the Observation on Pole Placement?
- How is the Controllability described with the help of an example?
- How Is Controllability defined?
- How to check whether state feedback controller can be designed for given system or not and check its controllability (part 1)?
- How to check whether state feedback controller can be designed for given system or not and check its controllability (part 2)?

**Controllability Decomposition and Observability**- How to check that which part of the system is controllable?
- What are Controllable Decomposition and its example?
- What is the Observability?

**Control Engineering - Final Quiz**