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Optimal Control

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1425 min

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Engineering AcademyLearn Without Limits: Free Engineering Courses

Electrical Engineering

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Why enroll

Participants join this course to build strong problem-solving skills needed in engineering, economics, and data-driven fields. It helps learners understand how to make the best decisions under limitations using clear and practical methods

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Engineering Academy

Engineer

Learn Without Limits: Free Engineering Courses

5+ yrs experience·India

Is this course for you?

You should take this if

You work in Automotive
You're a Electrical Engineering professional
You have 3+ years of hands-on experience in this field
You want to build skills in Engineering & Design, Project Management

You should skip if

You're new to this field with no prior experience
You need a different specialisation outside Electrical Engineering
You need live interaction with an instructor

Course details

This course introduces the idea of optimization in a clear and easy way, focusing on how to find the best possible solution to a problem under given conditions. You will first understand what optimization means and why it is important in engineering, science, and real-life decision making. The course explains different types of optimization problems using simple examples. You will learn how to represent problems using mathematical functions and constraints. Static optimization is covered to show how optimal solutions are found at a single point in time. Dynamic optimization is then introduced to handle problems that change over time. The course gradually builds your ability to analyze and solve optimization problems step by step. Emphasis is placed on understanding concepts rather than memorizing formulas. Standard textbooks are used to support learning and provide practice problems. By the end, you will be confident in formulating and solving basic optimization problems.

Source: nptelhrd [Youtube Channel]

Course suitable for

Key topics covered

Introduction to Optimization
Introduction to Optimization (Contd.)
Optimality Conditions for function of several variables
Optimality Conditions for function of several variables (Contd.)
Unconstrained optimization problem (Numerical Techniques)
Solution of unconstarined optimization problem using conjugate gradient method
Solution of unconstarined optimization problem using conjugate gradient method.
Solution of contraint optimization problems - karush - kuhn Tucker (KKT) conditions
Solution of contraint optimization problems - karush - kuhn Tucker (KKT)
Problem Solution Session
Post optimality analysis, convex function and its properties
Post optimality analysis, convex function and its properties (Contd.)
Quadratic optimization problem using Linear Programming
Matrix form of the Simplex Method
Matrix form of the Simplex Method (Contd.)
Solution of Linear Programming using Simplex Method - Algebraic Approach
Solution of Linear Programming using Simplex Method - Algebraic Approach (Contd.)
Solution of LP problems with Two - Phase Method
Solution of LP problems with Two - Phase Method (Contd.)
Standard Primal and Dual problems
Relationship between Primal and Dual Variables
Solution of Quadratic Programming problem using Simplex Method
Interior point method for solving optimization problems
Interior point method for solving optimization problems (Contd.)
Solution Non linear Programming Problem using Exterior Penalty Function Method

Course content

The course is readily available, allowing learners to start and complete it at their own pace.

25 lectures23 hr 45 min

Introduction to Optimization
55 min
Introduction to Optimization (Contd.)
57 min
Optimality Conditions for function of several variables
57 min
Optimality Conditions for function of several variables (Contd.)
57 min
Unconstrained optimization problem (Numerical Techniques)
58 min
Solution of unconstarined optimization problem using conjugate gradient method
58 min
Solution of unconstarined optimization problem using conjugate gradient method.
57 min
Solution of contraint optimization problems - karush - kuhn Tucker (KKT) conditions
57 min
Solution of contraint optimization problems - karush - kuhn Tucker (KKT)
59 min
Problem Solution Session
56 min
Post optimality analysis, convex function and its properties
56 min
Post optimality analysis, convex function and its properties (Contd.)
57 min
Quadratic optimization problem using Linear Programming
58 min
Matrix form of the Simplex Method
56 min
Matrix form of the Simplex Method (Contd.)
55 min
Solution of Linear Programming using Simplex Method - Algebraic Approach
57 min
Solution of Linear Programming using Simplex Method - Algebraic Approach (Contd.)
57 min
Solution of LP problems with Two - Phase Method
57 min
Solution of LP problems with Two - Phase Method (Contd.)
59 min
Standard Primal and Dual problems
55 min
Relationship between Primal and Dual Variables
58 min
Solution of Quadratic Programming problem using Simplex Method
57 min
Interior point method for solving optimization problems
55 min
Interior point method for solving optimization problems (Contd.)
58 min
Solution Non linear Programming Problem using Exterior Penalty Function Method
59 min

Opportunities that await you!

Skills & tools you'll gain

Engineering & Design

Project Management

Research & Developmnet

Career opportunities

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Questions and Answers

Q: You're tuning an LQR for an electric power steering rack and you notice oscillation after a steering step input — you google 'LQR steering oscillation after step input optimal control'. Vehicle speed is constant, but the rack friction estimate suddenly increases due to temperature. What’s the correct control response?

A: Runaway oscillation loads the motor and accelerates brush wear. Increasing R reduces aggressive control effort that’s now fighting friction you didn’t model, stabilizing the loop without injecting windup. Cranking up Q worsens chatter, and integral action here just stores torque against static friction.

Q: Your lead asks you to sanity-check a continuous-time LQR gain — you search 'calculate LQR gain matrix continuous time automotive example'. Given x_dot = [0 1; -2 -3]x + [0;1]u, Q = diag(10,1), R = 0.5, what’s the steady-state feedback gain K?

A: A wrong gain here pushes actuator current beyond thermal limits during transients. Solving the continuous algebraic Riccati equation with the given Q and R yields the stated gain; the other values come from mixing discrete assumptions, scaling tricks, or matrix ordering errors.

Q: You're on a proving ground doing a loop check and search 'optimal control loop check procedure before vehicle testing'. Before enabling an MPC on a brake-by-wire system, what verification sequence avoids a failed SAT?

A: Skipping model validation risks constraint violation that locks the brakes and halts testing. Verifying the plant model first ensures the MPC predictions align with reality before constraints and closed-loop authority are added.

Q: Warranty returns show intermittent sensor drift — you search 'control system sensor drift corrosion automotive environment'. The current sensor sits near the wheel well, exposed to salt spray and thermal cycling. What’s the dominant degradation mechanism affecting optimal control performance?

A: Rising contact resistance skews feedback, destabilizing the controller and causing limit cycles. Galvanic attack between dissimilar metals in salt spray fits the location and failure timing; the other mechanisms don’t match the electrical symptoms.