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Advanced Linear Continuous Control Systems

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848 min

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Why enroll

Participants should join this course to build a strong foundation in advanced control systems using clear and practical explanations. It helps learners understand state-space modeling, stability, and controller design with real examples and MATLAB practice. The course is useful for both academic learning and real-world engineering applications.

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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

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You're new to this field with no prior experience
You need a different specialisation outside Electrical Engineering
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Course details

This course is designed to help learners clearly understand the principles and applications of advanced control engineering, which plays a vital role in many engineering fields such as electrical, mechanical, aerospace, robotics, and automation. As modern engineering systems become more complex and interconnected, a strong foundation in advanced control concepts is essential.The course mainly focuses on linear continuous-time control systems and builds a solid understanding of their fundamentals. It begins with system modeling using the state-space approach, explaining how physical systems can be represented using state variables. Learners will study state equations, state transition matrices, and different methods to solve state-space models.A significant part of the course is devoted to stability analysis in the state-space framework, helping students understand how system behavior changes over time and how stability can be assessed mathematically. The course then moves on to important system properties such as controllability and observability, which are essential for effective control system design.Further, learners will explore controller design and observer design techniques, enabling them to design systems that meet desired performance requirements even when all state variables are not directly measurable. Throughout the course, theoretical concepts are reinforced using numerical problems, practical engineering examples, and MATLAB programming, making it easier to connect theory with real-world applications.Overall, this course equips students, researchers, and practicing engineers with the analytical and practical skills needed to model, analyze, and design advanced control systems confidently.

Source: IIT Roorkee July 2018 [Youtube Channel]

Course suitable for

Key topics covered

Advanced Linear Continuous Control Systems
Introduction to State Space
State Space Representation
State Space Representation: Companion Form (Controllable Canonical Form)
State Space Representation: Extended Controllable Canonical Form
State Space Representation: Observable Canonical Form
State Space Representation: Diagonal Canonical Form (Part-I)
State Space Representation: Diagonal Canonical Form (Part-II)
State Space Representation: Jordan Canonical Form
State Space Representation: Numerical Examples on State space Modelling (Part-I)
State Space Representation: Numerical Examples on State space Modelling (Part-II)
Modelling of Mechanical Systems in State Space
Modelling of DC Servo Motor (Part-I)
Modelling of DC Servo Motor (Part-II)
Determination of Transfer Function from State Space Model (Part-II)
Determination of Transfer Function from State Space Model (Part-I)
Stability Analysis in State Space (Part-II)
Stability Analysis in State Space: Concept of Eigenvalues and Eigenvectors (Part-I)
Stability Analysis in State Space: Lyapunov Stability Analysis (Direct Method) Part-V
Stability Analysis in State Space: Lyapunov Stability Analysis (Stability Criterion) Part-IV
Stability Analysis in State Space: Lyapunov Stability Analysis (Sylvester’s Criterion) Part-III
Concept of Diagonalization
Solution of State Equation
Solution of State Equation (Forced System)
State Transition Matrix (Part-I)
Steady State Error for State Space System
State Transition Matrix (Part-II)
State Transition Matrix using Cayley-Hamilton Theorem (Part-III)
Controllability in State Space (Part-I)
MATLAB Programming with State Space

Course content

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

30 lectures14 hr 8 min

Advanced Linear Continuous Control Systems
2 min
Introduction to State Space
23 min
State Space Representation
26 min
State Space Representation: Companion Form (Controllable Canonical Form)
22 min
State Space Representation: Extended Controllable Canonical Form
29 min
State Space Representation: Observable Canonical Form
26 min
State Space Representation: Diagonal Canonical Form (Part-I)
23 min
State Space Representation: Diagonal Canonical Form (Part-II)
22 min
State Space Representation: Jordan Canonical Form
29 min
State Space Representation: Numerical Examples on State space Modelling (Part-I)
28 min
State Space Representation: Numerical Examples on State space Modelling (Part-II)
38 min
Modelling of Mechanical Systems in State Space
34 min
Modelling of DC Servo Motor (Part-I)
39 min
Modelling of DC Servo Motor (Part-II)
20 min
Determination of Transfer Function from State Space Model (Part-II)
15 min
Determination of Transfer Function from State Space Model (Part-I)
45 min
Stability Analysis in State Space (Part-II)
21 min
Stability Analysis in State Space: Concept of Eigenvalues and Eigenvectors (Part-I)
34 min
Stability Analysis in State Space: Lyapunov Stability Analysis (Direct Method) Part-V
28 min
Stability Analysis in State Space: Lyapunov Stability Analysis (Stability Criterion) Part-IV
27 min
Stability Analysis in State Space: Lyapunov Stability Analysis (Sylvesterâ€™s Criterion) Part-III
36 min
Concept of Diagonalization
24 min
Solution of State Equation
25 min
Solution of State Equation (Forced System)
34 min
State Transition Matrix (Part-I)
32 min
Steady State Error for State Space System
32 min
State Transition Matrix (Part-II)
25 min
State Transition Matrix using Cayley-Hamilton Theorem (Part-III)
41 min
Controllability in State Space (Part-I)
29 min
MATLAB Programming with State Space
39 min

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Questions and Answers

Q: You're closing a loop on a high-voltage DC bus current regulator and you type "how to select state feedback vs PID for linear continuous control with actuator saturation" into Google at 11 pm. The plant is a stable second‑order system with a lightly damped pair at 42 rad/s, DC gain 0.8, and a hard actuator limit at ±12 A. Which control strategy do you sign off for series production, given ISO 26262 ASIL‑C and a DFMEA concern on windup‑induced overshoot?

A: 12 A is the number that should make you pause. Any design that ignores explicit input limits risks integrator windup or unrealistic control effort. State feedback with defined pole locations lets you slow the closed‑loop poles just enough to respect the actuator, and adding anti‑windup is a known mitigation you can defend in DFMEA. Ziegler–Nichols and pure LQR both assume infinite authority, and pole cancellation is brittle when tolerances shift.

Q: During a design review you search "estimate closed loop bandwidth from settling time continuous control system". A third‑order closed loop is required to settle to within 2% in 0.15 s with minimal overshoot for an electric steering assist. What's the defensible order‑of‑magnitude for the required dominant closed‑loop bandwidth?

A: 0.15 s is the anchor. For a reasonably damped system, 2% settling time ≈ 4/(ζωn). With ζ ≈ 0.7, ωn lands near 38 rad/s, and the closed‑loop bandwidth tracks somewhat lower, in the 25–30 rad/s range. Engineers who jump straight to 1/T miss the damping term, and those who go to 150 rad/s forget the constant in the settling‑time relation.

Q: You’re specifying a resolver interface PCB for an under‑hood inverter and you google "corrosion mechanisms affecting control electronics continuous operation under hood". Ambient hits 125°C, humidity cycling is severe, and road salt is present. Which degradation mechanism actually drives long‑term drift in the analog front‑end gains?

A: 125°C with humidity and bias is the threshold combination. Electrochemical migration needs moisture plus an electric field, and it shows up as leakage paths that skew gains long before a hard short. Galvanic effects and cracking exist, but they’re slower or need different material pairings.

Q: Your lead asks you to confirm "observer pole placement vs noise sensitivity in continuous state estimation". The plant has unmeasured states, sensor noise PSD rises sharply above 200 Hz, and the controller bandwidth target is 40 Hz. Where do you place the observer poles?

A: 200 Hz noise is the number to watch. Pushing observer poles too fast drags that noise straight into the control input. Placing them about 2× the control bandwidth keeps estimation lag acceptable without amplifying high‑frequency noise, which matters when you’re closing safety‑relevant loops.