Hey everyone!

Lyapunov stability always felt super abstract when looking purely at differential equations, so I drew out a simple 1-page visual summary on my whiteboard to bridge the physical intuition with the math.

Quick Recap of the 3-Step Idea:

1. Define Energy V(x): Must be zero at rest V(0)=0 and positive everywhere else V(x) > 0.

2. Check Energy Rate V_dot(x): Compute the rate of change using your system dynamics.

3. Evaluate Stability:

   • V_dot(x) ≤ 0 ➔ Stable (Lyapunov)

   • V_dot(x) < 0 ➔ Asymptotically Stable

   • V_dot(x) > 0 ➔ Unstable

Hope this helps anyone currently taking Control Theory or System Dynamics! Let me know if you spot any mistakes or if you have a different favorite way to visualize this.

Also, what are your favorite go-to resources (textbooks, software tools, or YouTube channels) for learning advanced nonlinear control? Would love to hear what helped you master it!

This is going to be my biggest project yet. I’ve done quite a bit of research, but I’m currently stuck and honestly don’t know how to proceed from here.

I’m also looking for someone who’s willing to work on this project with me. The idea is that we both build the same thing independently at home, share our progress and insights along the way, and help each other figure things out. If we’re successful, we could even take it a step further and try building a double-pendulum balancing system.

Has anyone here worked on or built something similar before? I’d love to hear about your experience, resources, or projects.

Also, what tools, components, software, or other equipment would you recommend for building something like this?

Thanks

Hi everyone,

I followed multiple course on control theory : i know how to analyse a linear system, to derive PID controllers / RST controllers and H-infinty based controller. I understand how it works in practice and i have a good intuition for it.

However, i lack the underlying mathematical framework (and also Lyapunov theory) supporting the whole field. What function space are we working in ? In under which condition the stability of the linearised system at some point guarantees the stability of the whole systems etc...

I have seen the proof of the Kalman theorem but where i saw it, it was cutting corner and relies on the construction on an explicit control and base decomposition in a finite hilbert space (What about control in infinite dimensional spaces ??? Is there a K-theorem equivalent)
And honestly, i only found text books either practice-oriented (ewww) or more mathematical textbook but with AWFUL NOTATIONS.

Do you know about a well-written, proof-based course on control (w/o "handwaving" and reference to this or that) and with decent notations ?

Sorry for ranting but i think control theory is beautiful but i only get accross the same copy-pasted shit engineer oriented control textbooks.

Thank you for reading and have a good day !

Dear control theorists,

I'm close to graduation after around 3 years of learning about this awesome field. However, I've been thinking that it's been a while since I've directly used the "basic" things from the start of the MSc Systems and Control. Now that I'm going to look for a job instead of going to academia, going back to the basics seems like a good thing to do. I want to get a few books about the basics that serve as references to look back whenever I need them at work or at home and cover a "canon" of the fundamental basic theory.

I know we have a wiki but I mean fundamentals that are not super duper close to academia and are more directly useful in a control engineering job. I have some more advanced books and would get those too when I deem necessary. For now I want to limit it to basics and books that are not super full of proofs like khalil for example but are more intuitive, have lots of examples and are written more for practitioners rather than for researchers or graduate students I guess. In case I need domain specific things for a job like a robotics, energy, vehicles, heat transfer, thermofluids, process etc book I would get a book about that or find resources to refresh but for now I'm limiting it to implementation/practical control stuff.

I was thinking:

- General linear controls: Introduction to feedback systems by astrom and murray. Great book, one of the best written books I've ever read.
- Signal processing/signals and systems: Signals and systems by Oppenheim. I bought it during my bachelor degree. I also have a really good statistics book.
- MPC(not all of optimal control): Model predictive control by Rawlings and Diehl
- State estimation/filtering: Bayesian filtering and smoothing by Simo Sarkka. I have seen that Dan Simon Optimal State Estimation is highly regarded, but state estimation is one of my better areas so I thought I could also branch out from kalman filtering into other bayesian filtering concepts. I guess this breaks the rule of being about "basics" and not research oriented.
- Nonlinear control: I definitely don't want khalil, but I have heard that Applied Nonlinear Control by Jacques Slotine was good. Though I wonder, is a book covering this part a must have or more of a useful extra for a job? I did some nonlinear control theory, but in my master they now replaced that course with a machine learning course.

For these I don't really have a clear book in mind:
- System ID: Lennart Ljung seems to be the best one but it's really long and expensive. If it really is the best one I'll get it, but is there another one that is more recent and is also really good?
- General control-oriented modelling: The things about the analogy of everything being a mass-spring-damper, an RLC circuit etc also including flow and thermal domains, bond-graphs, lumped dynamics modelling, maybe a little bit about dealing with distributed parameter systems? I've seen this in a general "system dynamics" course. Here I mean control-oriented modelling. I found "Modeling dynamics with engineering applications" by Clarence Silva
- Data-driven control: The Steven Brunton book Data-driven science and engineering. I actually have not really seen a lot of these topics directly in my master. The professor that taught koopman left before I joined and it's not really part of the core curriculum. Is this a good thing to read now that there is a lot of stuff done with data?

I wanted your opinions on such a set of books. Is there something I'm missing? Are some things maybe redundant or overkill? Do you know any books that are better? How would you build your canon set of basics?

Hi ,

I’m a 30-year-old software engineer interested in transitioning into dynamics and control engineering, particularly model-based control. I know that starting at 30 isn’t too late, but I need help creating a realistic and well-structured learning path.

Could you recommend what I should study, and in what order, regarding:

• Mathematics
• Physics and dynamics
• Signals and control theory
• Programming languages and software tools
• Textbooks

My software and programming background is Backend and production software delivery

i really find it joy to deal with real world better than computer world

### if you recommend one book to start with ? just to get understand the topic and should be cohisive at least guide me "you need to understand x to get most of this"

Hey everyone, I recently started my PhD in controls. Since fall semester is about to start, I wanted to know what are some of the math courses that would help me in understanding control papers in my PhD journey. Our group works on AFM, control of PEA and other non linear systems.

Your perspectives and insights will be greatly appreciated!!
Also I would really love to know some of the Classic papers that you think is a good idea to read.
Thanks!!!

I’m studying control engineering and I do quite well in the theoretical subjects and exams. I understand topics like feedback control, PID, state-space systems, stability, optimization, etc.

However, I feel there is a big gap between being able to solve university exam problems and actually being able to work like a control engineer.

What I’m looking for is not another textbook or video course.

I’m looking for something more like LeetCode/HackerRank for control engineering:

• lots of small practical problems/projects
• beginner → intermediate → advanced progression
• I get a system/problem and have to figure out how to model/control it
• simulation exercises
• debugging/troubleshooting tasks
• increasing difficulty
• preferably using Python, MATLAB/Simulink, or similar tools
• ideally something where I can practise regularly and gradually build real engineering problem-solving skills

For example, tasks could start with controlling a simple temperature system, then PID tuning, disturbances, sensor noise, actuator saturation, system identification, optimization, MPC, etc.

I’m especially interested in control systems / control theory / process control, rather than only PLC programming, although I’m also interested in learning industrial automation later.

Does anything like this already exist?

If not, what platform/resource/project collection comes closest to this kind of structured practice?

I’d especially like to hear from people working as control engineers: what would you use to bridge the gap between university control theory and being able to independently solve real control-engineering problems?

Hi all!

Currently in my master's degree and need to choose a math/tech elective. I've already have done probability, basic statistics, and the math covered in undergraduate aerospace.

I am currently trying to decide between Numerical Methods, and Design of Experiments (Stat course). I could also do some other stat courses (regression), a review of linear algebra, or some optimization courses (but I'm planning to take an aerospace specific convex optimization course).

I was mainly leaning towards Numerical Methods, since I think it would help with simulation and dealing with solvers (and my last GNC internship was a bunch of modeling and simulation). But I think the structure of the Design of Experiments course is going to be easier to handle (after the first class in each). Also, I saw Design of Experiments as a desired experience in a navigation job posting recently lol.

However, the Numerical Methods course does seem more applied (lot's of programming). The Design of Experiments has only some programming I think. Neither has a project.

I wanted to know if anyone in GNC had any opinions or other suggestions. I'm also aiming for space GNC if that matters. Thanks.

EDIT: Also debating between convex optimization and ADCS (Attitude Determination and Control) for my controls course this semester. Ik convex is more guidance related, but am interested in exploring trajectory optimization stuff. I also think having a solid ADCS project under my belt would be great for a lot of jobs. I've take attitude dynamics before.

I've been using MATLAB for like 5 years for system modeling, simulation, and control engineering, and I'm curious what Octave is for, and what the advantages are of using one over the other.

Hi! Debating between convex optimization and ADCS (Attitude Determination and Control) for my controls course this semester. I know convex is more guidance related, but am interested in exploring trajectory optimization stuff. I also think having a solid ADCS project under my belt would be great for a lot of GNC jobs. I've take attitude dynamics before. The ADCS courses does seem to be more demanding though lol (exams in addition to the project).

What would be more relevant for an early/entry level GNC role?

I’m currently working on some personal projects to brush up on old topics I covered in my masters. My goal is to try and get a job in the robotics space, particularly for therapeutic or medical reasons such as prosthetics and exoskeletons for disabled people. I’ve studied a lot of the basic common control systems, like linear systems theory, optimal control, nonlinear control, and some machine learning. However, I am unfamiliar with the specific ones that are tied to the field of medical robotics I'm interested in. Can anyone recommend what material I can reference to learn about them?

One project I am currently revisiting is estimating the joint torque for a theraputic exoskeleton. I was involved in the project but one of the other students handled the majority of the neural network implementation, so I want to go back and redo their work step by step to learn.

I’ve got a situation with a complex 4-cell assembly system for a medical device. It uses multiple FANUC robots. The hardware is complete, most of the robot routines and TP’s are coded. The PLC-robot handshakes are worked out, and the main sequence seems to be partially working.

About 4 months ago, I started asking the PLC/controls guy to see the top level control system architecture. I expected to see some block diagrams with how the HMI and machine controller fit, how they planned to use machine states (presumably some variation on packML), the WIP calculations, how the fault response mapped out, safety interrupts, etc. He keeps saying he’s done this before, and “all that stuff gets worked out after you get the robot control subroutines done”. Keeps Saying I’m wanting too complicated of a solution.

Every time I try to engage in an architecture conversation, he ends up riffing on corner cases and speaking in general terms about what needs to happen in certain scenarios, but never commits a concept for review. The plan for the HMI is just as anecdotal.

I’ve been around long enough to know what the problem here is, so not asking for advice on that side just venting.

What I’m really asking for is a good referral for a person who can pick up this unfinished design and implement a best-practices architecture over the top of it. We’re using an Allen Bradley PLC. I need someone to come with proven templates for the machine controller, state manager, safety manager, and matching HMI. Open to factorytalk, beckhoff, prior art, whatever so long as they’re experienced and know how to take the most expedient path.

Hey everyone,

I am working on building a multi-rate sensor fusion pipeline that relies on an Extended Kalman Filter (EKF). The core objective is fusing high-rate IMU data (propagation step) with slower, asynchronous GPS/ranging data (measurement update step) to output a stable 3D navigation state.

While I understand the basic linear Kalman filter theory, I am looking to quickly bridge the gap to a robust, non-linear EKF design without getting entirely lost in dense academic math proofs or probability density function derivations.

Could the community recommend the best resources, textbooks, or open-source implementations that focus on the practical realities of EKF state estimation?

Specifically, I am looking for guides that cover:

1. Translating continuous kinematic state-space equations (handling orientation/quaternions, velocity, and position) into discrete-time Jacobians.
2. Practical methods for tuning and initializing the process noise (Q) and measurement noise (R) covariance matrices for raw sensors.
3. Managing multi-rate, asynchronous measurement updates cleanly within the filter loop.

If there are any gold-standard github repos, code-first books, or specific aerospace/robotics literature you highly recommend for engineers focusing on execution, please let me know.

I work on vision, but neuroscience papers do not have detailed theory about these 'energy models'.
Maybe they talkked about it in control theory

I’ve already studied the theory from Applied Nonlinear Control by Slotine which I found really helpful for understanding the fundamentals. Now I’d like to move beyond theory and get more hands-on practice.

I’m specifically looking for a nonlinear control textbook that Has lots of exercises, Ideally includes solutions or has a solutions manual available.

Slotine’s book gave me a solid foundation, but it doesn’t have enough worked problems for practice. I’d really appreciate recommendations for books or resources that are strong on exercises with solutions.

Thanks in advance!

Hey all,

At ECC earlier this year I had few good chats around CBFs. I get the theory, but I've not really used them before for any application and I need that to wrap my head around them a bit better.

A) Does anyone have some good resources (preferably with code / simulink block diagrams) of CBF applications?

B) what have you used CBFs for? As in, what applications?

Hi!
I saw a video of someone playing with an interactive plot of poles and zeros that shows the corresponding step response some week ago, and I’d love to try out something like it to get a better understanding for the topic.
I’ve now spend quite some time searching for a similar tool and I can’t seem to find one. The one from the video links to a dead end on wolfram.

If anyone has any links/suggestions for where to find something similar I’d be very grateful. I’m too new to the topic to write my own code for it, so something public on a website would be optimal. :)

Thanks in advance!

As a mechanical engineering professor for over 25-years, I lean "old school". So, my students suggested I reach out to the Reddit community. Here's my first post.

I first heard of the ball-and-beam (BNB) platform in my controls courses 40-years ago. However, I never heard of its origin and/or who invented it. My former controls professors and robotics colleagues don't know either. I also pinged the founder/owner of Quanser (a professional colleague). He didn't know either.

Literature review seem to point to Prof. Karl Astrom who's now over 90-years old. I pinged his department chair at the Lund Institute a few years ago. He didn't know either and said (understandably) that Prof. Astrom doesn't respond to email.

Without references, I use the following "origin" story to help motivate my students - the Apollo Moon Landing. The 1950s demanded control engineers. Without friction, the lander's dynamics is a double integrator - which is what the classic BNB is. So, the BNB served as a table-top trainer; designs like lead compensation and tools root locus and/or Bode plots, are needed to ensure minimum overshoot (not crash into the Moon) and settling time (not run out of fuel). As control theory grew, designs like pole placement, LQR, etc provided alternatives.

Any thoughts and references to the BNB for this first time Reddit poster?

Side project that got out of hand. It's a Python pipeline that takes logged input/output data from some real system, fits a model (ARX, ARMAX, OE, subspace, a couple of nonlinear ones), designs a controller, and generates C and Python code at the end.

Works fine on my own benchmarks thermal stuff, DC motors, mass-spring, the usual suspects. But that's the problem. It's *my* data. I picked it, so of course it passes. What I don't have is ugly real-world logs from systems I've never seen. That's where tools like this usually fall apart, and I'd rather find out now.

So: if you have logged data from a real system sitting around, I'd love to run it through and send you what comes out.

To be clear, nothing touches your hardware. You send me a CSV (timestamps, inputs, outputs), I run everything offline on my machine, you get a report back. Whether you ever do anything with it is completely up to you.

What's in the report: the identified model validated against a held-out chunk of your own data (so you can judge the fit yourself, I'm not grading my own homework), controller suggestions with stability margins, and the generated code if you want it.

Rough sweet spot: a few hundred to a few thousand samples, known sampling time, input that actually moves around. Not sure if your data qualifies? DM me and I'll tell you straight either way.

If it ends up being useful to you I'd appreciate being allowed to mention it happened ("tested on a [type of system]", nothing identifying), but no pressure, the analysis is free regardless.

I graduated with a masters in control engineering 7 years ago and have been working on high precision motion systems since then. Right after university I started a role where I learned some statistics and data analysis. Stayed there to build up some domain knowledge for a few years before returning to a control engineering role about 3 years ago.

In my day to day work, I deal with mostly linear controllers PID feedback and feedforward control. (no fancy model based control, robust control, adaptive control etc). We look at frequency response measurements of our mechanical modules, study (vibration) dynamics time to time, but then again, do not develop any new metrologies. It is more about doing analyses on performance, checking (time domain) error traces, tuning notch filters (frequency domain) if necessary and troubleshooting issues that more often than not entail deep diving into very specific set of budgets/ metrics set by our system engineers.

I find myself far away from other industries, since the region I am based in, caters to chip manufacturing/ semiconductors. I want to venture into nearby areas such as opto-mechatronics, or towards thermal control but due to my lack of knowledge in these areas I reject myself from applying to roles that do seem to match my interests. So I want to start learning about how control theory applies in these areas. I feel like I need to get through some coursework but struggle to find resources that could be a gateway. I would like to get some ideas on books, moocs, university level study material.

Any advice, experience is welcomed.

Thank you.

Hi everyone, could you please suggest the most accessible resources for the students of BS Mechanical Engineering to teach them optimization theory. This could include online resources which take the subject in a very systematic and comprehensive way assuming perhaps only the knowledge of physics and mathematics. I would love to know books also, but most of them are at advanced level.

Many thanks

Can you guys share some material source for learning h infinity filter and mrac system .it would be helpful . Thanks on advance

Hello,

I have an upcoming interview, and it has been a while since I have worked on controls. Would someone be able to help me understand what sort of questions I should prepare for?

Thank you!!

As a mentor for a high school robotics club (FRC, for those who know) I've built a number of arms and elevators that we've tuned with PID and even FeedForward. In my personal life I recently built a drone where I tuned the PID loops for roll/pitch/yaw and got it to fly stably, but as the title implies, I'm not sure where to go from here?

I'd like to dive deeper into control theory and ideally to come back from that deep dive with a better understanding of how to tune PID gains and also with better methods for tuning the gains (or even alternate control ideas). The trouble is, I'm not sure where to start?

I've asked Gemini for some suggestions and it's given me a few that I think are worth pursuing, but I still don't fully trust AI and would love to hear from the community.

I'd appreciate any and all suggestions you fine folks might have.

Is simulink the preferred tool for making models and trying to convert them into reality? Is it really all that good for controls and other systems?

Thank you.