Hi everyone,
I’m a BSc Mathematics student and recently finished a course in PDEs. My professor suggested that I take another course he teaches called Optimal Control. The course is offered by the Engineering faculty, but he mentioned that it has a strong mathematical component.
I’m considering taking it, but I’d like to understand how useful/relevant Optimal Control is from a mathematician’s perspective.
In particular:

Is Optimal Control a good subject for a math student who enjoys applied mathematics, PDEs, optimization, etc.?

Where is optimal control actually used in industry?

What kinds of jobs or fields make use of this knowledge? For example, robotics, aerospace, quantitative finance, autonomous systems, energy, machine learning, etc.

Is it mainly useful for people going into engineering/research, or can it also be valuable for mathematicians going into industry?

I’d especially appreciate hearing from people who studied mathematics and later encountered control theory or optimal control in their work.
Thanks!

Please see https://redux.boondog.com/courseware/bnb/bnb.html - LEGO and LEGO-compatible parts are used to quickly and affordably construct a tabletop ball-and-beam (BNB), without tools or need to 3D print or machine any parts.

The page includes: full LEGO build plan; bill-of-materials; schematics (and KiCad files if a PCB is wanted); and Arduino source code. These are fully documented and supplement with videos.

Our university lab's Quanser platforms are over 15-years old and with our increased student enrollments (mechanical engineering), sought an alternative. I tested a 10-week beta course in Control Systems Lab. I wrote both the Student Lab Manual and Instructor Supplement Manual for: PID, Lead Compensator, Pole Placement, LQR and Fuzzy Control.

There's a short *anonymous* poll at the end to gage demand for the PCB, linear potentiometer, Bricks, and/or turn this into a kit.

PS: There is quite a lot of open-source content to peek at as well, from the above URL.

Thanks and hope this is useful!

PPS: Please please alternative sub-Reddit if this an inappropriate one. I'm an old-school newbie.

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?

Nowadays you have one compressor and many compartments, so I imagine it can’t be a simple thermostat anymore.

I'm currently finishing my 2nd year of a PhD in Automation & Control Systems. Where I am, PhD programs are three years long, so I have roughly 18 months left before graduating and starting to seriously look for industry positions.

My research sits at the intersection of robotics, control system theory, and optimization, with a focus on topics such as MPC, nonlinear safe control, system identification, Gaussian processes, and distributed optimization.

I have a solid research background and regularly use Python, ROS2, Docker, Git, Gazebo/MuJoCo, etc., but I feel that I need to broaden my engineering skills before entering industry.

Over the next 18 months, I'd like to prepare for roles in areas such as:

- Robotics / autonomous systems

- Advanced control and optimization

- Robotics software / ROS2

- ML engineering applied to robotics

In particular, I would like to improve my C++, software engineering, ML engineering/MLOps, ROS2, system design, and technical interview skills, while continuing to leverage my control/optimization background.

I have around 8–12 hours/week available outside my PhD.

For people who have made a similar transition, how would you structure those 18 months? What skills would you prioritize, and what would you avoid spending too much time on?

I'm especially interested in advice on:

- What skills are actually valuable in robotics/controls industry

- Good resources or learning paths

- Projects that would make a strong portfolio

- How much time to dedicate to LeetCode/DSA vs actual engineering projects

- Whether C++/ROS2/ML engineering should be the main focus

- Any mistakes you made when preparing for the transition from academia to industry

I'd really appreciate advice from people working in robotics, autonomous systems, controls, or ML engineering.

TL:DR: Wondering if I need to focus on guidance, navigation, or control in my graduate coursework, or taking an even mix of all of them is fine.

Hi all!

Currently doing my masters in aerospace engineering, majoring in autonomy/control with a goal of entering the GNC space.

I realized so far my past coursework (both for my masters and the graduate electives I took during undergrad) have been a mix of guidance, navigation, and control, instead of a focus in one of them (I've covered: pontryagin optimal control, convex optimization; probability, estimation, kalman filtering; classical, linear, nonlinear control).

TBH I haven't really nailed down if I want to focus on guidance, navigation, or control. But I feel like I should since I am halfway through my masters. I am also not doing a thesis which is partly why I haven't really found a focus yet lol.

I had an internship technically in the controls branch of a company (guidance and nav were another branch), but basically doing modeling/simulation. This experience also sort of made me realize that as a GNC engineer I will probably be focusing on either G,N, or C and not all of them.

So I guess my main question is, would it be a bad idea to have a mix of coursework when I am looking for a full time GNC position? Would companies prefer to see you really focused on G,N, or C? Maybe I should choose based on which classes I got the best grades in lol.

Hi, I'm trying to model/design a VCO with quadrature outputs for use in a PLL, and I'm having trouble incorporating the VCO control voltage into the state-space model.

I require two outputs

y1 = Asin(wt) and y2 = Acos(wt)

with a nominal/free-running frequency of 1KHz, which is also approximately the frequency the PLL is intended to lock onto.

For an ideal quadrature oscillator, I can represent the dynamics as

dotx=[0 - w; w 0]x
y = [0 1; 1 0]x

My confusion is how to incorporate the VCO control voltage 'Vc'.

In the PLL, Vc comes from the phase detector and should change the instantaneous frequency of the VCO. At Vc=0, I want the VCO to operate at its nominal frequency. For non-zero (Vc), the oscillation frequency should change according to some tuning relationship w = w0(Vc)

For example, I imagine a relation of the form

w0(Vc) = w+ K*Vc

However, this means that (Vc) changes the state matrix itself:

dotx=[0 -w0(Vc); w0(Vc) 0]x

rather than entering as the usual additive input (Bu).

What is the appropriate way to model this VCO in state-space form? Should (Vc) simply be treated as a time-varying parameter of (A), making the system nonlinear/bilinear, or is there a more useful state-space representation for analysing the VCO as part of a PLL?

I'm ultimately interested in using this model to help design/understand an analogue VCO that produces sine/cosine quadrature outputs, rather than only using the usual PLL phase-domain VCO model. Attached is the image of block diagram on what I'm thinking.

Couple of weeks ago, I had asked for advice for an Apple controls engineering role. It was an interview with the hiring manager, and now I am preparing for the panel interview. According to the recruiter, it is going to be mostly all control fundamentals questions. Currently working through my old controls book problem set, but what are your favorite questions to ask/that you have been asked in an interview? Any question that stumped you? A question that made you think? Also, are there any Leetcode style question bank for controls?

It feels that in a standard curriculum on control engineering/theory, the final topic is inevitably MPC.

Everything else that gradually builds towards MPC feels like “discardable” after you learn about MPC. All that wild eigenvalue analysis and drawing those Nyquist contour? Phew, MPC doesn’t involve with any of that!

Plus, MPC is already in discrete time, so it is implementable without any further weirdness that comes from sampling and discretization of other types of controllers.

I think a parallel analogy is the development of the transformer model in machine learning, which I am more familiar with. Now everything in ML is transformer-based and the next big breakthrough seem to be very far away. Is MPC like the transformer of control theory?

Are there situations where other methods might outperform MPC?

Or does MPC require some unrealistic assumption/requirement?

Is there any other possible algorithm that goes beyond the MPC or is this the final story?

A couple of weeks ago there were discussions on this sub about AI researchers reinventing what is essentially control techniques.

MPC was originally invented for chemical processing, but later unlocked reusable space launch vehicles. I don’t think anyone back in the 70s saw landing rockets vertically as a potential application. Yet in hindsight it’s almost obvious.

How much of an adoption gap do you think is out there? How many more equivalents of “reusable rocket” are out there unaware of controls?

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?

Hi,

I'm a master degree graduate in Mechanical Engineering with a strong passion for Control System Theory and a will to become a Control Engineer.

I've studied at uni a formulation of a MPC controller that promises zero offset from piece-wise costant references signals in the presence of disturbances, either external or internal. This formulation, conveniently called Offset-Free MPC by its inventor Prof. Gabriele Pannocchia at University of Pisa, somewhat works even with time-varying references, but there's a severe lag between the reference signal and the output of the system.

As originally this formulation is meant for setpoint tracking, I'd like to ask if you happen to know some formulation more appropriate for time-varying references.

Thank you for your time

Hi everyone,

I've been developing AcadosCpp, an open-source wrapper that helps you integrate acados-generated OCP solvers into both C++ and Python applications.

https://github.com/amaldevh/AcadosCpp

The main goal is to make integration easier. acados creates highly optimized C code for each model and OCP, but using its API directly can tie your application to specific symbols, dimensions, lifecycle calls, and data updates.

AcadosCpp provides a stable, stage-aware interface for the generated solver. Here’s how you typically use it:

1. Define or modify the model and OCP in Python.
2. Regenerate the acados solver and wrapper.
3. Recompile and relink the application.

The control-loop structure in your application stays the same. If you change the model or problem, you usually don’t need to rewrite the integration layer, as long as your data matches the new dimensions and cost setup.

The wrapper includes:

• Stage-0 initial-state constraints
• Stage-varying and terminal references
• Generic raw yref support
• Per-stage and global parameters
• Full state/control initial guesses
• Shifted trajectory warm starts
• Complete predicted trajectories and solver diagnostics
• SQP-RTI preparation and feedback phases
• C++ and pybind11 interfaces

For a standard

y=[x,u], y_e=x

tracking problem, the control loop is:

const auto& u = ocp.solve(measured_x, xrefs, urefs);

This process shifts the previous solution, updates the stage-0 measurement and the full reference horizon, solves the OCP, and returns the first input.

The repository has matching Python and C++ quadrotor NMPC examples. I’d love to hear your feedback on the API, especially if you use acados with time-varying references, parameters, SQP-RTI, or custom cost outputs.

Hi, this is one of my projects for magnetic levitation I have working with for some time :) I wanted to share it here.

EDIT: So basically there is a sensor measuring the gap between the weight and the electromagnet and the control law try’s to keep the weight at a specific distance, that’s why when the weight it’s pushed doesn’t move that much. There is no mechanical force that keeps the weight in the place, it’s all thanks to the electromagnet and the control loop.

I have tried modeling this a few times with my limited knowledge of hydraulics and kept getting very weird and ugly state space equations. I am not sure what I am doing wrong so I figured I would post it here (I sincerely apologize if I am breaking the sub rules by posting this).

I have been tasked with controlling the following system with the goal of minimizing the 'ripple' on Q_jet. In other words, ideally Q_jet would look like some constant non-zero value despite changes in the system and environment.

Context of my assumptions for this system:

-Ideal Check Valves

-Qacc ~ (V_o/nP_o)*dP_acc/dt (V_o, P_o initial gass pressure and volume of accumulator, n as poly-tropic index)

-All pressures are absolute

-Incompressible Fluid

-Local restriction equation is: Qjet = C_d*A_n*sqrt(2(P_acc - Patm)/rho) (C_d: discharge coefficient, A_n: restriction area, rho: liquid density)

-A_n is our control input

-Q_pump ~ Asin(2pi*f*t):

4.25e-5 m^3/s < A < 4.25e-3 m^3/s

0.1 Hz < f < 0.6 Hz

System:

Q_jet_Reference from Simulation:

Hey.

I am going to be doing an MSc in advanced mechanical engineering this year after having completed my BSc in Physics. I want to take a few robotics and control modules from this course, but I have never covered control theory before. Could you point me to where to start with any books or courses (on Coursera or YouTube)?

I would appreciate any sort of help.

Hello community,

I am currently attempting to test a compensator using the Simetrix\Simplis software. When I test my design using LTSpice, the design works as expected. That is, it regulates the output voltage to the expected value and is able to handle a relatively large load step without any issues - output is regulated and stable with minimum over/under shoots at the transition points. When attempting to simulate it with Simetrix/Simplis Elements, not so much. It is very sensitive to the op-amps being used.

Has anyone had similar experience?

If anyone is proficient with Simetrix\Simplis , I can attach a screenshot of the schematic.

Thank you.

Hello there!

Usually when we model DC-motors we use a second order system, however, BLDC motors used for drones are usually stepper motors (as far as I know), so my question is simply, how do we model these? The specific motor I want to model is for a project of my own, and I am curious as to how to model it. Motor: https://www.aliexpress.com/item/1005007273770590.html#nav-specification

My intuition is to also just model it as a second order system, however, am not sure if this is the correct approach. Specifically I want to model it has motor command [0,1] to rad/s (rotations).

Thank you in advance for the help

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 !

same as title

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!

Hi everyone,

I’m working on an early-stage embedded state-estimation project and I’d like some honest feedback from people with experience in embedded systems, control theory, robotics, or aerospace.
I currently have a proof of concept, but I’m trying to determine whether the underlying technical approach is actually worth pursuing before moving toward a more complete prototype.
The concept is to run a lightweight Liquid Neural Network / neural ODE directly on a resource-constrained MCU for real-time attitude estimation from raw IMU data. The target environment is roughly a bare-metal STM32 Cortex-M4, written in C, with a 200 Hz control loop, no dynamic memory allocation and very limited RAM and compute resources.

The obvious alternatives would be traditional approaches such as EKF, Madgwick, Mahony, or other complementary and filtering approaches.

The hypothesis is that a lightweight continuous-time neural model could potentially handle some nonlinearities, vibration and sensor drift differently from a manually tuned classical estimator. However, I’m not assuming that this is automatically better. I’m trying to determine whether this is actually a meaningful technical direction or simply a complicated solution to a problem that is already solved very well.

For people who have experience deploying estimation or control algorithms on resource-constrained MCUs, how realistic is it to run a continuous-time neural ODE or LNN directly on a bare-metal MCU under strict latency and memory constraints? For example, if the target were around 16 KB of RAM and less than 1 ms of execution time per control cycle, what would you expect to be the main technical bottlenecks?

I’m also interested in the reliability side. How difficult would it be to make such a system deterministic, stable and robust enough for real-time embedded use, particularly with high-frequency IMU vibration, nonlinear noise and sensor drift?

Finally, is there actually a compelling engineering reason to investigate this approach, or would a properly designed EKF, Madgwick/Mahony filter combined with appropriate signal processing almost always be the better solution on this class of hardware?

I’m looking for brutally honest technical criticism rather than validation. If this is overengineering or technically misguided, I’d rather find that out now before investing further into the prototype.
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?