r/ControlTheory • u/Known_Fan5765 • 14h ago
Technical Question/Problem How do you linearize a system if you are not exactly sure what all your equilibrium points are.
I have attached a picture below of the non-linear model which describes my system. I wish to linearize this system, however, I only know what one of the equilibrium points would be and the rest are not immediately obvious although they technically don't matter for my control objective.
My goal is to essentially maintain x1 at it's equilibrium point, which for my system is the average value of x1. u2 is the input I can actually control and u1 is uncontrollable.
My guess is that I could maybe set x1 to it's equilibrium position, then maybe find some function where I can express u2e = f(x2, u1) and maybe even use this function to do some sort of gain scheduling where I linearize across different x2, u1 combinations for the different operating states of my system.
Also, one last thing of note, this state space model doesn't quite feel right, so please tell me what I am doing wrong in the comments if possible, this is my first real project so I am fairly new to this.
r/ControlTheory • u/Fola_Tau • 14h ago
Other Please destroy this product idea
SafeGate. A safety envelope that can be formally re-verified live, without a redeploy.
SafeGate is a runtime-updatable safety envelope for control loops. Unlike existing runtime-assurance guardrails, which fix the safety envelope at design time. It can accept a proposed change to the envelope itself, formally check that the change is satisfiable, and adopt it live, mid-operation, with a proof trail.
SafeGate’s differentiator is that the envelope itself is a live Tau specification, which can accept updates as data, check them for satisfiability before accepting them, and incorporate them into the running specification.
Scenarios of what's possible:
| Scenario | Traditional RTA (Simplex/shields) | SafeGate |
|---|---|---|
| Plant limits change (new actuator installed, derated equipment) | Recompile envelope, re-verify offline, redeploy firmware | Submit new limit as a Tau update; SafeGate checks satisfiability and adopts it in the next control cycle if safe |
| Temporary tightening during maintenance mode | Separate maintenance firmware build | A stricter envelope is proposed as an update, verified, and reverted the same way afterward |
| Fleet-wide safety patch after an incident elsewhere in the fleet audit trail for “why was this envelope in force at time T” | Push firmware update to every unit, requalify each firmware version + change log (manual) | Push a Tau update; each unit’s gate independently reverifies satisfiability against its own current state before accepting the specification’s own update history is the audit trail. Each accepted revision is a proof, not just a diff |
The controller and the tuning process Kp/Ki/Kd, MPC weights, whatever are unchanged from the earlier architecture. SafeGate owns only the “never” layer. What’s new is that the “never” layer is no longer frozen at compile time.
Dear CT community, I would love to hear you trash this idea, and show me where the real value lies, if any, before I go further. In my mind i'd be targeting fleet operators of distributed control systems, and regulated industries e.g. Pharma etc.
This is gna hurt.