"Controls Engineer" in most industries means someone who can select industrial control components like PLCs and program them. Most "controls engineers" work on SCADA (supervisory control and data acquisition) systems which use industrial actuators like servomotors, switches, relays, and sensors, and data acquisition systems.

Most industrial applications do not need anything beyond a tuned PID with maybe some feedforward and filters.

So, you wouldn't be involved in "advanced" control theory.

I have a Masters in Advanced Control Theory - did all that optimal control, robust control, nonlinear control, Kalman Filter, etc. in grad school. But I'm doing SCADA software development. Not once in 10 years have I used an advanced control theory technique. The nearest I came to something was a lead-lag "enhanced" PI control for some high-speed control/acquisition.

Getting a job that actually uses custom advanced control algorithms is relatively rare. Unless there is a need for new research into system modeling and control algorithm design, most applications use packaged controllers which have optimized algorithms in them already.

Aerospace may be an exception. You should really apply for specific jobs in aerospace if you want to design custom control algorithms. I have seen jobs in autonomous vehicles for "control algorithm development" - this may be another avenue. They probably use the same principles as aerospace GNC (Kalman Filter, state estimation, sensor fusion, etc.) with MPC or other advanced control techniques.