It depends upon what kinds of control systems you work on. MATLAB can be quite useful, but there is also quite a bit of work to be done in very routine areas such as HVAC design, Generation turbines, Water treatment, petrochemical refineries, and many other places.
Most of these jobs are relatively hands-on and very straightforward. Yes, I took all that fancy math and I can still use it. However, as my mentors told me: If you're using more than a book and a scientific calculator to get your primary design you're probably doing something wrong. Someone has done these calculations before you came along and it is best to use their work, unless it is known to be wrong or deficient in some way.
The vast majority of my career has been like this. I have applied some heavy math on occasion, but those instances are few and far between.
Even in complex fields such as fluid dynamics, there are usually response curves that follow exponential or logarithmic functions. There are very few cases of abstract non-linear matrices. If you find yourself in such territory, take a good hard look around and make absolutely certain that you're not re-inventing someone else's work. You will probably find an appropriate approximation or "plant equation" that can adequately describe what you will need to do.
The reason I discourage new engineers from doing what they learned in school is because it is easy to make mistakes and overlook a critical element. At the energies and expenses involved here you REALLY do not want to make mistakes. I'm not suggesting that we forget these fundamentals, but I am suggesting that we look to leverage the work of others that has already been proven.
So you ask what tools we use? I start with a pencil, paper, and a calculator. When I have a concept, I'll refine it with more detailed calculations. However in most cases, I won't go into heavy analysis unless there is a very specific reason for it. Situations like that exist when designing for situations that have never been explored before. Very few other situations need that sort of attention.
Remember, the design doesn't need to be perfect. It merely needs to be good enough. Almost nobody is willing to pay for "perfect."
This is the reality of the engineering world. Your professors can refine a design so that it is nearly ideal for a very specific range of conditions. However the real world has unexpected conditions, sloppy sensors, poor maintenance with wear and tear, and you'll need to include some slop in your model. When you acknowledge the degree of slop that exists in most applications, you'll realize that it is rarely ever worth working past three digits of accuracy in most cases.
Again, the most important tools are a pencil and a brain.
I've been in this career of controls engineering for nearly 27 years. It is exciting, interesting, infuriating, funny, and occasionally even dangerous. I recommend it highly even if you don't often get to play with all the cool math toys they taught in school.
