I agree with everything Runei as stated above.
Here is some insight from a controls engineer who graduated as an ME.
Yes, systems are controlled by the use of electrical signals and digital processing. However, as a mechanical engineer, the systems you will be controlling are mechanical. With that being said, you will learn the dynamics and mathematical models for such systems during your ME academic career. Mechanical systems made up of mass, springs, and dampeners. Fluid systems made up of pressure, flow, regulators, and valves. Thermal systems made up of heat transfer, turbines, and engines. All of this should be covered in your ME classes, which are not covered in EE classes. The other benefit of having an ME background as you are taught the skills to design and manufacture parts, fixtures, and other components for your system.
The understanding of these math models play key roles in determining their response, and more importantly how to control their response. But it is still absolutely necessary to understand how electrical circuits and processing plays a part in all of this, the basics of which will most likely be taught in one or two classes as an ME. Motor controllers, pump drivers, signal filtering for sensors/transducers, etc are electronic and if you plan on designing these (even if at a basic, low testing level) it is crucial to have a general understanding of circuit components.
Also, most systems are not controlled solely on electronics/mechanics but monitored and digitally controlled through the use of a software/programming interface. I personally use LabVIEW for my work, but their are other avenues such as PLC and embedded processing using C based processors.
You will not learn everything you need to know from a bachelors degree, mechanical or electrical. Taking a real interest and perhaps personal hobby into understanding basic control systems was the most important decision I made in my academic career. I started by controlling the speed of an inexpensive DC motor using a photo interrupter as a tachometer (some things you can read about) and created a LabVIEW program to control and display the response. This is the "go-to" beginner control project.
Anyways I hope these comments help. If you want to provide more info on what exactly you would like to practice as a control engineers we may be able to advise further.