Jurist, Amy-MiMi and California81 thanks a lot for your input.
I tried to involve most of your corrections.
I am struggling most with finding another expression for the sentence: "Continuous involvement in the day-to-day business of the flight test department allowed me to create a comprehensive synthesis and my achievements led to an award as a “high-performing intern”." 
Would anyone have another solution that sounds better and conveys the same meaning? ;)
Here is the current version:
--------------------------------
Dear Professor X,
Dear Dr. Y,
Having a great interest in applied research in aerospace engineering, the PhD Thesis at (company) posted on the website of the (department) directly appealed to me. 
I recently earned a Master of Science degree with distinction in Mechanical Engineering from (university). During my Master’s program I specialized in aerospace engineering with a special emphasis on control engineering and structural dynamics. Furthermore, I acquired knowledge in the field of aeroelasticity as an exchange student at (university). In the course of a study and research period at (university) in (city), (country), I dealt intensively with mechatronic systems and machine vibrations.
It has long been clear to me that, following my studies, I want to do research in the field of applied control engineering and structural dynamics. In this regard, I am looking for a topic that is of great relevance for an aerospace company that is recognized worldwide, as it is the case with this PhD position in collaboration with (same company). My fascination with both the products and the working environment of (same company) was strengthened during a six-month internship at (same company) in (city), where I was part of the (department). There, my task was to analyze and categorize malfunctions of the new (propulsion system). Continuous involvement in the day-to-day business of the flight test department allowed me to create a comprehensive synthesis and my achievements led to an award as a “high-performing intern”.
I am convinced that my strong analytical thinking capabilities are an excellent basis for the successful completion of this PhD; in the past they helped me obtain the highest grades on both exams and research projects. My high level of commitment also led to several awards and scholarships. Furthermore, I demonstrated my ability to explain complex issues in a simple way in the course of various positions as a research assistant at my home university. There, but also during several stays abroad, my open-mindedness and very good communication skills allowed a rapid integration in very diverse working groups.
I consider the advertised PhD position to be the perfect opportunity for me to make full use of my acquired knowledge and combine it with my great interest for innovations in the aerospace industry. I would appreciate the opportunity to meet with you to further discuss my motivation and my qualifications. Thank you very much for your time and consideration, and I look forward to hearing from you.
Yours sincerely,
-----------------------
And I'm looking forward to your corrections!
Best
Martin