The origins of CTAC date back to 1987 when a research group was formed at Coventry Polytechnic between the Department of Mathematics and the Department of Electrical, Electronic and Systems Engineering. The research group, originally known as the Control Theory & Applications Group (CTAG), became known as CTAC when it was recognised as a research centre of excellence in 1992; being awarded external funding at the same time that the institution became Coventry University.

The research activities of CTAC continued to grow steadily over the years. It became renowned for solving real industrial problems and it earned both national and international recognition in the field of control systems. In March 2015 the established research centres at Coventry University were dissolved and formally closed.

In October 2014 CTAC Associates LTD was incorporated as a registered company and it was launched in January 2015. CTAC remained dormant until the re-launch in April 2022.