A PID (Proportional, Integral, Differential) controller by definition has integrators and differentiators. But these can be simulated in microcontroller code so you don't need additional hardware for that.
Google PID controllers for tutorials on this subject.
My preference is to do such loops using Fuzzy Logic since it's easier and more intuitive than PID loops in a microcontroller. In general, it consists of a series of If-Then statements, which are usually easier to understand and optimize then the code for PID loops. But not many are familiar with Fuzzy Logic so shy away from it. If interested just Google "fuzzy logic".