The power of the PID largely remains untapped. I have recently documented the extensive capability of the PID but being a realist, I expect MPC is going to take over more and more of the role of the PID.
Here is a new section on Model Predictive Control Best Practices for the next edition of the Guide to the Automation Book of Knowledge that is the primary resource for the ISA Certification of Automation Professionals (CAP) Program.
For advanced regulatory control, when do I use Model Predictive Control (MPC) instead of PID control? There are many PID techniques for dealing with batch operations, abnormal operation, startups, and transitions. Feedforward, ratio control, and override control are a main stay for PID control.
For basic control, when do I use Fuzzy Logic Control (FLC) and Model Predictive Control (MPC) instead of PID control? The automation and integration of FLC and MPC into distributed control systems makes these a more viable choice. Surprisingly, there may be less decisions and expertise required than for PID control.