
PID controllers are mostly linear, manually tuned algorithms. they are effective in stable environments but struggle with the complexity and variability of most modern control situations. PID cannot optimize toward multiple goals unless you accomodate custom tunning for different setpoint. PID is best suited for single input- Single output (SISO) systems and for anything but the simplest situation multiple PIDs loops are often required.
Limiting factor: tuning the system faces multiple trade-off

MPC is beneficial in feedback and feedforward but still lack the capability to model the complexity and variability of some complex systems. it represent a valuable improvement upon PID particularly to help in real time parametrization but requires a reliable process models. aditionally solving the model, in real-time, is a mathematical optimization problem that requires a lot of compute.
Limiting factor: difficult to create a reliable model at the edge

Deep learning models, handle highly complex, high-dimensional data and handle relationships between variables that are intricate and nonlinear. Neural Networks (NN) are used as mapping functions from high dimensional data to control actions. NN can optimize control performance toward multiple goals.
Limiting factor: not an evolution, completely different approach to real time control