Sure! Here are some use cases where MPC might be preferred over PID:

1. Complex, nonlinear systems: MPC can handle systems with complex dynamics, such as those with nonlinear behavior, multiple inputs and outputs, and time-varying characteristics. PID control, on the other hand, may struggle to control such systems, especially when the system has constraints.
2. Systems with constraints: If the system being controlled has physical limitations on states and control inputs, then MPC can be an attractive option. This is because MPC can incorporate constraints into the control design, ensuring that the system operates within safe bounds. In contrast, PID control cannot easily handle constraints, and often requires ad-hoc tuning to ensure stability.
3. Multi-objective optimization: If the control objectives are conflicting, MPC can optimize multiple objectives simultaneously, which is difficult to achieve with PID control. For example, if the objective is to simultaneously minimize tracking error and control effort, then MPC can find the optimal balance between these two objectives, whereas PID control may require a trade-off between them.

On the other hand, here are some use cases where PID might be preferred over MPC:

1. Simple systems: For simple, linear systems with few inputs and outputs, PID control can be an effective and easy-to-implement solution. The tuning of PID parameters can be done by hand, and the control output can be computed using a simple algorithm.
2. Real-time requirements: PID control is computationally simple and can be implemented in real-time with minimal delay. In contrast, MPC requires more computational resources and can introduce additional delay due to the optimization process.
3. Robustness: PID control is inherently robust, and its performance can be reasonably stable even in the presence of model uncertainties or disturbances. In contrast, MPC relies heavily on the accuracy of the prediction model, and can be sensitive to modeling errors.
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