Hi there,
Yes, you can definitely switch between different controllers. We call this feature "bumpless transfer". In your MPC controller you need to check the option in block dialog to use "external manipulated variable". This is explained here .
You also need to ensure bumpless transfer for when you switch from MPC to PID controller. If you use Simulink PID Controller block, you do that by using tracking mode feature, as explained here .
Finally, here is a link to our webinar where we designed both PID and MPC controllers for a robot arm and compared them by switching between them and comparing performance.
Hope this helps.
Arkadiy