Connection between PID, Pole placement and LQR
LQR or PPR regulators are both state-space regulators, which use the states of the system in order to bring the poles of the closed loop system to some desired locations. They do this by multiplying the states with a constant matrix of gains and feeding the result back as an actuating value, i.e. u = -Kx.
Technically, LQR and PPR regulator is the same regulator, but different methods have been used to calculate the gain matrix K. As long as the system is observable and controllable, it is possible to place all closed loop poles to a specific location. 

PID controllers however use the output measurement of the plant (instead of the states) and since the controller structure is fixed, it can only provide restricted dynamics, i.e. it is generally not possible to directly place poles of the closed loop system to desired locations.

That means, in general, there is no way of getting a PID out of a state space controller or vice versa. You need to use other PID designing techniques in order to stabilize your system.