How can I stabilize this system using MPC?

Question

I'm a rookie in control science. I've been learning MPC recently and I got trouble with a plant: $$ G(s)=\frac{-0.65 s+1}{-0.7 s^2-0.05 s+1.5} $$ This is a nonstable plant with both positive poles and zeros. I tried some methods like PID and dyanamic matrix control (though it may not be very useful for nonstable plant). Unfortunately all of them failed.
The only way that I succeed is by using the MPC Toolbox in matlab, but I cannot see the detail algorithm as the Toolbox only generate simulink model or matlab code (very simple)
I want to know is there a simple controller that can stabilize this plant and make no-error tracking for a step input? I really want an MPC implementation for it (will state space MPC be helpful?)
Thank you very much:)

Answer 1

Well, I've found a solution by transfering the plant to a state-space model. I designed a state-feedback controller to stabilize the plant and applied a PID to track the reference input.
The structure of the controller is as shown in the following picture:

The feedback gain is created by the matlab function 'place'. Due to the positive zero, the plant is a nonminimum phase system. The PID parameters should be negative. I chose [P,I,D]=[-2, -1.5, 0]. The output is: