Dear Gary Wu

The model (system/plant) dynamics can not be changed, we need to design a feedback controller such that it need to take care system dynamics(RHP,RHZ). The location of the poles and zeros provide qualitative insights into the response characteristics of a system.

# Main objective of control system is to make unstable process into stable process, this can be done using feedback control (PID). 

If you want to find the RHP or RHZ of system, use transfer function model of the system and find poles and zeros using matlab command easily.  The control design for system with RHP,RHZ is a challenging. Many methods is available in literature to find PID controller parameter for unstable (RHP) and non-minimum phase system. 

http://virtual.cvut.cz/course/syscontrol/node69.html

https://www.facstaff.bucknell.edu/mastascu/eControlHTML/PID/PID3.html

http://ctms.engin.umich.edu/CTMS/index.php?example=Introduction§ion=ControlRootLocus

https://in.mathworks.com/help/control/ref/pzplot.html

s = tf('s');

G1 = 1/(2*s+5)

G2=1/(10*s+1)

G3=1/(20*s-1)

G4=(5*s-1)/(40*s+1)

% 4th order model with RHZ,RHP

G=G1*G2*G3*G4

pole(G)

pzplot(G)

I'd develop the closed loop equations in the frequency domain. You could keep the controller C(s)=p(s)/q(s), say and you could fix a closed loop desired transfer function. From the closed loop, you could obtain C(s). That frequently works but you may obtain noncausal controllers if you do not choose the closed loop transfer function in a suitable way for your system.