Hi Mohit,

Having a stable open loop plant G doesn't necessarily guarantee a stable closed-loop system. For a unity negative-feedback loop, the stability of a closed-loop system can be determined by the characteristic polynomial of (1 + G). If G = numG/denG, then the characteristic polynomial is denG + numG.

Example #1: Stable plant, unstable closed-loop system

Gp = (s − 2)/(s^2 + 2*s + 1)

pole(Gp) = {−1, −1}

Gcl = feedback(Gp, 1) = (s − 2)/(s^2 + 3 s − 1)

pole(Gcl) = {−3.30278, 0.30278}

Example #2: Stable plant, stable closed-loop system

Gp = (s − 2)/(s^2 + 1*s + 3)

pole(Gp) = {−0.5000 ± 1.6583i}

Gcl = feedback(Gp, 1) = (s − 2)/(s^2 + 2*s + 1)

pole(Gcl) = {−1, −1}

To handle NMP systems, one alternative is to use Prof. Masayoshi Tomizuka's Zero-Phase Error Tracking Control (ZPETC).

Dear Mohit,

the system you attached to your massage is a MIMO system.

The behaviors of such systems do not depend on their element zeros.

its non-min phase behavior depends on transmission zero and for your system it seems to be huge.

in this case, you could not handle it with common control design approaches.

1- you should use a compensator to move them.

2- use a robust control design technique to deal with them

see :

1] K. Zhou, J.C. Doyle, K. Glover, Robust and Optimal Control, Prentice Hall, 1996.

2] Skogestad, Ian Postlethwaite, Multivariable Feedback Control: Analysis and Design, Wiley, 2005

Skogestad, Ian Postlethwaite, Multivariable Feedback Control: Analysis and Design, Wiley, 2005

is a good reference to start with.

Hi:

Please refer to the attachment for a possible solution.

CL

reffer this two book; Applied Nonlinear control JEAN-JACQUES E. SLOTINE Massachusetts Institute of Technology,

non-linear control system by alberto isidori 3rd edition

@Mohit Gupta a belated reply. If an appropriate all pass filter is cascaded with your NMP Transfer Function it can be converted into a MP TF. It may solve your problem.