Hello!

In your situation it is possible that when you add a pole the closed-loop systems looses stability. Hence the best practice here is to design a proper controller from the begining.

However, having said that, in your case to avoid stability issues I would move the additional poles to the very left if possible.

Hi Nikolaos,

Apart from what Stanislav has mentioned, you should also consider the system noise in mind. Noises are typically high frequency phenomena and you don't want your controller to have be very sensitive to noises (i.e. controllers having large gains at high frequencies). Hence, if you are aiming for a system bandwidth of w Hz, then adding few low pass filters to your controller (i.e. adding poles) with cut-off frequency between 5w and 10w is preferred. You don't want the poles to be sitting way to the left and thus allowing high-frequency noise to creep in.

Mayank

Hello,

May be you can add a filter like 1/(Ts+1)^n to make the controller proper. You can search it from Internal Model Control related papers. 

But the best way is to design a new controller i think

hope this help.

Hello

There are in my opinion excellent texts and methods available as mentioned in various answers above .But,I believe Practical vision clears all your doubts.One  system,where you can see this problem is the stabilisation of a cart balanced Inverted pendulum.FYI there is a zero at the origin and a pole on the right hand side which makes it inherently unstable system.The Primary objective is to stabilise the system but it is also important to design the transient response of this system.There is a lot of literature available on this particular problem.Please,go through it and if possible design a controller for yourself in Matlab/Simulink.You will have a first hand understanding of various problems involved.

Hi,

You can use any control design technique such as root locus design, frequency base design approach, pole placement approach, etc.

Pole placement is recommended to assure proper stability.

(1) The low-pass filter function is very useful in the control engineering practice, as suggested by Osman Çakıroğlu.

For example,

The paper [HY10] used the low-pass filter function to make an improper controller be implemented in the real-world network traffic control system.

J(s)=(\gamma s + 1)/(\beta s + 1)^3

[HY10] Y. Hong, O.W.W. Yang, "Robust Explicit Congestion Controller Design For High Bandwidth-Delay Product Network: A H∞ Approach," Proceedings of IEEE International Conference on Communications (IEEE ICC), Cape Town, South Africa, May 2010. Available in the following RG Link.

https://www.researchgate.net/publication/221167543_Robust_Explicit_Congestion_Controller_Design_for_High_Bandwidth-Delay_Product_Network_A_H_Approach

The book [MZ89] recommended a low-pass filter function which has the form

f(s)=(\gamma s + 1)/(\lamda s + 1)^n

to make unstable processes be stabilized before applying adaptive IMC.

[MZ89] M. Morari and E. Zafiriou, Robust Process Control, Prentice-Hall, Englewood Cliffs, NJ, 1989.

http://www.amazon.ca/Robust-Process-Control-Manfred-Morari/dp/0137821530

(2) The following RG question also discussed the similar topic.

Is there any specific technique to stabilize an unstable discrete system before applying adaptive IMC?

https://www.researchgate.net/post/Is_there_any_specific_technique_to_stabilize_an_unstable_discrete_system_before_applying_adaptive_IMC

Conference Paper Robust Explicit Congestion Controller Design for High Bandwi...

As others have mentioned, use a low-pass filter with repeated poles on the real axis, in the LHS of the complex s plane. Make sure it is properly normalized to yield unity (linear) gain at s = 0. Use as many poles as you need to make the trn fcn proper. Increasing the number of poles will increase high-frequency attenuation.

And yes [MZ89] is a great book! Their approach is pretty much - design a controller by inverting the plant (using IMC), then add a low-pass filter for robustness.

Dear  Nikolaos,

Good Day,

I recommend that you use state feedback controller Design using pole placement to stabilize your system, so ignore your first controller design since it did not work and start again by using pole placement ,here few websites and articles for you to see.

http://www.mathworks.com/help/control/ref/place.html

https://www.youtube.com/watch?v=1MXGmktHmCU

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

https://matlabexamples.wordpress.com/2013/10/31/state-feedback-controller-design-using-pole-placement-technique/

http://radio.feld.cvut.cz/matlab/toolbox/control/getstart/desig24a.html

Pole placement will work well if you have a good plant model, but it is not particularly robust, so measures are usually required to address this problem (i.e. add a low pass filter!).  

You can use Diophantine equations to design a proper controller.

I think you can study from this book: https://books.google.com.my/books?id=vJrSBQAAQBAJ&pg=PA149&lpg=PA149&dq=an+improper+controller&source=bl&ots=WtpKAJkm9E&sig=vqnGlqNtqlM7pGvWO4dPIfFXtgg&hl=en&sa=X&ei=Ne8kVZD3FYmiugTz_4GYBw&ved=0CEUQ6AEwCA#v=onepage&q=an%20improper%20controller&f=false

May i please know is your controller PID or what?

Have you tried pole placement technique to stabilize your system before using controller?

I completely agree with the response by Mayank Baranwal.

It looks strange that the degree of the numerator of the controller is much higher (row much ?) than the degree of the denominator.

I suggest that before designing the controller you examine the plant transfer function (corrector x sensor). It will be difficult to place the unity gain frequency in a frequency  region where the plant transfer function has a high slope (proportional to 1/f^n with n>>2). It would require derivators (associated with high frequency poles to keep it proper) that will enhance the system noise. You can possibly  accept a lower unity gain frequency where the plant transfer function is better behaved, or redesign your sensor and/or actuator to have higher bandwidth ones.

To make the controller proper, augment the controller with an n-order lag filter assuming that the controller numerator order is n-order as high as that of the denominator, e.g., if numerator is 1 order higher than the denominator, augment the controller with a first-order lag filter.

Next, after deciding the order of the augmented filter, it is necessary to choose a proper value/s for the filter time constant/s.. Of course, one need to consider the noise effect, so the time constant cannot be too small otherwise, the noise effect on the control response will be severe. On the other hand, if one use a too high value for the filter constant, the controller robustness would be degraded, or even leads instability. One suggestion is to use the smallest time constant in your process model as a basis for setting the value for the time constant. E.g., if the smallest time constant is 1, perhaps you could try with 1/4 of the value as an initial setting. Check for the controller robustness, i.e.,  is it seriously degraded or not. If yes, try lowering the controller gain to recover the original robustness; otherwise, no further change is required.

I completely agree with the response by Jobrun Nandong.

The problem is the search Nikolaos Kourkis simulation of a compromise between dynamic performences desired from the controller and the conservation of its robustness, well understood it will start with time constants as low as possible.

nikolaous  pole and zero concept you talking about. if you study the behaviour of steady state of any trasfer function and then find steady state parameters then it is easy to you to estimate its behaviour. for stability we add poles on left of s-plane. so you should add extra s terms on denomenator part of any controler and plot its characteristics in polar or nyquist plot.