The system is highly nonlinear and we want to increase it's closed loop bandwidth. but the system bode is still quite strange and difficult to extract exact bandwidth frequency info. please describe this closed loop behavior and bandwidth frequency.
Nonlinear systems do not have a meaningful frequency response!!
for the exact same frequency you might get different gain and phase by changing the amplitude
Hi
Not my field of expertise, so you have to read the below with a grain of salt.
Looking at the phase it looks to me like the phase you see in systems where you start to get wave propagation between sender and receiver, i.e. no longer closed loop standing wave patterns but propagating waves.
To speculate a bit - for a non-linear system, my gut feel is that the wave propagating signature might tie in with some kind of non-linear phase destroying phenomenon which effectively removes any possibility to form a closed loop system (which you need to form a standing wave = mode).
That said, the increasing amplitude is atypical for such systems unless it ties in with a smaller portin of the system being excited at higher frequency, i.e. that the magnitude from a physical sense should drop rather than increase with frequency.
Just my 2 cents
Claes
Your Bode plot looks like one of a highpass. What kind of "bandwidth" are you trying to extract from it?
Yes, after cutoff frequency, the gain trend is increasing which is quite suspicious to me as this may cause instability at higher frequencies. Is there any different criteria for BW frequency other than -90phase , -3dB in this case?
For a "highly nonlinear" system, you would probably be better off looking at its response in the time domain. Frequency response really only has significance for a linear time invariant (LTI) system (where the frequencies are all independent of each other).
Yes, your closed loop system provides unstable response due to effect of zero or some high value of derivative gain. However, phase plot provides lagging response may due to right hand side zero. If you can provide more physical information regarding system than we can get more idea regarding behaviour. You can also refer book on "process control" by thomas marlin.
As mentioned already by H.L.Kennedy, it would be better to investigate the time response. More than that, for a "highly non-linear" system it is IMPOSSIBLE to create a meaningful BODE plot. All such analyses in the frequency domain are valid for LINEAR systems only!.
That means: From the Bode plot of a non-linear system you cannot derive any information about stability.
- I dont know if I agree if the time plot is a better way to judge the stability of the system. I mean, the bode diagram is just the fourier transform of the impulse response, so then how can you have a time plot if you cannot have a bode plot ?.
- The issue of course is that if the system is nonlinear, the time plot is different depending on the magnitude of the impulse given. So, in a certain way, you may need to approximate the system with a linear system in one way or another.
- If we assume for sake of simplicity (as a first approximation), that the system is linear, this bode plot is not sufficient to judge stability of the system. The stability criterium is that the phase shift must be smaller than 180 degree when the amplitude response is unity. We can see this is fulfilled for the frequencies given, but for higher frequencies, the gain will go down again, cross unity, and there the phase criterium must be met also. (A system with high gain for very high frequencies is impossible to built.)
- When looking at the bode plot, this looks very strange, however, to the point I suspect error in the measurement.
I think the systems is in stable and non-minimum phase. but you need this shape in a larger and wider range or interval.
Thanks everyone and specially I agree with Henri. I had a question regarding the bandwidth frequency of this system. Will it be at -90 phase as there is no -3db point in magnitude plot or there is any other criteria like cutoff frequency=BW frequency?. Because if i just consider cutoff frequency=BW frequency that it will be around 12Hz and if i will consider -90degree phase then it will be around 50Hz.
To get a better intuitive feel of how your plant behaves, try inputting pulses (of different amplitude and duration) and look at how it responds. If your freq resp plot is any indication, you will probably see high-frequency ringing. If that is the case, then you might be better off designing a low-pass controller (e.g. a lag compensator) to narrow the loop bandwidth, rather than trying to increase it.
Nonlinear systems do not have a meaningful frequency response!!
for the exact same frequency you might get different gain and phase by changing the amplitude
I agree with Fassih! You can have a linear TF (bode description) if you look at small signal responses - i.e. small-signal model at diffrent operating points using white noise input. At least this way you will see if the SSM gain/phase are affected by operating point. If you have the equztions for this system, you can derive the SSM as a function of input amplitude, etc. up front. One last point, given the response seems to look like a derivative at higher frquencies, it might help to do this study with the input considered as the derivative of your current input...
I would ask a different question. Does the system have a representative open loop response? There are a large class of nonlinear systems whose open loop response are indicative of the closed loop response. Of course, the problem becomes easier to handle if these non linear systems are "linearized" around an operating point. A good example of course are phase locked control and oscillator systems.
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