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Like you mentionned, you cannot cancel a right-half-plane zero (or a zero outside the unit circle) by placing a pole on it. A unstable pole in your compensator will make the command of your controller unbounded (i.e. it will reach infinity). There are no ways to cancel a right-half-plane zero. It's sometimes possible to "remove" a right-half-plane zero by ...


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It is very strange phenomena that one object is completely dropped out of attention of researchers. It is Urysohn operator. First of all Urysohn is equivalent to multiple parallel Hammersteins and Urysohn followed by static nonlinearity is a model of any deterministic dynamic object, it maps any given input to any provided output. I obtained Ph.D. in ...


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The easiest is Urysohn adaptive filter: http://www.ezcodesample.com/UAF/UAF.html It can build nonlinear model by few lines of code. The theoretical details can be found here http://www.ezcodesample.com/NAF/index.html The site has downloadable coding sample. Besides UAF, the other common methods are: Kernel LMS, Voltera LMS, Neural networks, Point cloud. ...


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Note that for a small sampling interval $T$, $\big(d[k+1]-d[k]\big)/T$ is a good approximation for the velocity. So if you fit $au[k]+b$ to a given set of measurements $v[k]$, it is valid to conclude $$d[k+1]=d[k]+T\big(au[k]+b\big)\tag{1}$$ In the text you refer to they might have normalized $T$, so it changes the units without changing the values of $a$ ...


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Approaches can be any of the following: Model the noise that you expect, for ex: gaussian (least squares in Minimum variance unbiased estimator for a linear signal model in presence of gaussian noise). Based on this model try and estimate the noise variance, the regularization term should be close to noise varainace. Deploy machine learning techniques based ...


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See the image (found in this article). Inject a signal into the loop somewhere (I show it below as going between the controller and the plant). Then measure the input to the plant and the output from the plant. Note that the image is a bit confusing -- it assumes that the normal command to the loop is 0 or some constant. It would be better to actually ...


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Looks like you've done a lot of work on your projects. As @MarcusM├╝ller said, by far the majority of people start with ReLU and go from there. It doesn't have the "vanishing gradient" problem that tanh has for example. All your questions are open ended but common for designing neural networks. There are so many "nobs to turn" to try and make your network be ...


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The book is correct, there is no discrepancy. When we reverse a system in time, only the time-variable will get negated and not the shift. Time-reversal does not mean that the whole argument of $x[n]$ gets negated. Take example of a sequence : $x[n] = {\hat{0},1,2,3,4,5}$. Shift this by 2 samples, so $x_{shift}[n] = {\hat{0},0,0,1,2,3,4,5}$. Now, reverse ...


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One option from the realms of adaptive filtering is the Least Mean Squares (LMS) filter depicted below: The idea is you take the output of the unknown system, compare it with the output of your adaptive filter and minimize the difference by tweaking the filter coefficients, using a LMS algorithm. When the error $e(n)$ is zero (or more often, lower than a ...


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As mentioned in the comment, I modified the code given here and was able to adapt the LMS filter with error tapering to zero. The only assumption I made is that (since I am not an audio expert and do not know how the channel from speaker to the microphone would look like), I assumed a 10 tap channel with only first 3 non-zero values (multi-path reflection ...


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The reason x[n] must be white is because the solution will effectively spectrally weight the channel response based on the amount of energy present in each spectral frequency location. A white noise source provides equal weight to all frequencies. If energy is not present in any particular frequency bin, a proper solution cannot be found for that frequency. ...


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True that a chirp signal helps to get the FRF, but every time we change the frequency we can't reach the steady state, so this will cause bias in the estimation. As an advice try to use the multisine excitation, they are more suitable for such cases.


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