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On each individual device, the speaker output can get subtracted from the microphone before it gets sent to other locations. This prevents others from hearing themselves through your microphone. When using two devices in within audible range of each other, the devices cannot subtract the speaker audio from the microphone audio because the information path ...


5

As you pointed out, there are many state-space realizations of one particular transfer function. The reason is that a transfer function only represents the input-output behavior of a system (observable and controllable dynamics) and not the internal states. That being said, you can directly write state-space realizations from a transfer function with the so-...


5

The final value of the step response is the DC gain of the closed-loop transfer function, which is generally different from the open-loop DC gain. Assuming unity gain feedback, the feed-forward transfer function $G(s)$ equals the open-loop transfer function, and the closed-loop transfer function is given by $$C(s)=\frac{G(s)}{1+G(s)}\tag{1}$$ The final value ...


4

Open loop gain at DC is -3dB or .707 and 0 degrees. We don’t know the forward gain but assuming it is the open loop gain, the closed loop gain would be $.707/(1+.707)= .4148$, matching the first plot. (With 60 degrees of phase margin however I would have expected a response closer to the third plot, but as explained in the comments this is due to my ...


4

The transfer function is $H(s) = \frac{16.94s + 579.5}{s^2 + 507.2s + 1224}$ This transfer function has 2 poles, one slow pole at -2.4248 and a fast pole at -504.7752. The function has a slowish zero at -34.2. Good news, your poles and zero are all in the left-half plane. It is much easier to control a system with zeroes and poles in the left-half plane ...


3

The Explanation from @ScienceGeyser provides a good explanation to the phenomenon. There are two more things to address the question on how is this phenomenon avoided. The feedback read by the microphone is not identical to the audio sent to the speakers. There is the physical response from the speakers, the acoustic of the device and the environment, if ...


2

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 ...


2

I have heard that the word comes from "plant" as in "steam plant". But I don't know of any historical research that's been done to pin down the term. I did just check my copy of "On Governors" by James Clerk Maxwell himself (that guy got around). At least in 1868, Maxwell wasn't using the word "plant" for "thing ...


2

This is due to the delay that occurs between the recording process and the playback process. The voice audio signal has to be recorded by the microphone and then played back by the speaker. If 2 separate devices are used, then recording and playing back the audio are 2 different events, so your own voice will be played back to you. In the same device the mic ...


2

My question is, why is this half of the PWM update time? Why doesn't it also consider the delay until the next input ADC sample? You answered this yourself -- it's the effective, average delay. So I guess what my question is, stated rigorously, is that if the controller's transfer function in the Z-domain is C(z), how do we model the system for stability ...


2

A transfer function describes an LTI system. As such, the given system can be described by a transfer function. However, if there are non-zero initial conditions, the system is no longer linear because there's a contribution in the output that does not depend on the input signal but only on the initial conditions. Consequently, the transfer function cannot ...


2

The closed loop poles are the roots of the polynomial $$D(s)=s^2+2s+2+K\tag{1}$$ and, according to the root locus plot, they are $s_{1,2}=-1\pm 2j$. Consequently, we get $$2+K=|1+2j|^2=5\quad\Longrightarrow\quad K=3\tag{2}$$ With $K=3$ we obtain $$H(0)=\frac{K}{2+K}=\frac35\tag{3}$$ which leaves step response $C$ as the only option.


1

First, typically when you're exerting a force on something and getting a position, the acceleration varies instantaneously with force. A more or less universal equation of motion for a single-axis linear system would be $m \ddot x = f_v(\dot x) + f_p(x)$. For a mass-spring-damper system, it'd be $m \ddot x = b \dot x + k x$. So you can easily express that ...


1

From the root locus plot, the open loop transfer function has a real-valued pole at $s_0=0$ and a complex conjugate pole pair $s_1=-1.5+ 2j$ and $s_1^*$. There's also a zero at $s=-2$. Consequently, $G(s)$ is given by $$G(s)=\frac{s+2}{s(s-s_1)(s-s_1^*)}$$ The closed-loop transfer function is $$H(s)=\frac{kG(s)}{1+kG(s)}=\frac{k(s+2)}{s(s-s_1)(s-s_1^*)+k(s+2)...


1

The problem with your example is that $\infty\cdot 0$ isn't necessarily equal to zero. The only way to judge what is happening in the limit $K\to\infty$ is to divide the original equation by $K$: $$\frac{D(s)}{K}+N(s)=0\tag{1}$$ Now it is obvious that for $K\to\infty$ the actual value of $D(s)$ is irrelevant, as long as it is finite. Consequently, the only ...


1

No such thing as a single frequency of the noise. That's exactly why it's called white; it has power in all frequency ranges, but not at a single frequency. Finally, is there a frequency-domain representation of Gaussian white noise? Yes, a constant power spectral density for all frequencies. That's like white light (which contains also a continuum of all ...


1

Assuming $P$ is the transfer function of your process and $C$ the transfer function of your controller. The closed-loop transfer function of a standard control loop, with the controller in the normal path, is $$ G(s) = \frac{C(s)P(s)}{1+C(s)P(s)}$$ while the transfer function of your alternative controller is $$G_{alt}(s) = \frac{P(s)}{1+C_{alt}(s)P(s)} $$ ...


1

As near as we can tell by experiment, causality is nature's way of doing its thing. Causality says that if you have a system $y(t) = h\left(x(t), t\right)$, and it is causal, then $y(t_0)$ is dependent only on values of $x(t)$ for $t < t_0$*. Causality doesn't say you can't combine systems into larger systems (as a rather pertinent example, you can ...


1

K is the gain parameter for which you will be at any particular point on the root locus. As you increase K, the closed loop poles will start from the open loop poles and move toward the open-loop zeros as depicted in the root locus showing all possible locations of closed loop poles versus gain K. This is because the general form for the closed loop and open ...


1

DC component is the zero frequency component. If you look at the DFT expression, this would mean summing up the input. So in mathematical terms this would be the sum (or the running sum) based on your application. In terms of filtering again this would be an averaging filter. Like moving average.


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"Plant" doesn't only refer to the living thing that has chlorophyll; it, in the context of control, refers to a technical system with in and output – some production line, a whole factory, a nuclear power plant. As such, there's nothing more intuitive than the word itself: a plant is what is being controlled.


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I get what you are trying to say so I will use the same terminology that you used. Open-loop information is open-loop transfer function Close-loop information is close-loop tranfer function With Nyquist and Bode plots, you use the open-Loop information --> plot K*G(s) For the root locus, you use the close loop information for the Routh criterion ( ...


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