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6 votes
Accepted

How can a system be unstable if $L(j\omega)$ is never exactly $-1$?

You cannot make conclusions about the stability of a system by only considering its transfer function evaluated on the imaginary axis $s=j\omega$. Replacing $s$ by $j\omega$ in the transfer function ...
Matt L.'s user avatar
  • 90.3k
5 votes
Accepted

What is the Reference in Control Theory?

Imagine that you're heating (or cooling) a home with a modern furnace (or air conditioner). the reference or set point is the temperature that you set your thermostat to be. the feedback signal is ...
robert bristow-johnson's user avatar
4 votes
Accepted

Do we use closed loop or open loop information in Bode plot, Nyquist plot and Root Locus?

The root locus is a way to see how the poles of your system vary from their open loop locations to their closed loop locations. If the closed loop system is $$ C(s) = \frac{O(s)}{1+KO(s)} $$ where $O(...
Peter K.'s user avatar
  • 25.8k
4 votes

Do we use closed loop or open loop information in Bode plot, Nyquist plot and Root Locus?

The bode plot is just a plot showing the frequency representation of your system. Any transfer function has one, hence you can use it to see the response of both closed or open loop. Nyquist and the ...
LJSilver's user avatar
  • 768
4 votes
Accepted

Calculate transfer function of two parallel transfer functions in a feedback loop

Your two transfer functions are in parallel, i.e they simply add up. So your feedback transfer function is simply $G(z) = H_1(z)+H_2(z)$. You want to makes sure that the magnitude of $G(z)$ is smaller ...
Hilmar's user avatar
  • 45.3k
4 votes

How can initial conditions be taken into account to calculate a system's terminal value using the final value theorem or some other technique

Ah ha! There's a lot of obfuscation in the problem as stated, plus a bit of over-emphasis on the final value theorem. $$H(z) = \frac{z^{-1} \phi / (1 - \phi z^{-1})}{1 - z^{-1} \psi / (1 - \psi z^{-...
TimWescott's user avatar
  • 12.8k
3 votes
Accepted

Determine stability of feedback system from open loop transfer function and Nyquist stability criterion gives different results

However when I look at the closed loop transfer function, I would say that this system is unstable for 𝐺𝐻=−1. In this case the transfer function becomes infinity so a bounded input will result in a ...
TimWescott's user avatar
  • 12.8k
3 votes
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Why does the control effort increase if the bandwidth of the system is higher then the bandwidth of the plant?

Intuitively (and I leave it as an exercise for you to work it out with math), it's because you have to push harder on the plant to get it to move fast. Consider a bowl of honey and a spoon -- moving ...
TimWescott's user avatar
  • 12.8k
3 votes
Accepted

DSP using audio IO from PC using C++

The best performance you will be able to squeeze out of a PC is with an audio interface that supports ASIO. To be able to get near 10ms of total delay (input and output) you will also need a very ...
A_A's user avatar
  • 10.7k
3 votes

Frequency warping when integrators are replaced with backward-euler and forward-euler integration

To the extent this helps, here are some interesting magnitude and phase plots of the backward Euler (here using the method of impulse invariance mapping which for 1/s has the same result as backward ...
Dan Boschen's user avatar
  • 51.9k
3 votes
Accepted

What is the total impulse response in a system with feedback interconnection?

It is easier to work in the $s$-domain: $$Z=YH_2$$ $$Y=(X-Z)H_1$$ Hence, $$Y=(X-YH_2)H_1=XH_1-YH_1H_2\Rightarrow Y(1+H_1H_2)=XH_1$$ Therefore, $$H(s)=\frac{Y(s)}{X(s)}=\frac{H_1(s)}{1+H_1(s)H_2(s)}$$ ...
msm's user avatar
  • 4,295
3 votes

Non-causal FIR filter in the feedback loop

Is there a way to make this filter non-causal? Remember that non-causal filters aren't possible to interpret in any case, because "non-causal" literally means there's output caused by input ...
Marcus Müller's user avatar
3 votes
Accepted

What does the frequency of oscillating microphone feedback depend on?

Let's look at a simple block diagram The microphone receives the input sound but also reproduced sound from the loudspeaker. There are two transfer functions in place. One, $A(\omega)$ from the ...
Hilmar's user avatar
  • 45.3k
2 votes

Do we use closed loop or open loop information in Bode plot, Nyquist plot and Root Locus?

It looks like you are considering these analysis like part of a universal streamline desing process. These analysis techniques are simply tools that helps you understand the behaviour of your system, ...
Pier-Yves Lessard's user avatar
2 votes
Accepted

What does G(1) = 1 say about a system?

Static gain refers to the DC gain. Namely, it would be the ratio of the output and the input under steady state condition. Due to DC corresponding to $\omega=0$, in the $z$-domain DC would correspond ...
Tendero's user avatar
  • 5,020
2 votes
Accepted

Why is my filter unstable and self-oscillating in this case?

The question is not very specific so this will also be just a general answer. The stability of a composite linear-time-invariant (LTI) system composed of smaller LTI systems cannot be deduced from ...
Olli Niemitalo's user avatar
2 votes

Why does the control effort increase if the bandwidth of the system is higher then the bandwidth of the plant?

Bandwidth in control system usually mean open-loop bandwidth and is usually defined as the frequency where the open loop transfer function gain crosses the 0 dB gain. The open loop transfer function ...
Ben's user avatar
  • 3,777
2 votes
Accepted

Frequency warping when integrators are replaced with backward-euler and forward-euler integration

The important thing here is that there is no conventional frequency warping with the forward or backward Euler methods. Frequency warping would mean that the discrete-time (DT) and continuous-time (CT)...
Matt L.'s user avatar
  • 90.3k
2 votes

Determine stability of feedback system from open loop transfer function and Nyquist stability criterion gives different results

There are a few things I can note about your question. As far as I have always learned, the nyquist stability criterion is taken over the openloop transfer function. if you take the closed loop ...
Petrus1904's user avatar
2 votes
Accepted

Discrete time Final Value Theorem applied to feedback system

I would derive the total transfer function directly in the transform domain. Your input-output equation can be written as $$Y(z)\big(1-z^{-1}\big)=\alpha G(z)z^{-1}Y(z)+\beta z^{-1}X(z)\tag{1}$$ where ...
Matt L.'s user avatar
  • 90.3k
2 votes

How can initial conditions be taken into account to calculate a system's terminal value using the final value theorem or some other technique

After taking some more time to think about it, I think the problem is finally solved. I haven't digested Tim's answer yet, but from what I can see his approach is different. Furthermore, I thought it ...
Matt L.'s user avatar
  • 90.3k
2 votes
Accepted

Did Dialup Modem use closed or open loop power/volume control? How did they determine Tx level?

Did Dialup Modem use closed or open loop power/volume control? Yes. How did they determine Tx level? "Dialup Modem" is a very big term that spans > 50 years of technological ...
Marcus Müller's user avatar
2 votes

How do I reduce a block diagram with just a line as a feedback loop, I dont get how it adds K to the denominator

Let's call the transfer function of the filter $H(s)$: $$H(s)=\frac{K}{s(Js+B+KK_h)}=\frac{K}{D(s)}\tag{1}$$ From the diagram we have $$C(s)=\big[R(s)-C(s)\big]H(s)\tag{2}$$ from which you get $$\frac{...
Matt L.'s user avatar
  • 90.3k
1 vote

How to modify zeros and poles in a delta-sigma modulator loop?

i dunno, i might have posted this before. but here is a 2nd-order sigma-delta quantizer that operates not as an oversampled rate. so you can hear the quantization noise, but you can also hear the ...
robert bristow-johnson's user avatar
1 vote

How does the intuitive notion of causality fit in with control systems?

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 ...
TimWescott's user avatar
  • 12.8k
1 vote

Getting a single feedback peak from a basic 4 stages phaser

I've simulated your system, and since it's a four-stage phaser you do get two notches and one peak in between, if you don't count the more or less pronounced peaks at DC and at Nyquist. The frequency ...
Matt L.'s user avatar
  • 90.3k
1 vote

Getting a single feedback peak from a basic 4 stages phaser

If I follow the OP’s description properly, the description is what would be a comb filter, given the all-pass filters operate as delay lines (over a certain frequency range of operation). The sum of a ...
Dan Boschen's user avatar
  • 51.9k
1 vote

Role of Power Metric and LPF in AGC(Automatic Gain Controller)

Either power or rms value is typically used for AGC as a peak value would be much more variable given it is an instantaneous measurement. The low pass filter typically refers to the Loop Filter (and ...
Dan Boschen's user avatar
  • 51.9k
1 vote
Accepted

Does a RHP zero imposes some limitation in the time domain?

If a RHP zero imposes limitation on the bandwidth in the frequency domain, it also imposes limitation in the time domain. This is due to time-frequency duality. For example, if you want to have a ...
Ben's user avatar
  • 3,777
1 vote

Is there any solution for this bandpass feedback overload problem (besides increasing sample rate)?

You have build a classical feedback loop system here and the regular stability criteria apply. You could try to calculate the poles of the closed-loop transfer function and make sure they are ...
Hilmar's user avatar
  • 45.3k

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