What is a Bode plot?
Bode plot is a very important tool while designing and understanding filters and oscillators. It is a combination of two logarithmic plots of frequency response of a system, one showing relation between input and output in terms of magnitude and the other, phase angle shift. The plot is drawn on logarithmic scale. Horizontal axis always shows frequency, while the vertical axis shows magnitudes and phase angle shift wrt input.The graph was originally conceived by Hendrik Wade Bode in 1930s, and offers asymptomatic approximation of frequency response, using straight line segments. The straight line approximations of actual curve makes it easy to analyse a circuit. These plots are quite accurate and helpful tool in analysis.The approximation shows a linear relation in magnitude over an effective working rangeof a frequency filter, and slope defines degradation or fall in response over frequencies. The point on straight line plot where the magnitude starts falling, is called knee point.
Control Engineering: How do you calculate the angle of departure of [math] G(s) = \frac{1}{s^3+4s^2+5s}[/math]for the root-locus plot?
Your departure angle will be -63.5° and not 117° or -45° as mentioned in comment.Calculation of Breakaway point:We can write, for arbitrary gain, K, [math]\frac{dK}{ds}=-(3s^2[/math]+[math]8s[/math]+[math]5)=0.[/math] Which gives, s = -1.6 and -1. This is reflected in your graph.Calculation of intersection point with imaginary axis:From Routh’s array, we can solve the equation- [math]s^3[/math]+[math]4s^2[/math]+[math]5s[/math]+[math]K=0.[/math] After obtaining the auxiliary equation, 4[math]s^2[/math]+20=0, we get s = ±j 2.83, which is again reflected in the graph.Calculation of departure angle [as required in question]:If we are interested in calculation of departure angle at A [see image], Correct formula is: 180° + [{summation of all angles of zeros contributing at A}-{summation of all angles of poles contributing at A}].[math]Φ=180+[∑(\angle Z) - ∑(\angle P)][/math]Labeling the graph correspondingly,In the given transfer function, there are no zeros, so [math]∑(\angle Z)=0.[/math]To Point A, angle contribution is from two poles- one from origin and other from its conjugate part itself which is obviously 90°. From O, the angle towards A, is [math]tan^{-1}(\frac{1}{2})[/math], which is 26.5° or 153.5° in positive direction.Hence, [math]Φ=180°+[0-[90°+153.5°]]=180°-243.5°= -63.5°[/math]
What is the use of bode, Nyquist and root locus plot in control system?
These plots gives us the information about system parameters which helps to design and improve the effectiveness of the system/Controller.While designing any controller there is always at-least one system parameter is there that we don’t know about it and it affects system stability, to deal with it we use Root locus to check the range of this unknown parameter for which the system will work as per our requirements. After modelling the system, we should know about whether the system has sufficient gain margin and phase margin or not. Sometimes it looks like the system is stable but it doesn’t have sufficient gain and phase margin which can cost loss in stability. To avoid this we need to add Compensator in the system. For designing the compensator we get data from bode plot.Suppose we don’t have the model for the system but we have the frequency response of the system by plotting this frequency response on complex plane we can check system parameters and the stability of the system.If you have doubts regarding Concepts in Control theory do watch the YouTube lectures on Control Theory by Brian Douglas (Brian Douglas).
Can I get a list of my past addresses from the post office?
No, the post office doesn't provide that sort of information. Think about it. I'm sure you will remember. Maybe look in any papers you have, things you've save, old mail, etc. And if you really think about it, you should be able to remember pretty closely to the exact times. I don't think it HAS to be exact. Just be careful. If you're changing jobs as frequently as you're moving, it might bode in your favor when applying for jobs. Going forward, keep records.
How do I determine sampling rate from a bode diagram?
"Four Bode plots are displayed together with the four pole zero maps of the corresponding discrete-time transfer functions. The transfer functions represent the discrete-time operation of some continuous-time plants preceded by a ZHO. The discrete-time transfer functions have been obtained using sampling times Ts = 1 s, Ts = 0.1 s, Ts = 0.01 s, or Ts = 0.001 s.For each Bode plot, determine the corresponding sampling time." The bode diagram is given by Phase(deg) and Magnitude(dB) at the Y-axis and Frequency(rad/sec) at the X-axis. I know it's hard to determine without the bode diagram attached but could anyone please tell me how roughly what to look at?
How can I recognize different types of filters from pole-zero plots?
To understand the magnitude vs frequency of a pole-zero plot:Identifying the transfer function of the pole-zero plot, Wikipedia shows a good example of the conversion: Pole–zero plotHere’s an example:The transfer function of this pole-zero plot would be:H(s) = (s+2)/(s+0.5i)(s-0.5i)2. Bode plotting: Bode Examples - Erik Cheever
How do you draw a bode plot in the time domain?
As Sameer Bobade notes you cannot do this in the time domain. However you may apply either a step input or fixed magnitude sine wave input (chirp signal) and vary their frequency to see the time domain effects. As you increase the frequency of the step the system output will reach the cut-off frequency or even resonant peaks as per the bode diagram. The same applies with a sinusoidal reference and the output will show same peaks and cut-off at the relevant frequencies. In both cases the magnitude of the input will deviate from the input reference as per the frequency of the bode diagram. I have done and demonstrated this using electrical machines and it is very effective in relating time and frequency domain. Recall this is how you would measure your bode diagram plot as Magnitude of Output / Magnitude of Input vs frequency.
What are the limitations of time domain analysis in control systems?
Control system analysis is carried out in either time domain or frequency domain. The domain of analysis depends largely on the design requirements.Every advantage the frequency domain analysis has can be viewed as a disadvantage for the time domain analysis. That way, the analysis in the frequency domain is very simple and quick. Stability determination using a frequency response plot can be done in very quick time with no effort. The popularity of Bode and the Nyquist plots is a clear indication of this. In time domain analysis, the analysis becomes cumbersome for systems of high order. In frequency domain analysis, the order has a little effect on the time or effort of analysis. A simple example: Determining the stability using Routh-Hurwitz criteria becomes increasing time-consuming when the order increases. In a Nyquist plot, the effect of increased order is negligible.