# Control Systems Theory: Determing break frequency mathematically.

• btbam91
In summary, the speaker has an open loop transfer function with a known value for the break frequency and is trying to determine the value of the time constant. They are unsure how to proceed mathematically, but understand how to do it with a bode plot. They also request to see a bode plot with exact values and caution against using "t" as a variable in the transfer function.
btbam91
Hey there.

I have an open loop transfer function TF = K/(t*s^2 + s) where K is known. Given a value for the break frequency (say, w_b = 10 rad/s), I have to determine the value of the time constant, t.

I understand how do this with a bode plot, but not entirely sure how to proceed mathematically.

Thank you!

btbam91

First, rewrite the function into K/s(Ts+1) = (K/T)/s(s + 1/T).
So now, looking at it that way, for what value of ω does the break occur?

I would like to see or have described your Bode plot with exact abscissa and ordinate values. If you did this right it's obvious what the gain and the time constant are. It's also very helpful to understand the relationship between your TF and the Bode plot.

BTW don't use t in your transfer function. t is always a variable. Use T or tau.

## 1. What is control systems theory?

Control systems theory is a branch of engineering and mathematics that deals with the analysis and design of systems that are able to control themselves or other systems. It involves the use of mathematical models to understand and predict the behavior of systems, and use this understanding to design controllers that can regulate the behavior of the system.

## 2. What is break frequency in control systems theory?

Break frequency, also known as the bandwidth or crossover frequency, is a measure of the highest frequency at which a control system can effectively regulate the output of a system. It is the frequency at which the magnitude of the system's output response drops below a specified threshold value.

## 3. How is break frequency determined mathematically?

The break frequency of a control system can be determined mathematically by analyzing the transfer function of the system. This involves finding the frequency at which the phase of the transfer function is equal to -180 degrees. This frequency is known as the phase crossover frequency and is equivalent to the break frequency.

## 4. Why is it important to determine the break frequency of a control system?

Determining the break frequency of a control system is important because it helps in designing controllers that can effectively regulate the output of a system. By knowing the break frequency, engineers can design controllers with appropriate gain and phase margins to ensure stability and performance of the system.

## 5. Are there different methods for determining break frequency mathematically?

Yes, there are different methods for determining break frequency in control systems theory. Some common methods include using the root-locus plot, Bode plot, or Nyquist plot of the system to find the phase crossover frequency. Another method is to use numerical methods, such as the frequency response function, to calculate the break frequency.

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