Speed of response and crossover frequency relationship

In SISO(Single Input Single output) cases, My professor keeps mentioning the speed of response and crossover frequency interchangeably. I don't really understand what the speed of response means also ? Does higher speed of response mean lower transient time? Also what is the relationship between crossover frequency and speed of response? I am aware that the crossover frequency is when gain is 0db on bode plot

• Typically cutoff is at the -3 dB mark. – schadjo Mar 27 '18 at 19:48
• Firstly be careful when using abbreviations be careful as they may not always be obvious to everybody. I'm guessing 'SISO' is referring to a Single Input Single output control loops. Secondly provide the context with a specific example and your thoughts. We are happy to help but your professor isn't interested in how clever we are. Hint: what happens if you take a simple RC low-pass filter and reduce its corner frequency. How does this affect the output voltage ability to follow the input. This isn't a control loop but should provide some insight. – Warren Hill Mar 27 '18 at 19:54
• I made a mistake between cutoff and cross over , sorry – aadil095 Mar 27 '18 at 19:55
• Crossover frequency is proportional to the time constant $\tau$ in a step response ( en.wikipedia.org/wiki/Step_response#With_one_dominant_pole ). But low-frequency gain $A_0$, and feedback factor $\beta$ are also important factors. – HKOB Mar 27 '18 at 21:11
• $\omega_c=1/\tau$ for a 1st order TF. What course are you doing that deals with quite advanced control topics (in other posts) and yet you haven't covered basic 1st order concepts? – Chu Mar 27 '18 at 22:23