Characterised by time constant; reaches 63% in one τ.
G(s)=K/(τs+1): step response y=K(1-e^{-t/τ}); time constant τ is the time to reach 63.2%; settling time ≈4τ; rise time ≈2.2τ. No overshoot. Describes RC circuits, thermal systems, tanks and simple actuators.
A room heater with τ=10 min reaches 98% of its final temperature in 40 minutes.
First-order responses describe many processes, such as heating or charging, and the time constant gives the speed at a glance.
Characterised by time constant; reaches 63% in one τ.
First-order responses describe many processes, such as heating or charging, and the time constant gives the speed at a glance.
The time for the response to reach 63.2 percent of its final change after a step input.
About four time constants, which is a useful rule of thumb for settling.
Typical applications include estimating how long a tank takes to reach a new level after a step change, predicting the charging time of a sensor capacitor and describing a thermocouple's response to a temperature step.
Study "Modelling mechanical and electrical systems" first (topic 46 of 101 in Signals, Control & Comms). It covers the groundwork this topic builds on.
DC gain K. Pole at -1/τ. Bandwidth 1/τ.
A room heater with τ=10 min reaches 98% of its final temperature in 40 minutes.
The next topic is "Second-order system response", which builds directly on this one.
It is classed as Intermediate in Signals, Control & Comms (topic 47 of 101). It is an intermediate topic. Work through the beginner topics in Signals, Control & Comms first.
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