**Nikola Šerman,**prof. emeritus

*Linear Theory*nserman@fsb.hr

*Transfer Function Concept Digest*

**10. ELEMENTARY BLOCKS**

#### 10.5 First Order Lead

When the zero of the transfer function (10.3) is a real negative number *z = – ω_{0}* and constant

*K*equals

*ω*, the transfer function becomes:

_{0}In control engineering this elementary block is often named *first-order lead*. Its only parameter denoted by * T *is referred to as

*time constant*

*where .*

**,****Fig 10.17** Block presentation of the first-order lead

The first-order lead can be interpreted as a parallel connection of a differentiator and the unity gain as its shown in fig. 10.18.

**Fig 10.18** First-order lead structure

First-order lead step response is shown in fig. 10.19

**Fig 10.19** First order lead step response – sum of Dirac’s *δ* function and unity step.

First-order lead frequency response in Nyquist diagram is shown in fig. 10.20.

**Fig 10.20** First-order lead frequency response in Nyquist diagram.

First-order lead frequency response in Bode diagram is shown in fig. 10.21

**Fig 10.21** First-order lead frequency response with *T* = 0.2 s in Bode diagram. Dashed lines present the respective characteristics of the first-order lag which confirm their mutual symmetry as expected.