Transfer Function Analysis and Design Tools

This page is a web application that simulate a transfer function.The transfer function is simulated frequency analysis and transient analysis on graphs, showing Bode diagram, Nyquist diagram, Impulse response and Step response.

And use this utility to design the transfer function at a given some poles and zeros or other paramaters.

Transfer Function:

Transient analysis condition is n≥m. maximum n=12

Example

G(s)=

10000 s2+50s+10000

The following form is an example to input G(s). Use the right form to simulate.
β=
α=

♦Transfer Function Design Tools (Tools Show∇)

The form of α and β values is rewritten by this tool to design the transfer function at given some paramaters.

Order poles on s-domain

Poles are ordered on s-domain of the transfer function inputted form of α and β. G(s) is rewritten that it solve the following equation.
  G(s) = {the transfer function of inputted old α and β}×H(s)

• 1st order system
        p=
  
• 2nd order system
    
      p1,p2=±j
      p1,p2=exp(±j )

Order zeros on s-domain

The system of H(s) is setted zeros z, z1 and z2 of a given the following form. The matrix of α and β as transfer function G(s) is rewritten to add zeros. The G(s) is solved the following equation.
  G(s) = {the transfer function of inputted old α and β}×H(s)
If α and β was blank, G(s) = H(s).

• 1st order system
    H(s)= s - z    z=
  
• 2nd order system
    H(s)=(s - z₁ )(s - z₂ )
      z1,z2= ± j
      z1,z2=exp(±j )

Design from ζ and ω₀ on a 2nd order system

Poles are ordered on s-domain of the transfer function inputted form of α and β. G(s) is rewritten that it solve the following equation.
  G(s) = {the transfer function of inputted old α and β}×H(s)
If α and β was blank, G(s) = H(s).

2nd order system
  
•Natural angular frequency ω₀=[rad/s]
•Damping ratio ζ=

Design the coefficient of s², s¹, s⁰

G(s) is rewritten that it solve the following equation.
  G(s) = {the transfer function of inputted old α and β}×H(s)
If α and β was blank, G(s) = H(s).

the transfer function
  H(s)=β₁s²+β₂s+β₃   

---

  β₁=0  β₁=1  β₁=

---

  β₂=0  β₂=2ζω₀ β₂=
    •Use the above form to input of ω₀, ζ

---

  β₃=0  β₃=ω₀²  β₃=
    •Use the above form to input of ω₀

Convert frequency

→

ω₀(natural angular frequency) from the transfer function of inputted α and β is converted that ω₀ is multiplied by a given ω_k.

  ω_k=    

Convert gain

G(s) transfer function of inputted α and β is multiplied by a given K.
    G(s)←KG(s)

  K=