How would one implement a lead compensator? I know how to use the transfer function form, but what does that correspond to? For example, if C(s)=Ki/s comes from u(t)=Ki*integral(e(t)dt), what produces C(s)=K*(s+a)/(s+b)?

Tim Chung, 25 Nov 02

One way to look at this is to note that C(s) represents the "transfer function" between the error signal and the control input to the plant, i.e. Hue.

In this manner, we can see that: 

         s+a     U(s)
C(s)= K ----- = ------
         s+b     E(s)
where U(s) and E(s) are the error signal and control input signal in the s-domain.

Solving for an expression for U(s) yields: 

     s+a                 a-b     
U(s)= K ----- E(s) = K (1 + ----- ) E(s)
s+b                 s+b

We can thus find an equivalent expression in the time-domain by taking the inverse Laplace transform for "what the lead compensator is doing."