# Lag-lead Compensation Techniques Based On The Root-locus Approach And Design

**Lag-lead compensator using operational amplifiers**

Then, using the value of β thus determined, choose the value of T_{2} such that

**Case 2 ****γ = ****β:**

If γ = β is required in the equation of G_{c}(s), then the preceeding design procedure for the lag-lead compensator may be modified as follows:

1. From the given performance specifications, determine the desired location for the dominant closed-loop poles.

2. The lag-lead compensator given by the equation of G_{c}(s) is modified to

where β > 1. The open-loop transfer function of the compensated system is G_{c}(s)G(s). If the static velocity error constant K_{v} is specified, determine the value of constant K_{c }from the following equation:

3. To have the dominant closed-loop poles at the desired location, calculate the angle contribution Φ needed from the phase lead portion of the lag-lead compensator.

4. For the lag-lead compensator, we later choose T_{2} sufficiently large so that

is approximately unity, where s = SI is one of the dominant closed-loop poles. Determine the values of T_{1} and β from the magnitude and angle conditions:

5. Using the value of β just determined, choose T_{2} so that

The value of βT_{2}, the largest time constant of the lag-lead compensator, should not be too large to be physically realized.