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 T2 such that
Case 2 γ = β:
If γ = β is required in the equation of Gc(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 Gc(s) is modified to
where β > 1. The open-loop transfer function of the compensated system is Gc(s)G(s). If the static velocity error constant Kv is specified, determine the value of constant Kc 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 T2 sufficiently large so that
is approximately unity, where s = SI is one of the dominant closed-loop poles. Determine the values of T1 and β from the magnitude and angle conditions:
5. Using the value of β just determined, choose T2 so that
The value of βT2, the largest time constant of the lag-lead compensator, should not be too large to be physically realized.