lag time compensation

ST. VINCENT PALLOTTI COLLEGE OF ENGINEERING & TECHNOLOGY : 

ST. VINCENT PALLOTTI COLLEGE OF ENGINEERING & TECHNOLOGY LAG COMPENSATION USING TIME DOMAIN PRESENTED BY NIRUL MASURKAR 7th sem Roll no. 31

Introduction : 

Introduction A lag compensator improves the steady state behavior of a system, while nearly preserving its transient response. in this state ,we consider how the root locus may be used to design a compensator so as to realize a desired improvement in steady-state response.

Unity feedback T.F : 

Unity feedback T.F Consider a unity feedback system with a forward path transfer function

Slide 4: 

We assume that at a certain value of K,this system has satisfactory transient response, i.e., its root locus plot passes through [or is close to] the desired closed –loop pole location sd indicated in fig.It is required to improve the system error constant Kp. Kv or Ka [depending on whether the system is type O.-1 or -2,respective] to a specified value without impairing its transient response.

Slide 5: 

These require that after compensation, the root locus should continue to pass through sd, while the error constant at sd, is raised to the specified value. To accomplished this, consider adding lag compensator pole-zero pair close to origin, with left of pole. If pole and zero is this pair are located close to each other, it will contribute a negligible angle at sd such that it continues to lie on the root locus of the compensated system.

Locating the lag compensator pole – zero pair : 

Locating the lag compensator pole – zero pair

The gain of uncompensated system at sd is given by : 

The gain of uncompensated system at sd is given by

For the system cascade lag time compensator : 

For the system cascade lag time compensator

The system gain as sd : 

The system gain as sd

The error constant Ke of uncompensated system : 

The error constant Ke of uncompensated system

The error constant of the compensated system is given by : 

The error constant of the compensated system is given by

Since the error constant : 

Since the error constant

Slide 13: 

Thus the parameter of the lag compensator is nearly equal to the ratio of desired error is nearly equal to the desired error constant to the error constant of the uncompensated system

Slide 14: 

Thank You