## ADAPTIVE CONTROL SYSTEM

adaptive controller is that which can modify the behavior of the plant processes when their are disturbances over the plant.

### AN EXAMPLE OFADAPTIVE SYSTEM

consider a lumped parameter system of spring and damper shown in figure. We know that to study the response of the system it is required to study about the differential equation.

where m is the mass of the system

x is deflection of mass from it’s mean position

c is the viscous damping coefficient

k stiffness of spring

now there are two condition that are given below

## FIRST CONDITION

if we consider that the parameter of dynamic model of the plant to be controlled are unknown but constant (here the constants are c & k). then we can generates the controller parameters if we know the value of constants (k&c).so in this case the adaptive control techniques provide an automatic tuning procedure in closed loop for the controller parameters. here we are assuming that the constants does not changes with environmental conditions. so after some time the effect of the adaption vanishes as the time is increases.

## SECOND CONDITION

Adaptive controllers are basically used to rectify the real time non-linearities. from the schematic we can easily understand that the control parameters are adjusted by an additional control system. this additional control system