$5$ Stability We have stability in a closed loop control system if we have no continuous oscillation. We must not confuse the problems and the different effects that disturbances &

Proportional band A controllers proportional band is usually defined, in percentage terms, as the ratio of the input value, or PV to a full or $100\%$ change in the controller output value or MV$.(1)$

THE formala of I system $?$

$OP=(\frac{K}{TlnT}){\displaystyle \underset{0}{\overset{T}{}}}$ERRdt

THE FIGARE BELOW SHOWS PHASE SHIFT OF DIFFRANTION $?$

$A=sine$

B $y=sinedt$

Derivative formula Formula for $D$ control:

$oP=K$Tper$(\frac{\text{P}\text{E}\text{R}\text{R}}{dt})$

Proportional mode $($P$)$ The most basic form of control. This can be used if the resultant offset in the output

Proportional, integral and derivative mode $($PID$)$ This is a full $3-$term controller, used where there is instability caused by the integral mode being used $($L$)$

Proportional and derivative mode $($PD$)$ This mode is used when there are excessive lag or inertia problems in the process.

$CD2$