PID Control
PID (Proportional, Integral, Derivative) Controller is used in DCS/PLCs to control the process precisely. For eg Controlling the Smooth Opening & Closing of Control valve.
To achieve it, we need to take feedback after the Control element. Suppose we want to control the Flow rate, we need to measure Flow using Flow transmitter downstream of Control valve, now if flow rate is more than setpoint, valve should close a little & if flow is less than setpoint, valve should open a little to maintain set flow.
Measured Flow will be called PV(Process Value), error e(t) = SP-PV at any given time.
 | = | Controller output/PID control variable |
 | = | proportional gain |
 | = | error value |
 | = | integral gain |
 | = | change in error value |
 | = | change in time |
Where Ki= Kp/Ti & Kd= Kp*Td where Ti & Td are Integral & differential time respectively.
as it is visible in formula u(t) is controller output which will be fed to Valve positioner to Open or Close valve. Increasing Kp will increase controller output
Kp is used to decrease rise time( time PV takes to reach setpoint)
Ki is used to eliminate Steady State Error( gap between output & setpoint curves).
Kd is used to reduce Overshoot (How much PV goes higher than SP) & Settling time( time taken by PV to reach close to setpoint in stable condition)
There are two types of PID controllers, Direct Acting & Reverse Acting.
Direct Acting Controller is the controller whose output increases/decreases with the increase/decrease in PV(Process Variable) value with respect to Setpoint by operator.
Reverse Acting Controller is the controller whose output decreases/increases with increase/decrease in PV value with respect to Setpoint by operator.
Ziegler Nichols Tuning Method: PID tuning is not so simple and it can upset the process,
it must be done very carefully not to upset the plant process which in turn could cause plant trip in certain conditons.
Ziegler Nichols gave a way to find the approximate values of Proportional Gain, Integral time, & differential time.
We need to draw a Tangent line on rising output, where K is value where output gets stable although its away from Setpoint.
Once we draw the tangent line we can measure value of T & L as shown in the graph.
Or use Auto tune to find initial values. Proportional gain Kp= Output response/error;
Td is proportional to Rate of change of PV.
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