University of Basrah for Gas and Oil

College of Oil and Gas Engineering

Process Dynamic and Control II

Dr. Seaar Al-Dabooni

Lecture(2)
 Final Control Elements and Controllers
1-2 IDEAL TRANSFER FUNCTIONS
 Control Valve
• A pneumatic valve always has some dynamic lag, which means that the stem position does not respond instantaneously
to a change in the applied pressure from the controller. From experiments conducted on pneumatic valves, it has been
found that the relationship between flow (Q) and valve-top pressure (P) for a linear valve can often be represented
• By a first-order transfer function; thus

• In many practical systems, the time constant of the valve is very small when compared with the time constants of other
components of the control system (negligible dynamic lag)
 Final Control Elements and Controllers
 Control Valve (Cont.)
• Consider a first-order valve and a first-order process connected in series (no interaction), as shown

• The relationship between the air pressure to the valve and the output from the process
(perhaps a reactor temperature) is

• For a unit-step change in the valve-top pressure P

where the TF is
 Final Control Elements and Controllers
Because the transducer and the converter will be lumped together with the controller for
 Controllers:
simplicity, the result is that the input will be the measured variable x (e.g., temperature and
fluid level) and the output will be a pneumatic signal p.
1) ON–OFF CONTROLLERS
a) Two-Point Control
A good example of two-point control is a thermostatically controlled heating system for housing which the demand
temperature is 70 °F (21 °C) as

Up ( charge ) curve dependent on speed of heating element and the down ( discharge ) curve dependent on
isolation the house , each charge and discharge is dependent on type of sensor.

*Another example is the valve is either fully open (on) or fully closed (off)
 Final Control Elements and Controllers
 Controllers (Cont.)
a) Two-Point Control
In practice, a dead band is inserted into the controller. With a dead band, the error reaches some finite positive value
before the controller “turns on.” Conversely, the error must fall to some finite negative value before the controller “turns
off.”

where P is the control output (control signal) and is the system error

Expanding the width of the dead band makes the controller less sensitive to noise and prevents the phenomenon of
chattering, where the controller will rapidly cycle on and off as the error fluctuates about zero. Chattering is detrimental
to equipment performance.
 Final Control Elements and Controllers
 Controllers (Cont.)
It's similar to two-point control, except in this case the controller has three states, such as
b) Three-Point Control
forward–off–reverse,(or up–off–down, hot–off–cold, and so on). Consider the case of a
floating oil-drilling platform that needs to stay over the wellhead on the ocean bottom.

The platform must not drift more than 5 ft away from the center, or the pipe may break. Two motors, A and B, are used to
keep the platform centered on the east-west axis (the north-south axis would be handled with other motors). If the
platform drifts more than 5 ft east, motor A comes on and drives it back toward the center. Motor B will come on if the
platform drifts more than 5 ft west. There are other cases in the above figures.
 Final Control Elements and Controllers
 Controllers (Cont.)
2) PROPORTIONAL CONTROLLER (Present)
Our goal is to reduce the error between the process output and the set point. The proportional controller, as we will see, can
reduce the error, but cannot eliminate it. If we can accept some residual error, proportional control may be the proper
choice for the situation.
The proportional controller has only one adjustable parameter, the controller gain. The proportional controller produces an
output signal (pressure in the case of a pneumatic controller, current, or voltage for an electronic controller) that is
proportional to the error .

Laplace transform
By using the deviation
variable
 Final Control Elements and Controllers
 Controllers (Cont.)
2) PROPORTIONAL CONTROLLER
Example
If the set point is 30, and the initial value for the robot arm is 0, then the error is 30-0=30, let the proportional gain is 2, then
the output control is 2*30=60 ( means, at certain sampling time (Ts), the motor moves to 30. In the second TS, let the actual
angel for the robot arm is 10, then the error is 30-10=20, and output control is 2*20=40, then the motor moves the arm slower
toward 30, and so on.
If the motor were directed to return to 0°,a new negative error would appear, causing a new (negative) motor torque to be
generated: Error = SP – PV= 0°– 30°= –30°; Output controller= Kc*Error= 2 *30°= –60, The negative sign of the output would
result in a change in polarity of the applied voltage to the motor, which would cause it to run in the opposite direction.
 Final Control Elements and Controllers
 Controllers (Cont.)
2) PROPORTIONAL CONTROLLER
Example
Proportional control is simple, makes sense, and is the basis of most control systems, but it has one fundamental
problem—steady-state error. In practical systems, proportional control cannot drive the controlled variable to zero
error because. This small force may not be enough to overcome friction. One way to decrease the steady-state error
due to friction is to increase the system gain, high Kc can lead to instability problems (oscillations). Another source of
steady-state error is the gravity problem, increasing the system gain can reduce the error, but proportional control
alone can never completely eliminate it. One way to deal with the gravity problem is to have the controller add in a
constant value (to its output) that is just sufficient to support the weight. This value is called the bias
 Final Control Elements and Controllers
 Controllers (Cont.)
2) PROPORTIONAL CONTROLLER

• The actual behavior of a proportional controller is

• The controller output will saturate (level out) at Pmax

• A special case of proportional control is on/off control. If the