Flow system control

1. Saif al-din ali Madi
Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
16/2/2020 1 | P a g e
[ control Laboratory II]
University of Baghdad
Name: - Saif Al-din Ali -c -

2. Saif al-din ali Madi
Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
16/2/2020 2 | P a g e
TABLE OF CONTENTS
OBJECTIVE......................................................................I
INTRODUCTION.............................................................II
THEORY.........................................................................III
APPARATUS....................................................................V
Calculations and results.................................................VI
DISCUSSION ...............................................................VII

3. Saif al-din ali Madi
Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
16/2/2020 3 | P a g e
Experiment Name: - FLOW SYSTEM CONTROL
1. OBJECTIVE
a) he objective of experiment is to obtain the flow control
system characteristics (parameters may be considered
including peak overshoot, rise time, settling time, period
and transport delay), shown in Figure (1)
b) Write response as a function of time.
FLOW SYSTEM CONTROL
2. Introduction
Proportional - Integral - Derivative (PID) controllers are used in most automatic process
Control applications in industry today to regulate flow, temperature, pressure, level, and
many other industrial process variables. They date back to 1939, when the Taylor arid
Foxboro instrument companies introduced the first two PID controllers. All present -
day controllers are based on those original proportional, integral, and derivative modes,
Electronic analog PID control loops were often found within more complex electronic
systems, for example, the head positioning of a disk drive, the power conditioning of a
power supply, or even the movement - detection circuit of a modern seismometer, toilet
bowl float proportioning valve and the fly - ball governor). PID temperature controllers
are applied in industrial Ovens, plastics Injection machinery, hot – stamping machines
and packing industry.

4. Saif al-din ali Madi
Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
16/2/2020 4 | P a g e
3. Theory
1- The three - term controller
The transfer function of the PID controller looks like the following:
Kp = Proportional gain
KI = Integral gain
Kd = Derivative gain
𝒖 = 𝒌 𝑷ⅇ + 𝒌𝒊∫ ⅇ ⅆ𝒕 + 𝒌ⅆ
ⅆⅇ
ⅆ𝒕
First, let 's take a look at how the PID controller works in a closed - loop system using the
schematic shown above, the variable (e) represents the tracking error, the difference between
the desired input value (R) and the actual output (Y). This error signal (e) will be sent to the
PID controller, and the controller computes both the derivative and the integral of this error
signal. The signal (u) just past the controller is now equal to the proportional gain (Kp) times
the magnitude of the error plus the integral gain (Ki) times the integral of the error plus the
derivative gain (Kd) times the derivative of the error, This signal (u) will be sent to the plant,
and the new output (Y) will be obtained. This new output (Y) will be sent back to the sensor
again to find the new error signal (e). The controller takes this new error signal and computes
its derivative and its integral again. This process goes on and on.
2- The characteristics of P, I, anal D controllers
A proportional controller (Kp) will have the effect of reducing the rise time and will reduce,
but never eliminate, the steady - state error: An integral control (Ki) will have the effect of.
eliminating the steady - state error, but it may make the transient response worse
A derivative control (Kd) will have the effect of increasing the stability of the system, reducing the
overshoot, and improving the transient response, Effects of each of controllers Kp, Kd, and Ki on a
closed - loop system are summarized in the table shown below.
CL RESPONSE RISE TIME OVERSHOOT SETTLING TIME S-S ERROR
Kp Decrease Increase Small change Decrease
Ki Decrease Increase Increase Eliminate
Ka Small Change Decrease Decrease Small Change
Note that these correlations may not be exactly accurate, because Kp, Ki, and Kd are
dependent of each other. In fact, changing one of these variables can change the effect of the
other two, for this reason, the table should only be used as a reference when you are
determining the values for Ki, Kp and Kd,

5. Saif al-din ali Madi
Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
16/2/2020 5 | P a g e
3- Second - order system
A second - order system response typically contains two first - order responses, or a first -
order response and a sinusoidal component. A typical sinusoidal second - order response is
shown in Figure3. Notice that the coefficients of the differential equation include a damping
coefficient and a natural frequency. These can be used to develop the final response, given the
initial conditions and forcing functions. Notice that the damped frequency of oscillation is the
actual frequency of oscillation. The damped frequency will be lower than the natural
frequency when the lamping coefficient is between 0 and 1. If the lamping coefficient is
greater than one the damped frequency becomes negative, and the system will not oscillate
because it is Overdamped.

6. Saif al-din ali Madi
Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
16/2/2020 6 | P a g e
𝒕 𝒔 = 𝟒𝑻 =
𝟒
𝝈
=
𝟒
𝕿𝒘 𝒏
(𝟐% 𝒄𝒓𝒊𝒕ⅇ𝒓𝒊𝒐𝒏 )
𝒕 𝒔 = 𝟑𝑻 =
𝟑
𝝈
=
𝟑
𝕿𝒘 𝒏
(𝟓% 𝒄𝒓𝒊𝒕ⅇ𝒓𝒊𝒐𝒏 )
Where:
3 - 1 Transient Responses Transients are caused by sudden or discontinuous changes in a
variable upon which the measured value depends. Depending upon the tuning of the
controller, the transient response will be under damped, over damped or critically damped.
3 - 2 Peak overshoot is the maximum amount by which the response exceeds the final steady
state value of the process variable. It is sometimes expressed as a percentage of the final
steady state value.
3 - 3 Rise time is the time taken for the response to increase from 10% of its final steady state
value to 90% of its final steady state value.
3 - 4 Settling time is the time taken for the response to reach its final steady state value, Within
some specified tolerance.
3 - 5 Periodic time or period) is the duration of one complete cycle of Oscillation. It can
therefore be measured as the interval between alternate crossings of the final steady state
value or the interval between successive peaks or successive troughs on the response curve.
3 -6 Frequency is the reciprocal of the period, i.e. the number of cycles per second which is
expressed in Hertz (Hz), sometimes the frequency is expressed in radians per second and the
relationship between the two units is that radians per second equals 2 times the frequency in
Hertz,
4. APPARATUS
To achieve the objectives of this experiment the following steps are followed:
1 - Operate the flow system shown in fig, 1
2. - Set Square Wave as input signal,
3 - Adjust the SP and PG to a
magnitude such as (SP = (2) and
proportional gain (PG) to (1))]
4 - Print the system response from
computer

7. Saif al-din ali Madi
Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
16/2/2020 7 | P a g e
5. Calculations and results
𝒚(𝒕) = 𝒉 +
𝒉
√𝟏 − 𝝃 𝟐
ⅇ−𝝃𝒘 𝒏 𝒕
𝐬𝐢𝐧 [(𝝎 𝒏√ 𝟏 − 𝝃 𝟐) 𝒕 + 𝒂]
= 𝒉 +
𝒉 ⅇ−𝝃𝒘 𝒏 𝒕
√𝟏 − 𝝃 𝟐
[ 𝝃 𝐬𝐢𝐧 (𝝎 𝒏√ 𝟏 − 𝝃 𝟐) 𝒕 + √ 𝟏 − 𝝃 𝟐 𝒄𝒐𝒔 (𝝎 𝒏√ 𝟏 − 𝝃 𝟐) 𝒕 ]
𝒕𝒂𝒏 =
𝒂
𝒃
=
−√𝟏 − 𝝃 𝟐 𝝎 𝒏
−𝝃𝝎 𝒏
=
𝐬𝐢𝐧 𝒂
𝐜𝐨𝐬 𝒂
𝐬𝐢𝐧 𝒂 = −√ 𝟏 − 𝝃 𝟐 ; 𝐜𝐨𝐬 𝒂 = − 𝝃
𝝃 → → 𝟎
= 𝒉 +
𝒉 ⅇ−𝝃𝒘 𝒏 𝒕
√𝟏 − 𝝃 𝟐
[ 𝟎 + √ 𝟏 − 𝝃 𝟐 𝒄𝒐𝒔 (𝝎 𝒏√ 𝟏 − 𝝃 𝟐) 𝒕 ]
= 𝒉 − 𝒉ⅇ−𝝃𝒘 𝒏 𝒕
𝒄𝒐𝒔 (𝝎 𝒏√ 𝟏 − 𝝃 𝟐) 𝒕
𝐬𝐢𝐧( 𝒂 ± 𝒃) = 𝐬𝐢𝐧 𝒂 𝐜𝐨𝐬 𝒃 ∓ 𝐜𝐨𝐬 𝒂 𝐬𝐢𝐧 𝒃
𝐬𝐢𝐧 [(𝝎 𝒏√𝟏 − 𝝃 𝟐) 𝒕 + 𝒂]= 𝒔𝒊𝒏 (𝝎 𝒏√𝟏 − 𝝃 𝟐) 𝒕 𝒄𝒐𝒔 𝒂 + 𝒄𝒐𝒔 (𝝎 𝒏√𝟏 − 𝝃 𝟐) 𝒕 𝒔𝒊𝒏 𝒂
= −𝝃 𝐬𝐢𝐧 (𝝎 𝒏√ 𝟏 − 𝝃 𝟐) 𝒕 − √ 𝟏 − 𝝃 𝟐 𝒄𝒐𝒔 𝝎 𝒏√ 𝟏 − 𝝃 𝟐 𝒕
𝒕𝒑 =
𝝅
𝒘 𝒏√𝟏 − 𝝃 𝟐
√ 𝟏 − 𝝃 𝟐 =
𝝅
𝒘 𝒏 𝒕𝒑
𝟏 − 𝝃 𝟐
=
𝝅
(𝒘 𝒏 𝒕𝒑) 𝟐
𝝃 = √𝟏 − (
𝝅
𝒘 𝟒 𝒕̅̅̅̅̅ 𝒑)
𝒚 𝐦𝐚𝐱 = 𝒉 + 𝒉ⅇ
−
𝝃𝜫
√𝟏−𝝃 𝟐⁄
𝑷. 𝑶 = 𝒑ⅇ𝒓𝒄ⅇ𝒏𝒕 𝒐𝒗ⅇ𝒓𝒔𝒉𝒐𝒐𝒕 =
𝒚 𝐦𝐚𝐱 − 𝒉
𝒉
=
𝒉 + 𝒉ⅇ
−
𝝃𝜫
√𝟏−𝝃 𝟐⁄
𝒉
= ⅇ
−
𝝃𝜫
√𝟏−𝝃 𝟐⁄
∗ 𝟏𝟎𝟎 %
𝒉 + 𝒉ⅇ
−
𝝃𝜫
√𝟏−𝝃 𝟐⁄
𝒉
≤ 𝟎. 𝟎𝟓
𝐥𝐧 ⅇ
−
𝝃𝜫
√𝟏−𝝃 𝟐⁄
= 𝐥𝐧 𝟎. 𝟎𝟓
−𝝃𝒘 𝒏 𝒕
√𝟏 − 𝝃 𝟐
= −𝟑
𝒕 =
𝟑√𝟏−𝝃 𝟐
𝝃𝝎 𝒏
= 𝒕 𝒔 ; √𝟏 − 𝝃 𝟐 = 𝟏
𝒕 𝒔 =
𝟑
𝝃𝝎 𝒏
→ → 𝒕 𝒔 ≥
𝟑
𝝃𝝎 𝒏

8. Saif al-din ali Madi
Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
16/2/2020 8 | P a g e
PG= 1.75, I =0.8
Max flow = 1.6 l/min, min flow 1 l / min, period = 60 sec
∆𝒙 = 𝟓𝟑𝒎𝒏 = 𝟏. 𝟔 − 𝟏 = 𝟎. 𝟔 𝑳 ∕ 𝒎𝒊𝒏
𝒕 𝒑 = 𝟐𝒎𝒎 ∗ (
𝟑𝟎𝒔ⅇ𝒄
𝟔𝟖. 𝟓 𝒎𝒎
) = 𝟎. 𝟖𝟕 𝐬ⅇ𝐜
𝒃 = 𝟗 𝒎𝒎 ∗ (
𝟎.𝟔 𝒍𝒊𝒕𝒕ⅇ𝒓 /𝒎𝒊𝒏
𝟓𝟑 𝒎𝒎
) = 0.10188 l/ min
𝒘ⅆ =
𝝅
𝒕𝒑
=
𝝅
𝟎. 𝟖𝟕
= 𝟑. 𝟓𝟖𝟒 𝒓𝒂ⅆ/𝒔ⅇ𝒄
𝟎. 𝟏 ∆𝒙 = 𝟎. 𝟏 ∗ 𝟎. 𝟔 = 𝟎. 𝟎𝟔
𝒍
𝒎𝒊𝒏
∗
𝟓𝟑
𝟎. 𝟔
= 𝟓. 𝟑 𝒎𝒎
𝟎. 𝟗∆𝒙 = 𝟎. 𝟗 ∗ 𝟎. 𝟔 = 𝟎. 𝟓𝟒
𝒍
𝒎𝒊𝒏
∗
𝟓𝟑
𝟎. 𝟔
= 𝟒𝟕. 𝟒 𝒎𝒎
𝐭𝐫 = 𝟓𝐦𝐦 ∗
𝟑𝟎
𝟔𝟖. 𝟓
= 𝟐. 𝟏𝟖𝟗 𝐬ⅇ𝐜
𝒃
𝜟𝒙
= ⅇ
−
𝝃𝜫
√𝟏−𝝃 𝟐⁄
→
𝟎. 𝟏𝟎𝟏𝟖𝟖
𝟎. 𝟔
= ⅇ
−
𝝃𝜫
√𝟏−𝝃 𝟐⁄
→ 𝐥𝐧 𝟎. 𝟏𝟔𝟗𝟖 = 𝐥𝐧 ⅇ
−𝝃𝜫
√𝟏−𝝃 𝟐⁄
−→
𝟏. 𝟕𝟕𝟑√ 𝟏 − 𝝃 𝟐 = 𝝃𝜫 → 𝟏. 𝟕𝟕𝟑(𝟏 − 𝝃 𝟐 ) − 𝝃 𝟐
𝜫 𝟐
= 𝟎
𝟏. 𝟕𝟕𝟑 = 𝝃 𝟐( 𝟏. 𝟕𝟕𝟑 + 𝜫 𝟐) → → 𝝃 = √
𝟏. 𝟕𝟕𝟑
( 𝟏. 𝟕𝟕𝟑 + 𝜫 𝟐)
−→ 𝝃 = 𝟎. 𝟑𝟗𝟎𝟐
𝒘 𝒏 =
𝒘ⅆ
√𝟏 − 𝝃 𝟐
=
𝟑. 𝟓𝟖𝟒
√𝟏 − ( 𝟎. 𝟑𝟗𝟎𝟐) 𝟐
= 𝟑. 𝟖𝟗𝟐𝟓
𝒓𝒂ⅆ
𝒔ⅇ𝒄
𝝈 = 𝝃𝒘 𝒏 = 𝟎. 𝟑𝟗𝟎𝟐 ∗ 𝟑. 𝟖𝟗𝟐𝟓 = 𝟏. 𝟓𝟏𝟖𝟖𝒓𝒂ⅆ/𝒔ⅇ𝒄
𝟎. 𝟎𝟐 ∆𝒙 = 𝟎. 𝟎𝟐 ∗ 𝟎. 𝟔 = 𝟏𝟐 ∗ 𝟏𝟎−𝟑
𝒍/𝒎𝒊𝒏
= 𝟎. 𝟎𝟏𝟐 ∗
𝟓𝟑
𝟎. 𝟔
= 𝟏. 𝟎𝟔 𝒎𝒎
𝟎. 𝟎𝟓 ∆𝒙 = 𝟎. 𝟎𝟓 ∗ 𝟎. 𝟔 = 𝟑𝟎 ∗ 𝟏𝟎−𝟑
𝒍/𝒎𝒊𝒏
= 𝟎. 𝟎𝟑 ∗
𝟓𝟑
𝟎. 𝟔
= 𝟐. 𝟔𝟓 𝒎𝒎
𝒕 𝒔 =
𝟑
𝝃𝒘 𝒏
=
𝟑
𝟎. 𝟑𝟗𝟎𝟐 ∗ 𝟑. 𝟖𝟗𝟐𝟓
= 𝟏. 𝟗𝟑𝟎𝟓 𝒔ⅇ𝒄 ∗
𝟔𝟖. 𝟓
𝟑𝟎
= 𝟒. 𝟒 𝒎𝒎
𝒕 𝒔 =
𝟒
𝝃𝒘 𝒏
=
𝟒
𝟎. 𝟑𝟗𝟎𝟐 ∗ 𝟑. 𝟖𝟗𝟐𝟓
= 𝟐. 𝟓𝟕𝟒 𝒔ⅇ𝒄 ∗
𝟔𝟖. 𝟓
𝟑𝟎
= 𝟓. 𝟖𝟕𝟕 𝒎𝒎

9. Saif al-din ali Madi
Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
16/2/2020 9 | P a g e
6. DISCUSSION
1. effect of changing on the system response
The scheme speeds up the system's response with an increase in oil and begins to move
away as it increases more

10. Saif al-din ali Madi
Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
16/2/2020 10 | P a g e
Working of PID Controller
With the use of low cost simple ON-OFF controller only two control states
are possible, like fully ON or fully OFF. It is used for limited control
application where these two control states are enough for control
objective. However oscillating nature of this control limits its usage and
hence it is being replaced by PID controllers.
PID controller maintains the output such that there is zero error between
process variable and set point/ desired output by closed loop operations.
PID uses three basic control behaviors that are explained below.
P- Controller:
Proportional or P- controller gives output which is proportional to current
error e (t). It compares desired or set point with actual value or feedback
process value. The resulting error is multiplied with proportional constant
to get the output. If the error value is zero, then this controller output is
zero.

11. Saif al-din ali Madi
Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
16/2/2020 11 | P a g e
P-Controller Response
This controller requires biasing or manual reset when used alone. This is
because it never reaches the steady state condition. It provides stable
operation but always maintains the steady state error. Speed of the
response is increased when the proportional constant Kc increases.
I-Controller
PI controller
Due to limitation of p-controller where there always exists an offset
between the process variable and set point, I-controller is needed, which
provides necessary action to eliminate the steady state error. It integrates
the error over a period of time until error value reaches to zero. It holds the
value to final control device at which error becomes zero.
Integral control decreases its output when negative error takes place. It
limits the speed of response and affects stability of the system. Speed of
the response is increased by decreasing integral gain Ki.

12. Saif al-din ali Madi
Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
16/2/2020 12 | P a g e
PI Controller Response
In above figure, as the gain of the I-controller decreases, steady state error
also goes on decreasing. For most of the cases, PI controller is used
particularly where high speed response is not required.
While using the PI controller, I-controller output is limited to somewhat
range to overcome the integral wind up conditions where integral output
goes on increasing even at zero error state, due to nonlinearities in the
plant.
D-Controller
PID controller
I-controller doesn’t have the capability to predict the future behavior of
error. So it reacts normally once the set point is changed. D-controller
overcomes this problem by anticipating future behavior of the error. Its
output depends on rate of change of error with respect to time, multiplied
by derivative constant. It gives the kick start for the output thereby
increasing system response.

13. Saif al-din ali Madi
Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
16/2/2020 13 | P a g e
PID Controller Response
In the above figure response of D controller is more, compared to PI
controller and also settling time of output is decreased. It improves the
stability of system by compensating phase lag caused by I-controller.
Increasing the derivative gain increases speed of response.
So finally we observed that by combining these three controllers, we can
get the desired response for the system. Different manufactures designs
different PID algorithms.
Tuning methods of PID Controller
Before the working of PID controller takes place, it must be tuned to suit
with dynamics of the process to be controlled. Designers give the default
values for P, I and D terms and these values couldn’t give the desired
performance and sometimes leads to instability and slow control
performances.Differenttypesoftuningmethodsare developed totune the
PID controllersand requiremuchattentionfrom theoperatortoselectbest
values of proportional, integral and derivative gains. Some of these are
given below.
Trial and Error Method: It is a simple method of PID controller tuning.
While system or controller is working, we can tune the controller. In this
method, first we have to set Ki and Kd values to zero and increase
proportional term (Kp) until system reaches to oscillating behavior. Once
it is oscillating, adjust Ki (Integral term) so that oscillations stops and
finally adjust D to get fast response.
Process reaction curve technique: It is an open loop tuning technique. It
produces response when a step input is applied to the system. Initially, we
have to apply some control output to the system manually and have to
record response curve.

14. Saif al-din ali Madi
Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
16/2/2020 14 | P a g e
After that we need to calculate slope, dead time, rise time of the curve and
finally substitute these values in P, I and D equations to get the gain values
of PID terms.
Process reaction curve
Zeigler-Nichols method: Zeigler-Nichols proposed closed loop methods
for tuning the PID controller. Those are continuous cycling method and
damped oscillation method. Procedures for both methods are same but
oscillation behavior is different. In this, first we have to set the p-controller
constant, Kp to a particular value while Ki and Kd values are zero.
Proportional gain is increased till system oscillates at constant amplitude.
Gain at which system produces constant oscillations is called ultimate gain
(Ku) and period of oscillations is called ultimate period (Pc). Once it is
reached, we can enter the values of P, I and D in PID controller by Zeigler-
Nichols table depends on the controller used like P, PI or PID, as shown
below.
Zeigler-Nichols table

15. Saif al-din ali Madi
Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
16/2/2020 15 | P a g e
PID Controller Structure
PID controller consists of three terms, namely proportional, integral and
derivative control. Thecombined operation ofthesethreecontrollersgives
control strategy for process control. PID controller manipulates the
process variables like pressure, speed, temperature, flow, etc. Some of the
applications use PID controllers in cascade networks where two or more
PID’s are used to achieve control.
PID Controller Structure
Above figure shows structure of PID controller. It consists of a PID block
which gives its output to process block. Process/plant consists of final
control devices like actuators, control valves and other control devices to
control various processes of industry/plant.
Feedback signal from the process plant is compared with a set point or
reference signal u(t) and corresponding error signal e(t) is fed to the PID
algorithm. According to the proportional, integral and derivative control
calculations in algorithm, the controller produces combined response or
controlled output which is applied to plant control devices.
All control applications don’t need all the three control elements.
Combinations like PI and PD controls are very often used in practical
applications.