Types of Controllers PID PD I PD

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Types of Controllers
Process control_ mechatronics
engineering
 Supervisor : Monther kanan.
 created by :Anaseem Alhanni.
 Technical college :Faculty of Technological Engineering.
 University :Al- Balqa' Applied University (BAU).
 11 . January . 2021

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contents
Control system ………………………………………..………...................... ….3
Types of Control System……………………………..……….....................….4
Parameterization of the 2nd Order Step Response…........................6
Process control…………………………………………….………........................7
Discrete (ON/OFF) mode………………………………….….....................….9
TWO-POSITION DISCRETE CONTROLLERS…………...........................12
Three-position controllers……………………………………....................…13
continuous-mode controllers……………………………....................……..16
Proportional controller………………………………………....................……16
Proportional Band PB…………………………………………….......................19
The examples of P-Only Control……………………………....................….21
INTEGRAL CONTROLLER……………………………………....................…..22
proportional-integral (PI) controller ………….………..........................…..26
Derivative controller………………………………………….............….............…29
Proportional Derivative controller PD………………….....................…..31
PID…………………………………………...……………….......………............……32
Applications………………………………………………………..................……35
Ziegler-Nichols Closed-loop method……………………….................…37
Instrument Symbols……………………………………………................……42
REFERENCE…………………………………………………........…….......……..55

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Control system is a combination of various elements
connected as a unit to direct or regulate itself or any other
system in order to provide a specific output is known as a
Control system.
Components of a Control System
1.Controlled process: The part of the system which
requires controlling is known as a controlled process.
2.Controller: The internal or external element of the
system that controls the process is known as the controller.
3.Input: For every system to provide a specific result,
some excitation signal must be provided. This signal is
usually given through an external source. So, the
externally provided signal for the desired operation is
known as input.

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4.Output: The overall response of the system achieved
after application of the input is known as output.
5.Disturbance is a signal that tends to adversely affect
the value of the output of a system.
TYPES OF DISTURBANCE:
1.aninternal disturbance is generated within the system.
2.an external disturbance is generated outside the system
and is an input.
Types of Control System
1. Open-loop control systems in this control system the
output is neither measured nor fed back for comparison
with the input.

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2.Closed-loop control systems in this control system the
actuating error signal, which is the difference between
the input signal and the feedback signal, is fed to the
controller so as to reduce the error and bring the output
of the system to a desired value.

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Parameterization of the 2nd Order Step Response
 Rise Time (tr) : the time taken for the output to go
from 10% to 90% of the final value.
 Peak Time (tp) :the time taken for the output to
reach its maximum value.

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 Overshoot :(max value -final value)=final value*
100.
 Settling Time (ts)- The time taken for the signal to
be bounded to within a tolerance of x% of the steady
state value.
 Steady State Error ess : The difference between
the input step value (dashed line) and the final
value.
Process control
Process control is a key part of almost every process
operation. The features of a process are usually measured
by process variables PV. The control of process variables is
achieved by controllers.
Our prime objective is to design and tune various
controllers and also analyze their performance.
Implementing an effective control structure to control a
process provide us various benefits like:

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1. Better regulation of yield.
2. Better utilization of resources like energy.
3. Higher operating frequency, increased production and
improved recording and reporting of process operations.
In process control loops, a controller’s job is to influence
the control system via control signal so that the value of
the controlled variable equals the value of the reference.
Controller mode is the way in which the controller
responds to deviation.

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A controller can have one of two modes that describes its
output signal = There are two main types of
controllers: discontinuous controllers andcontinuous
controllers .
A.Discrete (ON/OFF) mode:
 discrete-mode controllers produce a conditionally
stable response. This means that the system error

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fluctuates between a predetermined deadband,
creating a low-amplitude sinusoidal response.
 The starting and stopping of events is a discrete-
based system because the event is either true or
false, (i.e., started or stopped, open or closed, on or
off).
 This type of control system can also be made
automatic and is perfectly suited to computer-based
controllers.
 These discrete-state control systems are often
implemented using specialized computerbased
equipment called programmable logic controllers
(PLCs).
 control the heater is an example of a discrete-mode
controller.
 This is a type of control system concerned with
controlling a sequence of events rather than
regulation or variation of individual variables.

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 For example, the manufacture of paint might
involve the regulation of many variables, such as
mixing temperature, flow rate of liquids into mixing
tanks, speed of mixing, and so on. Each of these
might be expected to be regulated by process-control
loops. But there is also a sequence of events that
must occur in the overall process of manufacturing
the paint. This sequence is described in terms of
events that are timed to be started and stopped on a
specified schedule. Referring to the paint example,
the mixture needs to be heated with a regulated
temperature for a certain length of time and then
perhaps pumped into a different tank and stirred for
another period.

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Types of discrete-mode controllers are:
Two-position controllers turn the output
ON (100% open) or OFF (0% open) once the process
variable crosses an error deadband around the set point.
If the deadband is increased, the oscillation frequency will
decrease, but the error will be maximized.
ON/OFF controllers are appropriate for applications where
large-scale,sudden changes are uncommon and the process
reaction rate is slow.
The main application of tow position controller are :
1.Room heating or air conditioning system.
2.Liquid path temperature control.
3.Level control in large volume tank.

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the overshoot and undershoots of error around the upper
and lower setpoints.
This is due to both the process lag time and controller lag
time, indicated by the finite time required for control
element to reach new setting.

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B.continuous-mode controllers
 It used to avoid the oscillatory system response
caused by ON/OFF control.
 A continuous-mode controller sends an analog
signal to the process control field device to regulate the
process variable, bringing the error signal to zero in a
closed-loop system.
 The manner in which the controller produces the
control signal is called the control action.
 A continuous-mode controller behaves like a
multiposition controller with an infinite number of
positions.
Continuous-mode controllers use three different
modes to control the process:

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 It adjusts the control variable output in a manner
proportional to the error.
 Proportional or P- controller gives an output that is
proportional to current error e (t).
 It compares set point with the actual value or feedback
process value.
 It changes the manipulated variable in proportion to
the control difference.
 It reacts immediately to deviations in the system, and
corrects them quickly.
 The resulting error is multiplied with a proportional
constant to get the output.
 If the error value is zero, then this controller output is
zero.
CV (t ) = KPE +CV(E=0 )
KP :the proportional gain of the controller.
E :the current error.

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CV(E=0 ) : the controller output when the error
equals 0.
KP=CV/E
Tan β = CV/E =KP
 The proportional gain KP of the system is defined by
how much the control variable output changes for each
percent of error within the control band.

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 The proportional gain KP relationship between the
error and the control variable depends on the width of
the band upon which the controller is acting.
 The gain of a controller indicates how sensitive the
controller is to error.
Proportional Band PB
The proportional band is the change of the controlled
variable required to move the control element through
its entire positioning range.
PB=1/KP

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If KP increases, The PB decreases.
If KP increases, the sensitivity of the system increases.
Sensitivity is a measure of the change in output of an
instrument for a change in input.
Advantages of Proportional Controller
1. The proportional controller helps in reducing the
steady-state error, thus makes the system more
stable.
2. The slow response of the overdamped system can
be made faster with the help of these controllers.
Disadvantages of Proportional Controller
1. Due to the presence of these controllers, we get some
offsets in the system.
2. Proportional controllers also increase the maximum
overshoot of the system.

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Inner Loop Cascade Control
 P-Only Control is well suited for many cascade
applications as it provides an effective means for
counteracting upstream process disturbances.
 Within the cascade architecture it’s important to note
that the Controller Output of the outer loop serves as
the Set Point of the inner loop. The inner loop is able to
see and react to disturbances ahead of the outer loop.
 When tuned aggressively using the P-Only
configuration the controller is able to react faster than
the outer loop and thereby take the brunt of
disturbances. While overshoot – even significant
overshoot – can be expected its impact is confined to the
inner loop. Any offset associated with use of a P-Only
controller is typically corrected by the outer loop as long
as the outer loop is not excessively slow.

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 Offset An important characteristic of the proportional
control mode is that it produces a permanent residual
error in the operating point of the controlled variable
when a change in load occurs. This error is referred to
as offset.
ii. INTEGRAL CONTROLLER
 The offset error of the proportional mode occurs
because the controller cannot adapt to changing
external conditions—that is, changing loads. In other
words, the zero-error output is a fixed value.
 The integral mode eliminates this problem by
allowing the controller to adapt to changing external
conditions by changing the zero-error output.
 Integral action is provided by summing the error over
time, multiplying that sum by a gain, and adding the
result to the present controller output.
 You can see that if the error makes random excursions
above and below zero, the net sum will be zero, so the
integral action will not contribute.

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 But if the error becomes positive or negative for an
extended period of time, the integral action will begin
to accumulate and make changes to the controller
output.
 An integral controller will stop adjusting its output
once the error becomes zero.
 The integral gain KI indicates the sensitivity of the
output’s rate of change to the percentage of error that
occurs over time.
Ki=the integral gain in %of the controller output per
second per % error.
E =the error in %.

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Large Ki Small Error
Large rate of
change in the
controller output
Small Ki small Error
small rate of
change in the
controller output

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Ki = (d CV / dt) /E
[Ki] = (% /s) /%
Large Ki Small Ki.
Ki 1 is more sensitivity than Small Ki 2.

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 If it occurs step change (in error), the controller
will respond with a steep increase in output.
 When the error becomes zero, then the
controller will keep its output at its previous
level.
 The integral controller mode is also referred to
as reset action, because it automatically resets
the error to zero over time.
 It of controller has a fast response time by
(proportional action).
 It eliminates all residual error by (integral action).
 The type of connection PI controller :
1. In a series PI controller.

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2. In a parallel PI controller

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 Series PI controller is faster than Parallel PI controller.
 The term repeats KpE is used when referring to how
many times the proportional amount is repeated in one
minute.
parallel PI
controller
input of I
is Error
I and P action occur
independently of
each other
series PI
controller
input of I
is Kp*Error
I action occurs
after the P action
(dependent)

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• The output of a D controller is proportional to the rate of
change of the error in the system.
• dE/dt.
• KD=TD ,TD is the rate time.
• D action is not used by itself in a controller.
• the derivative action response to a step change creates an
infinite change in error over time
• causing the output of the controller to have 100% saturation
for an instant.
• If the error remains at its stepped up value, the controller will
sense no change and will return the control variable to 50%.
• it onlyproduces a change in output if there is a change in the
rate of error.
Standard
Derivative
controller
• The action is the change in the process variable rate over time.
• dPV/dt.
• It used by some PLCs, avoids the saturation of the control variable in
response to a step change in the set point.
• It cannot be used by itself because the error signal is not fed back to
the controller for error correction.
Modified
Derivative
controller

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1.STANDARD DERIVATIVE CONTROLLERS
 KD :the derivative gain constant in %(sec/%).
 d E/dt: the rate of change of error over the duration of
change in %/sec.
 CVnew :the control variable.
2.MODIFIED DERIVATIVE CONTROLLERS
d PV/dt : the rate of change of process variable over the
duration .

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v. Proportional Derivative controller PD
Parallel
standard PD
controller
Parallel
modified
PD
controller
Series standard
PD controller
Series modified
PD controller
Cv=kp+kD (dE/dt) cv=kpE-
kD(dpv/dt)
cv= kpE + kDkp
*(dE/dt)
cv=kp-
kpkD(dpv/dt)
a) The derivative action in a PD controller adds
stability to a closed-loop system by reducing the
amount of overshoot and undershoot in the
system’s response.
b) The derivative component acts as a “brake” in the
system, slowing the proportional response as the
process variable approaches its set point.

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PID
 The PID control scheme is named after its three
correcting terms, whose constitutes the manipulated
variable (MV). The proportional, integral, and derivative
terms are summed to calculate the output of the PID
controller. Defining as the controller output, the final
form of the PID algorithm is:
Taking the Laplace transform we obtain:

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Kp : Proportional gain.
Ki: Integral gain.
Kd: Derivative gain.
e: Error = Set Point – Process value.
t : Instantaneous time.
It can be concluded that PID controller has all the
necessary dynamics:
1. fast reaction on change of the controller input(D mode)
2. increase in control signal to lead error to zero(I mode).
3. suitable action inside control error area to eliminate
oscillations (P mode).

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Applications
 The best PID controller application is temperature control
where the controller uses an input of a temperature
sensor & its output can be allied to a control element like
a fan or heater. Generally, this controller is simply one
element in a temperature control system. The entire
system must be examined as well as considered while
choosing the right controller.
1. Temperature Control of Furnace
 Generally, furnaces are used to include heating as well as
holds a huge amount of raw material at huge
temperatures. It is usual for the material occupied to
include a huge mass. Consequently, it takes a high
quantity of inertia & the temperature of the material
doesn’t modify rapidly even when huge heat is applied.
This feature results in a moderately stable PV signal &
permits the Derivative period to efficiently correct for

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fault without extreme changes to either the FCE or the
CO.
2.MPPT Charge Controller
The V-I characteristic of a photovoltaic cell mainly
depends on the range of temperature as well as
irradiance. Based on the weather conditions, the
current and operating voltage will change
constantly. So, it is extremely significant to track
the highest PowerPoint of an efficient photovoltaic
system. PID controller is used to finding MPPT by
giving fixed voltage and current points to the PID
controller. Once the weather condition is changed
then the tracker maintains current and voltage
stable.

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Ziegler-Nichols Closed-loop method
Ziegler-Nichols Closed-loop method is used to obtain the
controller constants [KP, KI (or TI), and KD (or TD)] in a
system with feedback.
 It was the first proper algorithmic method for tuning
the PID controllers. It is not widely used today because
closed-loop behavior tends to be oscillatory and
sensitive to uncertainty.
 The main objective of the Ziegler-Nichols closed-loop
method is to find the value of the proportional-only
gain that causes the control loop to oscillate
indefinitely at a constant amplitude.
 This gain, which causes steady-state oscillations, is
called the ultimate proportional gain (KPU).
 (TU) the ultimate period is the time required to
complete one full oscillation once the response begins to
oscillate at a constant amplitude.
 Their methods were used for non-first order plus dead
time situations, and involved intense manual
calculations.

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Steps for Ziegler-Nichols Closed-loop method
tuning:
1. Remove integral and derivative action. Set integral
time (Ti) to 999 or its largest value or Ki=0 and set
the derivative controller (Td) to zero or Kd=0.
2. Create a small disturbance in the loop by changing
the set point. Adjust the proportional, increasing
and/or decreasing, the gain until the oscillations
have constant amplitude.
3. Record the gain value (Ku) and period of oscillation
(Pu).

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Instrument Symbols
The instrumentation associated with control systems
varies from sensors and transmitters to controllers,
computers, and PLCs. These are drawn as bubbles
with or without rectangles.
In general, the instrument symbol will be identified
by a letter code,which denotes its function, and by a
number code assigned by the designers, which may
identify the loop or some region of the plant.

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2. Temperature Controller.
3. Temperature transmitter.
4.Flow transmitter.
5.Flow Recorder.
6.Flow controller.
7.Flow Valve.
8.pneumatic line.
9.Electric.

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REFERENCE
1. Characterising the Response of a Closed Loop System _Signals and
Systems: 3C1
Control Systems Handout 2_Dr. David Corrigan.
2. COMPARISION OF PERFORMANCE ANALYSIS OF DIFFERENT CONTROL
STRUCTURES Bachelor of Technology in _ Electronics & Communication
Engineering
By SOMJIT SWAIN (108EI029).
3. The Electronics Engineers' Handbook, 5th Edition _ McGraw-Hill, Section
19.
4. Text book: K. Ogata Modern control Engineering. 5th edition.
5. https://instrumentationforum.com.
6. Process Control Instrumentation Technology _ Curtis D. Johnson
_ Eighth Edition.
7. https://controlstation.com.
8. http:// www.sapiensam.com/control/index.htm.
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