Pid control by Adarsh singh

PID
Controller
Adarsh Singh
B.Tech , 3rd Yr.
Student of Electrica
& Electronics
Engineering

The PID controller sometimes called three-term
control as it is the summation of the proportional,
integral and the derivative values.
A proportional-integral-derivative controller is
widely used in more than 95% of the industrial
controllers.
 PID controllers have also been found to be robust,
and that is the reason, it finds wide acceptability for
industrial processes.

The order of the controller is low, but it can be used in any
type of SISO system, e.g. linear, nonlinear, time delay etc.
Proper tuning of the controller is difficult. It is particularly
useful for controlling slow variables, like pH, temperature, etc.
in process industries.

The major reasons behind the popularity of P-I-D controller
are its simplicity in structure.
 The desired closed loop performances, such as fast
response, zero steady state error and less overshoot are
achieved through combination of P,I and D actions
respectively.
 PID controller looks like the following ;
• Kp = Proportional gain
• Ki = Integral gain
• Kd = Derivative gain
As Shown in Diagram …..

PID Mathematically:
• Consider the input error variable, e(t):
– Let p(t) = Kp*e(t) {p proportional to e }
– Let i(t) = Ki*∫e(t)dt {i integral of e }
– Let d(t) = Kd* de(t)/dt {d derivative of e }
AND let V(t) = p(t) + i(t) + d(t)
Then in Laplace Domain:
V(s) = [Kp + 1/s Ki + s Kd] E(s)

Proportional
P
• P depends on the present error.
Integral
I
• I on the accumulation
of past errors.
Differential
D
• D is a prediction of future errors,
based on current rate of change.

In fact, changing one of these variables can change
the effect of the other two.
PID controller has all the necessary dynamics:
fast reaction (D mode).
to lead error towards zero (I mode)
to eliminate oscillations (P mode).
“This “combination”, of “Present + Past + Future”,
makes it possible to control the application very well”

Integral Control
If we consider the integral action of the controller only, the
closed loop system for the same process is represented by the
block diagram as shown in Fig.
Proceeding in the same way as in this case, we obtain,
From the first observation, it can be seen that with integral
controller, the order of the closed loop system increases by
one. This increase in order may cause instability of the system
K/K+τs+ττs>2

CONT..
So the major advantage of this integral control action is that
the steady state error due to step input reduces to zero. But
simultaneously, the system response is generally slow.

Derivative Control
It functions to minimize the change of error, thus keeping
the system at a consistent setting.
The primary benefit of D controllers is to resist change in
the system.
Derivative controllers do not guide the system to a steady
state. Because of this property, D controllers must be coupled

The Characteristics of P, I, and D Controllers
 A proportional controller ( ) will reduce the rise time
but never eliminate the steady-state error.
An integral control ( ) will have the effect of
eliminating the steady-state error for a constant or step input,
but it may make the transient response slower.
A derivative control ( ) will have the effect of increasing
the stability of the system, reducing the overshoot, and
improving the transient response.

PID Controller Functions
• Output feedback
 from Proportional action
compare output with set-point
• Eliminate steady-state offset (=error)
 from Integral action
apply constant control even when error is zero
• Anticipation
 From Derivative action
react to rapid rate of change before errors grows too big

• The signal u(t) will be sent to the plant, and a new
output will be obtained. This new output will be
sent back to the sensor again to find the new error
signal. The controllers takes this new error signal
and computes its derivative and its integral gain.
This process goes on and on…
)
)(
)()(()(
0 dt
tde
KdtteKteKtu d
t
ip  

KdT
K
Twhere d
i
i  ,
1
integral gain
derivative gain
derivative time constantintegral time constant
D controller is not used alone because it can’t produce output.
PID Controller is most powerful but complex
controller.

Controller Effects
• A proportional controller (P) reduces maximum overshoot
responses to disturbances, but still allows a steady-state
error.
• Integral Controller ( I)does not exhibit steady state error,
but is relatively slow responding. It is particularly effective
for:
o very fast process, with high noise level
• A derivative control typically makes the system better
damped and more stable.

CL
RESPON
SE
SPEED OF
RESPONSE OVERSHOOT S-S ERROR
Kp Increase Increase Decrease
Ki Decrease Increase Eliminate
Kd Increase Decrease No Change
The effects of each of controller parameters Kp, Ki , Kd

Advantages and disadvantages of
controls

Closed-loop Response
Rise time Maximum
overshoot
Settling
time
Steady-
state error
P Decrease Increase Small
change
Decrease
I Decrease Increase Increase Eliminate
D Small
change
Decrease Decrease Small
change
• Note that these correlations may not be exactly accurate,
because P, I and D gains are dependent of each other.

Typical uses of P, I, D, PI, and PID controllers

Conclusions
• Proportional controller established the gain but
produces the steady state error.
• Integral controller reduces or eliminated steady-state
errors, but often makes the system less stable.
• Derivative controller usually increases damping and
improves stability, but has almost no effect on the
steady state error.
• These 3 kinds of control combined to from the PID
controller.

Pid control by Adarsh singh

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