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Presentation on
TYPICAL EXAMPLE OF 1st ORDER
SYSTEM AND EFFECT OF TIME CONSTANT
ON SYSTEM REPONSE
By
SHRI RAM BAJIYA
100104123
Content
 Example of 1st order system
 Cruise Control
 Velocity of car on the road
 Level control of a tank
 Effect of time constant on system response
Typical example of 1st order System
 Velocity of car on the road
• Control of velocity of rotating system
• Electric systems where energy is essentially stored in one
component
• Incompressible fluid flow in a pipe
• Level control of a tank
• Pressure control in a gas tank
• Temperature in a body with essentially uniform
temperature distribution e.g., a vessel filled with a
mixture of steam and water.
Velocity of car on the road
Cruise Control
The purpose of cruise control is to keep the velocity
of a car constant. The driver drives the car at the
desired speed, the cruise control system is activated
by pushing a button and the system then keeps the
speed constant. The major disturbance comes from changes of the slope of
the
road which generates forces on the car due to gravity. The cruise control
system measures the difference between the desired and the actual velocity
and generates a feedback signal which attempts to keep the error small in
spite of changes in the slope of the road. The feedback signal is sent to
an actuator which influences the throttle and thus the force generated by
the engine.
 the momentum balance can be written as
mdv/dt + cv = F − mgθ
where the term cv describes the momentum loss due to air resistance and
rolling and F is the force generated by the engine.
Level control of a tank
The couple tank is used as a control system, the input flowrate (qi) is controlled by
adjusting the applied voltage to the pump motor amplifier (vi). The liquid level is sensed
by a pressure transducer that produces an output voltage (y1), which is proportional to
the liquid level (h1).
Desired
Velocity
∑ ∑Controller
velocityThrottle
bodyEngine
F
Slope of road
PP
v1
q1 h1 y1
PUMP TANK SYSTEM
MODEL
LEVEL
SENSOR
Schematic Diagram of the overall system
Where;
vi = applied voltage to the pump motor
amplifier
qi= input flow rate
h1= liquid level
y1=output voltage
The pump flow rate, qi and the input voltage, vi, are related by an actuator
characteristic that is assumed to be linear as shown in figure. The same is
true of the level sensor characteristic.
 .
Flow rate
Slope=Ki
Pump input voltage Vi
qi
Sensor output
Slope=Ks
y1
Liquid Level h1
Pump and Level Sensor Characteristic
If Ki and Ks are the pump and sensor gain constants respectively, then
qi = ki . vi
y1=ks . h1
H1(s)= {kb/(Ts+1)}.q1(s)
From above equation can takes from the modeling of tank system.Combined these with
the system transfer function equation gives the standard first order system transfer
function,

(Y1/Vi)= G/(Ts+1)
G = ki.ks.kb
Where,
G = the system gain
T = the system time constant
Ki = pump characteristic
Ks = sensor characteristic
Vi
qi =kivi (Y1/Vi)= G/(Ts+1) Y1=ksh1
Y1
h1qi
LEVEL SENSOR
TANK SYSTEM
PUMP
Schematic Diagram of the overall system
Above Diagram shows the overall diagram of the tank system.
Finally, the experimental result of open loop test will be use to
obtain transfer function of the single tank system. The gain and time
constant can be taken from the output response of the open loop
result.
Effect of time constant on system response
 Time constant is the time it takes for the step response to rise 63%
of its final value.
 Consider the step response of fig. 1
By the figure we get that at t=T1 the
response will be 63% of its maximum
value i.e. time constant of this response
is T1
 Consider the step response of fig 2
By the figure we get that at t=T2 the
response will be 63% of its maximum value
i.e. time constant of this response is T2
Fig. 1
Fig 2
Now comparing the two responses
As it is clear form the figure that T1 is
smaller than T2 and figure also clear
that the first response is faster then
the second step response .
Therefore because of this , the time constant is use to measure how fast a
system can respond
Smaller the time constant, faster is the system response.
..
THANK YOU

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Shri ram bajiya contol ppt

  • 1. Presentation on TYPICAL EXAMPLE OF 1st ORDER SYSTEM AND EFFECT OF TIME CONSTANT ON SYSTEM REPONSE By SHRI RAM BAJIYA 100104123
  • 2. Content  Example of 1st order system  Cruise Control  Velocity of car on the road  Level control of a tank  Effect of time constant on system response
  • 3. Typical example of 1st order System  Velocity of car on the road • Control of velocity of rotating system • Electric systems where energy is essentially stored in one component • Incompressible fluid flow in a pipe • Level control of a tank • Pressure control in a gas tank • Temperature in a body with essentially uniform temperature distribution e.g., a vessel filled with a mixture of steam and water.
  • 4. Velocity of car on the road Cruise Control The purpose of cruise control is to keep the velocity of a car constant. The driver drives the car at the desired speed, the cruise control system is activated by pushing a button and the system then keeps the speed constant. The major disturbance comes from changes of the slope of the road which generates forces on the car due to gravity. The cruise control system measures the difference between the desired and the actual velocity and generates a feedback signal which attempts to keep the error small in spite of changes in the slope of the road. The feedback signal is sent to an actuator which influences the throttle and thus the force generated by the engine.
  • 5.  the momentum balance can be written as mdv/dt + cv = F − mgθ where the term cv describes the momentum loss due to air resistance and rolling and F is the force generated by the engine. Level control of a tank The couple tank is used as a control system, the input flowrate (qi) is controlled by adjusting the applied voltage to the pump motor amplifier (vi). The liquid level is sensed by a pressure transducer that produces an output voltage (y1), which is proportional to the liquid level (h1). Desired Velocity ∑ ∑Controller velocityThrottle bodyEngine F Slope of road
  • 6. PP v1 q1 h1 y1 PUMP TANK SYSTEM MODEL LEVEL SENSOR Schematic Diagram of the overall system Where; vi = applied voltage to the pump motor amplifier qi= input flow rate h1= liquid level y1=output voltage The pump flow rate, qi and the input voltage, vi, are related by an actuator characteristic that is assumed to be linear as shown in figure. The same is true of the level sensor characteristic.
  • 7.  . Flow rate Slope=Ki Pump input voltage Vi qi Sensor output Slope=Ks y1 Liquid Level h1 Pump and Level Sensor Characteristic If Ki and Ks are the pump and sensor gain constants respectively, then qi = ki . vi y1=ks . h1 H1(s)= {kb/(Ts+1)}.q1(s) From above equation can takes from the modeling of tank system.Combined these with the system transfer function equation gives the standard first order system transfer function,
  • 8.  (Y1/Vi)= G/(Ts+1) G = ki.ks.kb Where, G = the system gain T = the system time constant Ki = pump characteristic Ks = sensor characteristic
  • 9. Vi qi =kivi (Y1/Vi)= G/(Ts+1) Y1=ksh1 Y1 h1qi LEVEL SENSOR TANK SYSTEM PUMP Schematic Diagram of the overall system Above Diagram shows the overall diagram of the tank system. Finally, the experimental result of open loop test will be use to obtain transfer function of the single tank system. The gain and time constant can be taken from the output response of the open loop result.
  • 10. Effect of time constant on system response  Time constant is the time it takes for the step response to rise 63% of its final value.  Consider the step response of fig. 1 By the figure we get that at t=T1 the response will be 63% of its maximum value i.e. time constant of this response is T1  Consider the step response of fig 2 By the figure we get that at t=T2 the response will be 63% of its maximum value i.e. time constant of this response is T2 Fig. 1 Fig 2
  • 11. Now comparing the two responses As it is clear form the figure that T1 is smaller than T2 and figure also clear that the first response is faster then the second step response . Therefore because of this , the time constant is use to measure how fast a system can respond Smaller the time constant, faster is the system response.