Presentation on

TYPICAL EXAMPLE OF 1st ORDERSYSTEM 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 ControlThe purpose of cruise control is to keep the velocityof a car constant. The driver drives the car at thedesired speed, the cruise control system is activated by pushing a button and the system then keeps thespeed constant. The major disturbance comes from changes of the slope of theroad 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 inspite of changes in the slope of the road. The feedback signal is sent toan actuator which influences the throttle and thus the force generated bythe 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).

DesiredVelocity

∑ ∑ControllervelocityThrottle

bodyEngineF

Slope of road

PP

v1 q1 h1 y1

PUMP TANK SYSTEM MODEL

LEVELSENSOR

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, thenqi = 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=ksh1Y1h1qi

LEVEL SENSORTANK 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.

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