Class 11 - Mathematical Modeling of Pneumatic System
18
System Modeling Coursework P.R. VENKATESWARAN Faculty, Instrumentation and Control Engineering, Manipal Institute of Technology, Manipal Karnataka 576 104 INDIA Ph: 0820 2925154, 2925152 Fax: 0820 2571071 Email: [email protected] , [email protected] Web address: http://www.esnips.com/web/SystemModelingClassNotes Class 11: Modeling of Pneumatic systems
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Transcript of Class 11 - Mathematical Modeling of Pneumatic System
System Modeling Coursework
P.R. VENKATESWARANFaculty, Instrumentation and Control Engineering,
Manipal Institute of Technology, ManipalKarnataka 576 104 INDIAPh: 0820 2925154, 2925152
Fax: 0820 2571071Email: [email protected], [email protected]
Web address: http://www.esnips.com/web/SystemModelingClassNotes
Class 11: Modeling of Pneumatic systems
July – December 2008 prv/System Modeling Coursework/MIT-Manipal 2
WARNING!
•
I claim no originality in all these notes. These are the compilation from various sources for the purpose of delivering lectures. I humbly acknowledge the wonderful help provided by the original sources in this compilation.
•
For best results, it is always suggested you read the source material.
July – December 2008 prv/System Modeling Coursework/MIT-Manipal 3
Contents
•
Description of a Pneumatic system•
Model of the Pneumatic system
•
Some questions.
July – December 2008 prv/System Modeling Coursework/MIT-Manipal 4
What is a pneumatic system
•
Pneumatic system uses compressible fluid as working medium and it is usually air.
•
In pneumatic systems, compressibility effects of gas cannot be neglected and hence dynamic equations are obtained using conservation of mass.
•
In pneumatic systems, change in fluid inertia energy and the fluid’s internal thermal energy are assumed negligible.
•
In pneumatic system, the mass and volume flow rates are not readily interchangeable
July – December 2008 prv/System Modeling Coursework/MIT-Manipal 5
Description of Pneumatic system
•
Pneumatic devices involve the flow of gas or air, through connected pipe lines and pressure vessels.
•
Hence, the variables of pneumatic system are mass flow rate, qm
, and pressure P.•
The mass flow rate is a through variable and it is analogous to current. The pressure variable is across variable and is analogous to voltage.
•
The two basic elements of a pneumatic system are the resistance and capacitance.
July – December 2008 prv/System Modeling Coursework/MIT-Manipal 6
Definition for Pneumatic Resistance
•
The gas flow resistance, R is defined as the rate of change in gas pressure difference for a change in gas flow rate.
2, /, / sec
Changein gas pressuredifference N mRChangein gas flowrate Kg
=
July – December 2008 prv/System Modeling Coursework/MIT-Manipal 7
Definition for pneumatic capacitance
•
Pneumatic capacitance is defined for a pressure vessel and depends on the type of expansion process involved. The capacitance of a pressure vessel may be defined as the ratio of change in gas stored for a change in gas pressure.
2
,, /
Changein gas stored KgCChangein gas pressure N m
=
July – December 2008 prv/System Modeling Coursework/MIT-Manipal 8
Pros and Cons of Pneumatic systems
•
Advantages –
The air or gas used is non inflammable and so it offers safety from fire hazards.
–
The air or gas has negligible viscosity, compared to high viscosity of hydraulic fluids.
–
No return pipelines are required and since air can be let out at the end of work cycle.
•
Disadvantage –
The response is slower than that of hydraulic systems because of the compressibility of the working fluid.
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Applications of Pneumatic systems
•
Guided Missiles•
Aircraft systems
•
Automation of production machines•
Automatic controllers
…and many more
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Pneumatic system
Pi
= air pressure of the source at steady state (newton/m2)P0
= air pressure in the vessel at steady state (newton/m2)∆
Pi
= small change in air pressure of the source from its steady state ∆
P0
= small change in air pressure of the vessel from its steady state
July – December 2008 prv/System Modeling Coursework/MIT-Manipal 11
System dynamics
•
Rate of gas storage in vessel = rate of gas inflow
•
The mathematical model of a simple pneumatic system shown in figure is given by
•
Applying Laplace and rearranging the terms, we get
0 0id P P PPCdt R RΔ Δ −ΔΔ
= =
0 0id P P PPCdt R RΔ Δ −ΔΔ
= =
0 ( ) 1( ) ( 1)i
P sP s RCs
Δ=
Δ +
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Try for this system
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Description of the system
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Solution –
Part I
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Solution –
Part II
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Summary
•
The transfer function of the system presents the same order as that of the level system with respect to the assumed dynamics and structure.
•
The common thread however will be with respect to the capacitance and resistance of the system
July – December 2008 prv/System Modeling Coursework/MIT-Manipal 17
References
1.
Advanced Control Systems Engineering, Ronald Burns
2.
Modern Control Engineering, Ogata3.
Control Systems, Nagoor
Kani
…amongst others
July – December 2008 prv/System Modeling Coursework/MIT-Manipal 18
And, before we break…
•
Comparisons give us the cancer of the soul–
G. Jampolsky
Thanks for listening…
