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Process Control Engineering
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7/21/2019 04- Response of First Order Systems
http://slidepdf.com/reader/full/04-response-of-first-order-systems 1/20
PROCESS DYNAMICS
AND CONTROL4 – Matlab Solutions and Lectures on First Order Process
Engr. Anthony Hilmer S. Medrano
Ref: Process Dynamics and Control 2nd Ed by Seborg, Edgar and Mellichamp
Process Systems Analysis and Control 3rd Ed by D. Coughanowr and S LeBlanc
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Lecture Outline
• Transfer Function
• Forcing Function
• Response to Forcing Function
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Standard Form of For First Order Transfer
Function
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BLOCK DIAGRAM REPRESENTATION
OF TRANSFER FUNCTION
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Initial Value and Final Value Theorem
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FORCING FUNCTIONS
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STEP RESPONSE
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Example
• A thermometer having a time constant of 0.1 min is at a
steady-state temperature of 90°F. At time t =0, the
thermometer is placed in a temperature bath maintained
at 100°F. Determine the time needed for the thermometer
to read 98°F.
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Step Response Using Matlab
• tf () command
• step() command
• hold on command
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IMPULSE RESPONSE
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Impulse Response Using Matlab
• tf () command
• impulse() command
• hold on command
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RAMP RESPONSE
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SINUSOIDAL RESPONSE
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Sinusoidal Response
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Example
• A mercury thermometer having a time constant of 0.1 min
is placed in a temperature bath at 100°F and allowed to
come to equilibrium with the bath. At time t=0, the
temperature of the bath begins to vary sinusoidally about
its average temperature of 100°F with an amplitude of2°F. If the frequency of oscillation is 10/ cycles/min, plot
the ultimate response of the thermometer reading as a
function of time. What is the phase lag?
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Review Problems
• All End Problems of Chapter 4 of Process Systems
Analysis and Control by Coughanowr
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END!
