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Dynamic Behavior
In analyzing process dynamic and process control systems, it is important to know how the process responds to changes in the process inputs.
A number of standard types of input changes are widely used for two reasons:
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Step Input
A sudden change in a process variable can be approximated by a step change of magnitude, M:
The step change occurs at an arbitrary time denoted as t = 0.
Special Case: If M = 1, we have a “unit step change”. We give it the symbol, S(t).
Example of a step change: A reactor feedstock is suddenly switched from one supply to another, causing sudden changes in feed concentration, flow, etc.
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Example:
The heat input to the stirredtank heating system in Chapter 2 is suddenly changed from 8000 to 10,000 kcal/hr by changing the electrical signal to the heater. Thus,
2. Ramp Input
Industrial processes often experience “drifting disturbances”, that is, relatively slow changes up or downfor some period of time.
The rate of change is approximately constant.
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We can approximate a drifting disturbance by a ramp input:
Examples of ramp changes:
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3. Rectangular Pulse
It represents a brief, sudden change in a process variable:
Examples:
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Other Inputs
4. Sinusoidal Input
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Processes are also subject to periodic, or cyclic, disturbances. They can be approximated by a sinusoidal disturbance:
Examples:
60Hz electrical noise (in USA!)
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For a sine input (1st order process)
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Inverting,
note: φ is not a function of t but of τ and ω.
For large t, y(t) is also sinusoidal, output sine is attenuated by…
(fast vs. slow ω)
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5. Impulse Input
Examples:
Injection of a tracer dye.
Here,
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Second order process example, Example 4.2
note when Ce → 0, obtain 1st order equation (simpler model)
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Block Notation:
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Second Order Step Change
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