Chapter 5- Dynamic Behavior, PPT, Chemical Engineering, Semester, Engineering Notes - Computer Science Engineering (CSE)

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:

1. They are representative of the types of changes that occur in plants.
2. They are easy to analyze mathematically.

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1. 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 stirred-tank 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:

1. Ramp a setpoint to a new value. (Why not make a step change?)
2. Feed composition, heat exchanger fouling, catalyst activity, ambient temperature.

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3. Rectangular Pulse

It represents a brief, sudden change in a process variable:

Examples:

1. Reactor feed is shut off for one hour.
2. The fuel gas supply to a furnace is briefly interrupted.

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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:

1. 24 hour variations in cooling water temperature.

2. 60-Hz 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

• Here, 
• It represents a short, transient disturbance.
• It is the limit of a rectangular pulse for tw→0 and h = 1/tw

Examples:

1. Electrical noise spike in a thermo-couple reading.

2. 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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