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AE 21008

INTRODUCTION TO FLIGHT VEHICLE

CONTROLS

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DEFINITIONS

Controlled Variable:

Typically the output variable, or parameter, or

condition of the system, which is measured and

controlled.

Manipulated Variable:

Typically the variable that is adjusted or controlled

or varied by the controller to bring the ControlledVariable to a desired value.

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DEFINITIONS

Plant:

A piece of equipment, or parts functioning together to

perform a particular operation.

Process: An Operation to be controlled

System: A combination of

components/equipment to perform an objective.

Disturbance: Undesirable signal(Internal/external) that affects the value of the

System-Output.

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DEFINITIONS

Feedback Control:

An operation that keeps the output within

desirable limits, when beset by a disturbance, by

adjusting the Manipulated Variable(s).

Note: Predictable disturbances are

compensated for by internal adjustments

within the system. Unpredictable disturbancesare handled by the Feedback Control.

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DEFINITIONS

Open Loop Control System:

Output not compared with reference input.

Typical systems operating on a time or seasonal

basis.

Simple construction and ease of maintenance.

Less expensive than Closed Loop System

No Stability Issues

Convenient when output is difficult to measure, or

economically no feasible.

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DEFINITIONS

Closed Loop Control System:

A feed-back system that compares the output to adesired level of the controlled variable input,

determines the difference (error signal) andadjusts the Manipulated variable to make thedifference, or the error signal to a prescribedvalue.

Handles unpredictable external disturbance

Stability is a major issue and if not addressedproperly, may lead to oscillations in the system.

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EXAMPLE

Input

(Manipulated

Variable)

Process

Output

(Controlled

Variable)

Design an Aircraft Cabin Heating System

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COMPLEX VARIABLES

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COMPLEX VARIABLES

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COMPLEX VARIABLES

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COMPLEX VARIABLES

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COMPLEX VARIABLES

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COMPLEX VARIABLES

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COMPLEX VARIABLES

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POLES, ZEROS AND SINGULARITY

Definitions:

Ordinary Points: Points where the function G(s) is

analytic.

Singular Points: Points where the function G(S) is

not analytic.

Poles: Specific Singular points where G(s) or its

derivatives approach infinity.Zeros: Specific Singular points where G(s) equals

zero.

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POLES, ZEROS AND SINGULARITY

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POLES, ZEROS AND SINGULARITY

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EULERS THEOREM

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LAPLACE TRANSFORM

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LAPLACE TRANSFORM

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LAPLACE TRANSFORM

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LAPLACE TRANSFORM

All signals that can be physically generated have

Laplace Transform, i.e., the Laplace Transform

exists, i.e., the Laplace integral converges and is of

exponential order. The conditions of piecewisecontinuity and exponential order make the function

f(t) transformable in the Laplace domain, and these

conditions are sufficient for most applications.

Discussion on signal convergence and divergence.

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LAPLACE TRANSFORM

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LAPLACE TRANSFORM

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LAPLACE TRANSFORM

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LAPLACE TRANSFORM

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LAPLACE TRANSFORM

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LAPLACE TRANSFORM

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LAPLACE TRANSFORM

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LAPLACE TRANSFORM

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LAPLACE TRANSFORM

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LAPLACE TRANSFORM

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LAPLACE TRANSFORM

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LAPLACE TRANSFORM

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LAPLACE TRANSFORM

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LAPLACE TRANSFORM

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LAPLACE TRANSFORM

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LAPLACE TRANSFORM

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LAPLACE TRANSFORM

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LAPLACE TRANSFORM

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LAPLACE TRANSFORM

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LAPLACE TRANSFORM

Summary:

Differentiation in the time domain corresponds to amultiplication by s in the Laplace-domain.

Integration in the time domain corresponds to adivision by s in the Laplace-domain.

Differentiation in the Laplace-domain correspondsto a multiplication by t in the time domain (with asign change).

Integration in the Laplace-domain corresponds to adivision by t in the time domain.

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INVERSE LAPLACE TRANSFORM

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INVERSE LAPLACE TRANSFORM

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INVERSE LAPLACE TRANSFORM

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INVERSE LAPLACE TRANSFORM

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INVERSE LAPLACE TRANSFORM