Control Automatico

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16.060 Lecture 2
Introduction to Feedback Control

Karen Willcox September 4, 2003

Today’s Topics 1. Classiﬁcation of control systems 2. Open-loop and closed-loop control 3. Standard blockdiagrams 4. Tools of the trade Reading: 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7 to the top of page 14.

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1
1.1

Classiﬁcation of control systems (vdv 1.2)
Regulator systems

The output must beheld as close as possible to a desired value. Examples: •

1.2

Servomechanisms

The input varies and the output must be made to follow as closely as possible. Examples: •

•2

If we take a closer look, control systems can be classiﬁed as follows: 1. 2. 3. 4. 5. 6.

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2
2.1

Open-loop and closed-loop control (vdv 1.3)
Open-loop control

Example 1: anelectric toaster -the output, c, is the shade of the toast -we want to realize a constant output -we do this by choosing a setting on a mechanical timer -this setting is the system input, or referenceshade, r

This is not a high performance system. A system error, e = r − c will develop because of: 1. Disturbances acting on the system, e.g.: 2. Parameter variations of the system, e.g.:

4 Example 2: pilot roll control of an airplane The dynamics of the situation are as follows: • change of heading: requires a horizontal force • tip lift vector: requires angular acceleration • create rollmoment: ailerons change camber • move ailerons by displacing control wheel

We derive a linearized model to get the appropriate diﬀerential equation. Note: if you are uncomfortable with the conceptof linearization, check out http://web.mit.edu/aa-math for a revision. This is a math concept that you will see often throughout this class! δ is the angle of ﬂap deﬂection. φ is the roll angle.

5 Equations of motion:

How does the pilot know when to remove δ? S/he could practice and develop a time-displacement proﬁle for the control wheel, but what about: • disturbances, e.g. a wind...