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.
Classiﬁcation of control systems (vdv 1.2)
The output must beheld as close as possible to a desired value. Examples: •
The input varies and the output must be made to follow as closely as possible. Examples: •
If we take a closer look, control systems can be classiﬁed as follows: 1. 2. 3. 4. 5. 6.
Open-loop and closed-loop control (vdv 1.3)
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.:
4Example 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.
5Equations 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...
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