Contabilizacion De Costes - Conceptos Basicos, Apuntes - Contabilidad De Costes - Extracto del documento
Apuntes, Contabilidad De Costes
Classiﬁcation of control systems (vdv 1.2)
The output must be held 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: an electric 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 reference shade, 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.:
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 roll moment: 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 concept of 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.
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 gust • parameter variations, e.g. change of altitude
The solution is to use closed-loop control . . .
The pilot could observe the roll angle with respect to the horizon and compare the observed angle with the desir
But what happens if we ﬂy into a cloud?
We lose the feedback!
So let’s replace the pilot with a roll angle measuring system:
desired roll angle signal
roll angle signal
roll angle sensor
Figure 1: Roll angle measuring system.
• Comparator: • Error: • Feedback loop:
3 Standard block diagram of a feedback control system (vdv 1.3)
input r + -
plant or process
Figure 2: Standard block diagram.
Points of interest: 1. 2. 3. 4.
Tools of the trade
Linearized dynamic models (vdv 1.5)
Most physical systems are nonlinear. However, we can come up with linear models by linearizing the nonlinear equations about a particular operating point. You will need to use this concept in the labs. Homework drills should help you remember how it works.
Laplace transforms (vdv 1.6)
If you need to, go over the material you learned in Uniﬁed. There will be plenty of opportunity to practice this semester!
Transfer functions (vdv 1.7)
The transfer function of a system is the ratio of the Laplace transforms of its output and input, assuming zero initial conditions.
Figure 3: System input/output relationships.
C (s) = R(s) = G(s) =
(1) (2) (3)
Block diagrams (vdv 1.7)
”A topological arrangement of blocks showing cause and eﬀect relationships.”
desired motor + position error controller controller output voltage ampl ifier applied field voltage output motor position
Functional block diagram
Mathematical block diagram
Figure 4: Forms of block diagrams using the motor position servo of v
Let us consider a simpliﬁed version of Figure 1.3 with no dist