Stable Feedback and State Estimation Techniques
Stable Feedback: General Case
State: x = Ax + Bu, | x Î Rn, u Î R | |||||||||||
Control: u = –Kx with K =[K1 | K2 | Kn ]1´n | ||||||||||
D | ||||||||||||
+ | ||||||||||||
r | u | + | ̇ | + | y | |||||||
+ | B | ʃ | C | |||||||||
+ | ||||||||||||
Ax | ||||||||||||||||||||
A | ||||||||||||||||||||
K | ||||||||||||||||||||
ì | Figure 14-1. Closed-loop system state diagram. | |||||||||||||||||||
D | ||||||||||||||||||||
ïx | = ( A – BK )x = Afx | , | ||||||||||||||||||
\í | ||||||||||||||||||||
ïA | f | = A – BK ¬closed – loop matrix | ||||||||||||||||||
î | ||||||||||||||||||||
the characteristic polynomial for the closed-loop system is | ||||||||||||||||||||
det(sI – Af ) = det(sI – A + BK ) = 0 | ||||||||||||||||||||
Let the Design Specification require closed-loop eigenvalues at | –l1,-l2 , ,-ln . | |||||||||||||||||||
\a | c | (s) = (s +l )(s +l | 2 | ) (s +l | n | ) = s n+a | n-1 | s n–1+ +a | s +a | 0 | = 0 | |||||||||
1 | 1 | |||||||||||||||||||
Pole-placement design
Read MoreInduction Motor Formulas: Power, Speed, and Efficiency
Induction Motor Formulas
COSy = R2/R1+SN / %((R1+R2/SN)^2+(X1+X2)^2)
Apparent Power
SN = (%3) * V1L * I1L
Reactive Power
QN = SN * SENy
Active Power
PN = SN * COSy
Motor Input Power
3 * (R2/S) * IF2
If Connected in Delta
IN,F = VF / %((R1 + R2/S)2 + (X1 X2 )2)
IN,F = IN,L = (%3) * IN,F
If Connected in Star
IN,F = VF/(%3) / %((R1 + R2/S)2 + ( X1 + X2 )2)
Efficiency
REND = P2 / (P2 + Pcu,1 + Pcu,2 + PFe + Pm) * 100
Pcu,1 = 3 * R1 * I1F2
Pcu,2 = 3 * R2 * I1F2
PFe = 3 * RFe * I1F2
P1 = (%) * V1,L * I1L * COSy
P2 = PN =
Microcontroller Timers and Pin Configuration
Time Counters
Mode 0: The counter register is configured as 13-bit. When the maximum value transition occurs (THx.7 THx.6 … THx.1 THx.0 TLx.4 TLx.3 … TLx.0) = 1111111111111 to zero, the Interrupt flag is activated (TF0, for x = 0 or TF1, for x = 1). It is similar to Mode 1; however, in this case, the 16 bits of the counter register are used (pair TH/TL, THx.0 TLx.7 with THx.7 … … TLx.0); that is, the Interrupt flag is activated when the transition from FFFFh to 0000h occurs in TH/TL. In a
Read MoreTraffic Engineering Fundamentals: Flow, Speed, and Safety
Traffic Engineering Basics
Traffic Flow Definitions
Volume/Flow: The total count of vehicles passing a specific point on a road within a given timeframe. This can be measured annually, daily, hourly, or in shorter intervals, typically expressed in vehicles per hour [v/h] or vehicles per day [v/d].
Volume represents the actual number of vehicles observed or predicted to pass a point during a set period.
Road Capacity: The maximum traffic volume a roadway can handle using all available lanes, usually
Read MorePower Amplifiers: Types, Functions, and Key Features
What is the Function of a Power Amplifier?
The function of a power amplifier is to amplify an input signal applied to it, typically a few hundred millivolts from the preamplifier, to a signal of a considerable level, a few tens of watts, to vibrate the speaker membrane.
Define the Volume Control
The volume control adjusts the output power or volume developed by the speaker.
What is the Excitatory Stage?
The excitatory stage is a second stage of voltage preamplifiers, and its principal role is to raise
Read MoreImage and Sound Formats: Types and Characteristics
Image Formats: Types and Characteristics
There are several types of image formats, each with its own characteristics and uses:
- Raster Images or Bitmaps: These are formed by many points (pixels) that, as a whole, define the final image. Each of these points has a specific color, luminosity, and contrast. The image files contain the information of the image in a dot matrix (pixels), so-called raster. When you save a bitmap image to a file, the characteristics of all points are stored.
- Vector Images: