System Control - Basic - Exercise

Đây là những bài tập hết sức cơ bản nhưng tôi thấy nó xuất hiện trong các tài liệu thi của Professonal Engineer. Bác nào pro thì thông cảm...chờ tôi đi từ tư nghe.

1) Assume 8 bit, unsigned integers for the following.
a) Convert 99(10) to binary.
b) Convert 1001 0010(2) to decimal.
c) Compute 0110 1100 + 0101 0111

2) Assume 8 bit, signed (2''s complement form) integers for the following.
a) What are the maximum and minimum decimal values that can be represented?
b) Convert ?"100(10) to binary.
c) Compute 0110 1100 - 0101 0111

3) Assume an 8 bit, fixed point notation, where the 3 LSB?Ts are the fractional part. Also, assume 2''s complement form.
a) Convert ?"10.5(10) to binary.
b) Convert 1011 0.101(2) to decimal.
4) Assume an excess binary (with a bias of 128) system with 8 bits.
a) Convert 27(10) to excess binary.
b) Convert 1111 1000(XS) to decimal.

5) Assume an eight bit floating point number (s eee ffff) similar to IEEE 754 with an implied 1, and a bias of 4 (subtract 4 from eee).
a) What is 1 010 1010(2) in decimal?
b) How would 0.5(10) be represented in the computer?
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Bài tập thứ 2 có vẻ thực tế hơn 1 tí
2a) Given the variable x, which is an 8 bit unsigned number, describe how you would set bit3 to 1 without affecting the other bits. Note that the bit numbering begins at 0. This is helpful when you wish to turn on a motor or a light connected to bit 3 in a PLC or microcontroller without affecting other devices.
2b) Given the variable x, which is an 8 bit unsigned number, describe how you would set bit3 to 0 without affecting the other bits. This is helpful when you wish to turn off a motor or a light connected to bit 3 in a PLC or microcontroller without affecting other devices.
2c) Given the variable x, which is an 8 bit unsigned number, describe how you would keep the value of bit3 (1 or 0) and set all other bits to zero? This is helpful when you want to see if a switch connected to bit3 in a PLC or microcontroller is on or off.
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DAC/ADC
1) Given a 12-bit unipolar DAC (Analog Devicesâ?T DAC 8562) where the supply voltage is 5V, but the reference voltage is trimmed to 4.096V. (This could be converted to a bipolar DAC simply by adding a bias op-amp).
a) What is the resolution (V_lsb)?
b) What is the maximum voltage output (V_max)?
c) What voltage is output when a digital signal of 1111 0000 1111 is input?
d) What digital signal would you need to apply in order to get a voltage output of 3.452V?
2) Given a 12-bit bipolar ADC where the reference voltages are -10V and +10V. Note that the Analog Devicesâ?T ADC80 is a bipolar device uses complementary offset binary. Use complementary offset binary, just like the ADC80.
a) When a value of â?"9.9951V is input, what is the binary output?
b) When a value of +9.9902V is input, what is binary output?
c) When a value of 0.000V is input, what is the binary output?
d) What analog signal would you need to apply to get a digital output of 1011 0000 0000b?
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BASIC Programming
Problem:
Given the four coefficients of a cubic equation, a, b, c, d. Write an algorithm using Newtonâ?Ts root finding method to find one root of the cubic equation. Start your initial extrapolation at xi = 0. Print the result. Remember, Newtonâ?Ts method states: x_(i+1) = x_i â?" f(x_i) / fâ?T(x_i)
Stop when the difference between x_i+1 and x_i is less than 0.001. Be sure to comment your code well!
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PLC Program
Data: Assume the following inputs and outputs for a traffic light.
OP1: Green light North/South direction
OP2: Yellow light North/South direction
OP3: Red light North/South direction
OP4: Green light East/West direction
OP5: Yellow light East/West direction
OP6: Red light East/West direction
Flags: F0 to F31 (general use)
IP0: North/South car sensor (car is waiting at red light)
IP1: East/West car sensor (car is waiting at red light)
Problem:
Design a ladder logic program that incorporates the following rule(s):
1. Lights cycle 25 seconds green, 5 second yellow, 30 seconds red.
2. N/S should be opposite E/W. That is, if N/S is red, E/W should be green, then yellow
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PMDC Motors
Data: The following data is from an old Electro-Craft E-508-D PMDC motor.
Peak torque: 0.438 Nõ?Âm
Continuous torque at stall: 0.071 Nõ?Âm
Motor inertia, J: 1.059õ?Â10-5 kgõ?Âm2
Damping factor, B: 6.747õ?Â10-6 Nõ?Âm/(rad/sec)
Torque constant/voltage constant, KT=KE: 0.037 Nõ?Âm/A or V/(rad/sec)
Resistance, R: 3.36 ẻâ
Inductance, L: 0.0034 H
Problem:
Let the terminal voltage be 12 V and the assume there are no thermal effects (a bad assumption, but one that greatly simplifies the problem). Make the following graphs, with either torque or time on the x-axis:
õ? Current versus torque
õ? Speed versus torque
õ? Power versus torque
õ? Efficiency versus torque
õ? Step response to 12V input.
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Encoders
Data: Assume the following data when answering the questions.
õ? Agilent HCTL2016 Quadrature Decoder/Counter Interface IC
o http://literature.agilent.com/litweb/pdf/5988-5895EN.pdf
o Operates in quadrature
o 16 bit counter with 8 bit bus (2 bit multiplexer included)
õ? Agilent HEDR-5420-ES203 Housed Incremental Encoder
o http://literature.agilent.com/litweb/pdf/5988-9450EN.pdf
o 200 CPR
Questions:
1. How many counts per revolution will be generated when the two devices are
connected?
2. Suppose the encoder is placed on a 26õ? bike wheel (outside diameter) to measure
distance traveled. How far can you travel before the encoder õ?orolls overõ?? State
your answer in number of tire revolutions and also in inches traveled.
3. Illustrate how you would connect the HCTL 2016 IC to the Blue Earth 485
microcontroller, and explain the operation of all lines. Note, there are many ways to do this so just state your assumptions.
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Stepper Motors
Clifton Prec. Prod. 15-SHAL-32CG/H297
Stepper Motor 1.8 deg. 2-phase (4-wire)
Rated Voltage: 3.28 VDC
Rated Current: 2.0 amps
DC Resistance: 1.64 ohms/ phase
Holding Torque: 34 oz.- in.
Body Dimensions: 1.5 in. square flange X 2.0 in. length
Front Shaft Dimensions: 0.1875 in. dia. X 0.50 in. length
Rear Shaft Dimensions: same
Inertia: 3.5õ?Â10-4 oz-in-sec2
No Load Slew Rate: 2185 pps
Dynamic Torque: 23.4 oz-in @ 100pps
The above is a typical stepper motor used in an ATM. Refer to the given specs when answering the following questions. Note: MOOG bought Clifton Precision and this motor is now called the 15-SHAL-32CZ. (MOOG bought them from Litton Industries).
õ~ Is this stepper motor a bipolar or unipolar motor and how can you tell?
õ~ Suppose a torque of 10 oz-in is applied to the stepper when it is not moving (static). How much of a displacement angle can be expected?
õ~ How many steps are required to rotate the shaft 72°?
õ~ In order to avoid a resonant frequency, what is the maximum speed (in rad/sec) at which the stepper should be operated?
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Encoders
Data: Assume the following data when answering the questions.
õ? Agilent HCTL2016 Quadrature Decoder/Counter Interface IC
o http://literature.agilent.com/litweb/pdf/5988-5895EN.pdf
o Operates in quadrature
o 16 bit counter with 8 bit bus (2 bit multiplexer included)
õ? Agilent HEDR-5420-ES203 Housed Incremental Encoder
o http://literature.agilent.com/litweb/pdf/5988-9450EN.pdf
o 200 CPR
Questions:
1. How many counts per revolution will be generated when the two devices are
connected?
2. Suppose the encoder is placed on a 26õ? bike wheel (outside diameter) to measure
distance traveled. How far can you travel before the encoder õ?orolls overõ?? State
your answer in number of tire revolutions and also in inches traveled.
3. Illustrate how you would connect the HCTL 2016 IC to the Blue Earth 485
microcontroller, and explain the operation of all lines. Note, there are many ways
to do this so just state your assumptions.
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