Electronic Systems Engineering Assignments-

Assignment 1-

1) Develop a simple ladder logic program that will turn on an output X if inputs A and B, or input C, or input D is on. All inputs (A, B, C and D) and the output (X) are external to the systems. You are required to use proper addresses for the inputs and the output.

2) An operation requires timing a long period of 18 hours. Construct a timer program that will operate a lamp once the period has elapsed. A manual push button is used to reset the process. [Note: Make sure that you use values which are not out of range.]

3) Note: The following two questions are practice problems (#17 and # 18 of Chapter 08 in the Hugh Jack book (Automating Manufacturing Systems with PLCs). Solutions using the Allen Bradley counters and timer instructions are provided in the book. Repeat these problems using the Omron PLC instructions.

a) Design a conveyor control system that follows the design guidelines below.

i) The conveyor has an optical sensor S1 that detects boxes entering a workcell

ii) There is also an optical sensor S2 that detects boxes leaving the workcell

iii) The boxes enter the workcell on a conveyor controlled by output C1

iv) The boxes exit the workcell on a conveyor controlled by output C2

v) The controller must keep a running count of boxes using the entry and exit sensors

vi) If there are more than five boxes in the workcell the entry conveyor will stop

vii)If there are no boxes in the workcell the exit conveyor will be turned off

viii) If the entry conveyor has been stopped for more than 30 seconds the count will be reset to zero, assuming that the boxes in the workcell were scrapped.

b) Write a ladder logic program that does what is described below.

i) When button A is pushed, a light will flash for 5 seconds.

ii) The flashing light will be on for 0.25 sec and off for 0.75 sec.

iii) If button A has been pushed 10 times the light will not flash until the system is reset.

iv) The system can be reset by pressing button B

4) Write a program that will use timer (s) to flash a light. The light should be on for 2.0 seconds and off for 0.25 seconds. Do not include start or stop buttons.

5) A high-speed machine requires the number of parts to be counted before changing the dies for the next part. The number of parts is 52,200. Construct a counter program that will operate a buzzer and stop the process when the number of parts is reached. A manual reset is required.

Assignment 2-

Q.1- (a) Find energy of the signals plotted in Figure 1. Note that amplitudes are only non-zero for 0 ≤ t ≤ 4.

(b) Find the correlation coefficient ρ between the pulse x(t) and the pulses y_j(t), j = 1, 2, 3.

Q.2- A signal composed of sinusoids is given by the following equation:

x(t) = 4 + 3cos (250 πt+ (π/4)) + 4sin (500 πt)

(a) Determine the angular frequency (ω₀), time period (T_o), and the coefficients in the following representations:

Compact Trigonometric Fourier series: x(t) = c₀ + _n=1Σ^∞c_n cos(n ω₀ t + θ_n)                               

Exponential Fourier series: x(t) = _n=-∞Σ^∞D_ne^jnw0t

(b) Sketch the single-sided as well as two-sided spectra of x(t) indicating the magnitude and phase of each frequency component. Which harmonics are present in x(t)?

(c) Consider a new signal y(t) = x(t) 2cos (50 πt - (π/3)). How is the two-sided spectrum changed? Is y(t) periodic? If so, what is the period?

Q.3- Magnitude and phase spectra of a composite signal g(t) are shown in Figure 2.

(a) Write an equation for g(t) in terms of cosine functions.

(b) Is g(t) periodic? Explain why or why not. If its periodic, what is the fundamental frequency (f₀) and corresponding period (T₀) of g(t)?

(c) Consider a new signal h(t) = 10cos(2παt + π) + g(t). Assuming h(t) is a periodic with period T₀ = 0.01 sec, determine positive values for the frequency α that will satisfy the condition.

(d) Use any of the values for the frequency α obtained in (c) to modify the spectra of Figure 2.

Q.4- Magnitude and phase spectra of a composite signal z(t) are shown in Figure 3

(a) What is the maximum frequency present in z(t)?

(b) What is the fundamental frequency (f₀) and time period (T₀) of z(t)?

(c) What is the minimum sampling rate required to recover the original signal back?

(d) Assuming that z(t) is sampled at a rate of 1900 Hz, can we reconstruct the signal from the digital version?

(e) Use Parseval's theorem to find the power of z(t)?

Q.5- Given is the Fourier transform of x(t):

x(f) = j2πf/1+j2πf

Use table of the Fourier Transforms to find Y(f) of the following signals:

(a) y(t) = x(t/2 + 1)

(b) y(t) = (-10Cos(200πt))x(t+1)

(c) y(t) = ¼ dx(t)/dt

(d) y(t) = _-∞∫^t x(τ).dτ