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# Electrical Engineering

### Eigenvalue Equality & Matrix Invertibility

A) Show that the eigenvalues of A and AT are the same. b) Show that the matrix A is invertible if and only if A does not have a zero eigenvalues. c) Show that if the eigenvalues of A are... (see attachment for the rest of the question).

### Relationship Between Gain and Phase Margins

Find the relationship between the gain and phase margins for the two graphs attached.

### Linear Systems and State Space Matrices

I need some help with these questions: 2. Calculate the linear state space matrices A,B,C and D for system that is described by the state equations, for deviations from uop = [-1, 1]^T, xop = [1,1,0]^T and yop=  (see attached file for better formula representation). 3. A linear system is described by its transfer funct

### Bode Plot and Nyquist

A feedback loop transfer function is give as: L(s) = 9 (s+10)/(s+1)(s-30) Draw the corresponding Bode magnitude and phase angle plots for L(iw) for 0.1<w<1000 on the EdS Chart. Then sketch the complete Nyquist plot in the appropriate place of the EdS Chart. Is the closed loop system stable or unstable? Give the precise reasons

### PI controller design equation

The plant is given as P(s)=(P/(0.3-s))*e^(-0.1s). The only uncertainty is in p E [0.2, 0.6]. Derive the fastest PI controller G9(s)=k(1+(1/T_i*S)) such that the closed-loop system is stable and |S| < 6dB for all w and p. Use frequencies between 0.01 and 100 rad/s and the nominal plant with p=0.6. Indicate clearly both the

### Linear Systems and Second Order

The response of a second order system obtain in a step test is depicted in Figure 3. It is known that the nth overshoot Sn of the response is given by, where c is the damping ratio. Use this and the response obtained to: i. Find values of the damping ratio c and the natural radian frequency. ii. Deduce the system transfer fun

### Discrete-time Systems

What is the transfer function of the system in Figure 5. T=0.1 and the forward path transfer function of the ZOH combined with the plant may be taken as (see attachment) If the input in the above question is R(z)=1 derive the first three samples responses. Use the long division method i.e. express y(z^-1) = a_0 + a_1(z^-1)+a_

### Modelling and Simulation

Figure 2 shows a simplified diagram of an angular position control system where the field controlled generator acts as power amplifier to drive the motor. The motor drives an inertia load through an n:1 reduction gear box and viscous damping R which may be taken as proportional to speed. The generator output is eg=kgif. All othe

### Matlab and Designing Controller System

Consider the following system whose state space representation is as follows: (see attached file for better representation) x'1 0 1 0 x1 0 x'2 = 0

### Determine peak time and overshoot in a control system

A system with G(s) = K/(s(s+1)(s+4)) where K = 1 Design aPI controller so that the dominant roots are at s = -0.365+j0.514 and -0.365-j0.514. If a change of K = +50% or -50% occurs. Does the system peak time increase or decrease? Does the overshoot increase or decrease?

### Bandwidth of the closed-loop system

Consider the paper machine control in the attached file. Plot the bandwidth of the closed-loop system as K varies in the interval 1 &#8804; K &#8804; 50. What gain is required to provide a bandwidth of 10 rad/sec? See attached file for full problem description.

### Plotting Curves of the Compensated Systems: Matlab

Given the attach document, design a compensator such that the static velocity error constant is 4 sec^-1, phase margin is 50 degree and gain margin is 10 db or more. Plot unit-step and unit ramp reponse curves of the compensated systems with Matlab. Also draw a Nquist plot of the compensated system with Matlab.

Using the attached doc, this is a close-loop system, design a lead compensator Gc(s) such that the phase margin is 45 degree, gain margin is not less than 8 db, and the static velocity error constant Kv is 4.0 sec^-1. Plot unit step and unit ramp response curves of the compensated system with MATLAB

### Superposition Theorem - Independent Sources

Using Superposition theorem for independent sources (i.e. using ohm's law and applying the current divider rule) I would like to check the equations used to find the voltage across R4. RL is known so workings do not need to be shown. (See attached file for circuit diagram) This is a check for me as I am studying for an exa

### Gain Margin of a System

Consider the system shown in the attachment. Draw a bode diagram of the open loop transfer function, and determine the value of K such that the phase margin is 50 degrees. What is the gain margin of this system with the gain of K?

### Control signal processing problem

Consider the unity-feedback control system whose open-loop transfer function is G(s)= (as+1)/(s^2) Determine the value of a so that the phase margin is 45 degrees.

### Shift Register and D FF's

- - - Draw a 3 bit shift register with a positive edge trigger D FF and an Enable signal. Have the date enter from the left and shit to the right, when enable is off nothing should happen. Then draw the output under D,clock,E conditions.

### Inverse Nichols Chart

Question 4: a) Given P = [s/(-100) + 1]/[(s/4)^2 + 1.4(s/4) + 1], use the Inverse Nichols Chart to design a simple G(s) to achieve the following specifications. Show all design steps and sketch your final loop transfer function on the inverse Nichols Chart. i) Zero steady state error to a step output disturbance. ii) |1

### System Modeles

Consider the system modeled by: x' = Ax + Bu , y = Cx + Du where dim x=2 and dim u = dim y = 1 a) Given u=0 and the initial-state responses 1 x(0) = &#61535; y(t) = e

### De Morgan's Theorem

Realize the following function using only two-input NAND gates. See attachment for function. I do not understand how i would get this with NAND gates? Please draw out so i can see.

### Propagation Fundamentals- Cellular Systems

1. A cell is located over smooth, flat terrain. The system operates in the 1900 MHz band and the base station antenna is located 15 m above the ground. The mobile terminal is 250 m away from the base and its antenna is 1.5 m above the ground. (Use 1920 MHz in your computations.) (a) Compute the propagation loss. (b) What is

### Micro Electric Circuits

For the depletion-load amplifier, let W1=80microm, L1=4micrometers, W2=8 micrometers and L2=32 micrometers. If the body-effect parameter X=0.2, find the voltage gain neglecting the effect on ro. a. -44.72 V/V b. -45.6V/V c. 44.72 V/V d. 45.6 V/V

### System Modeled by Eigenvectors

See the attached file. Consider the system modeled by: x' = Ax + Bu , y = Cx + Du -5 1 -1 A = , B = , C=[1 0] , D=0 1 -5 1 a) Determine the transition matrix eAt using the eigenv

### Microelectric Circuits

For the circuit shown below, find the largest value that Rd can have while the MOSFET remains in saturation. Id = 0.5 mA, Vd = 1 V. The NMOS transistor has Vt = 2V. (see attached file for circuit layout) a. 16.0 k ohms b. 18.0 k ohms c. 20.0 k ohms d. 22.0 k ohms

### Working with Zener diode voltage regulators.

Please check my work and if incorrect give me the correct answer A shunt regulator utilizes a zener diode whose voltage is 5.1V at a current of 50 ma and whose incremental resistance is 8 ohms. The diode is fed from a supply of 12 V nominal voltage through a 220 ohm resistor. What is the output voltage at no load? a. 4.8 V

### Matrices and Infinite Series Method

Given the following matrices. 3 1 0 A = 0 3 1 0 0 3 3 1 0 A = 0 3 0 0 0 4 4 0 0 A = 0 3 1

### Root Locus and Routh-Hurwitrz

Please help solving this problem without matlab: a. Use Routh-Hurwitz to find vales of K so that L = k (s+1) / (s^2 +4) (s+10) has poles to the left of s= -2 b. Make a sketch of the root-locus of the above L(s) to explain the results above. You need to calculate the asymptotes (as s and k go to infinity) and angles of departur

### Control System Specifications and Response

I need some help with this question, look at attached files for better symbol representation and also diagrams: For a system with P = (3e^-0.1x / 2s + 1), it is desired that a step input disturbance, di = 3 sigma (t), results in an output of not more than 0.1. (Note that the dead time gives a relatively small effect in the clo

### Highpass Filter

Design a highpass filter with a cutoff frequency of 1000 Hz with a load resistance of 1000 ohms.

### State space representation

Consider the following system whose state space representation is as follows: a) Assume that the initial conditions are zero. If the reference input is a unit step input , compute x1(t), x2(t), and y(t) b) Find the transfer function of the system. c) Using the transfer function found in (b), Compute y(t). d) Plot x1