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Using MATLAB to Help Solving Problem on a System

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(la_7.doc)
A linear time-invariant discrete-time system has transfer function

H (z) = z² - z - 2
-----------
z² - 1.5z - 1

a. Use MATLAB to obtain the poles of the system. Is the system stable?
Explain.
b. Compute the step response using MATLAB commands like conv and residue.
c. Plot the first seven values of the step response. Is the response increasing
or decreasing with time? Is this what you would expect, and why?

(la_8.doc)

Question 1
a. Plot the Bode plots (both magnitude and phase) for the given transfer function

H (s) = 1000(s + 1)/(s+20)²

Use the command semilogx to make your plots.

b. What kind of filter is this? What is the bandwidth of the filter?

Question 2

Consider the system given by the following transfer function:

H(s) = 242.5(s +8)
---------------
(s + 2)[(s + 4)² + 81](s + 10)

a. Identify the poles and zeros of the system.
b. Is the system stable? Why or why not?
c. What is the steady-state value for the step response.
d. Use Simulink to simulate the step response. Use the 'Zero-Pole' continuous model for the system with a gain of 242.5. For the sink, you can use the step function provided. Please include a copy of the model along with a plot of the output either from the scope or the simout variables
e. Is the steady-state value from the simulation the same as in part c?
f. Is the response more like a first-order system or a second-order system?

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See Also This Related BrainMass Solution

Immune System Steady-State Simulation

See Attachment and it does need a simulink model and matlab script attached to solution. Thank you looking if you may need more time or credits let me know

Immune System Steady-State Simulation

The problem is describing the immune response triggered by encountering foreign antigens. This response is called the CTL (Cytotoxic T Cell) response. Suppose that (z), which are CTL Cells, eliminates infected cells. There are 4 variables: unifected cells (x), infected cells (y), free virus particles (v) and CTL cells (z). The equations are:
x'=λ-dx-Bxv
y'=Bxv-ay-pyz
v'=ky-uv
z'=c-bz

For this problem I am to create a Simulink Model and Matlab script using the following variables:
λ=1; d=0.01; a=0.05; B=0.005; p=1; k=50; u=5; b=0.05.

Problem 1) Let c=0. If c=0 then this will produce no CTL response. This basically gives an example of what would happen if there was no immune system. Make a Simulink model representing this simulation and determine the steady-state value by running the simulation and by running the "trim" function in matlab. The variables are:

x(0)=10;
y(0)=1;
v(0)=1;
z(0)=0
** These are the initial conditions inside the integrator block in Simulink

Problem 2) Go back to "Part 1" and linearize the system using the "linmod" function in matlab around the steady-state result from "Part 1"

Notes:
*** I have been working on this problem for some time and still having problems. I am having problems with my Simulink model, so I really need help on that one. I ran model with a step response of 0. The research that I have done on using the "trim" function, show that my trim function should look something similar to [vss,u,y,dx]=trim('CTLprob','[xinit,yinit,vinit,zinit]'). CTLprob is the name of my simulink model in this particular case. In Problem 2), I expect the [A,B,C,D]= linmod('CTLprob',vss,[])?? Vss is the column vector of the steady state values and I just need to find the matrices of A,B,C & D. I really need help on powering through this problem if you can help.

**If you think you have a better way of solving Problem 1 or 2 than what I described above, by all means help.

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