How to Simulate and Plot a Transfer Function in MATLAB?

[XcKyle93]

Homework Statement

Consider the system defined by Y(s) = H(s)X(s) with H(s) = K $\frac{s-a}{(s-b)(s-c)}$. Build a function in MATLAB to simulate this system for given values of a,b,c,K and various input signals x(t) (in the time or in s-domain). Include a function to display plots of the time functions x and y and the Bode plot of the transfer function. You can choose b,c so that the system is stable (that is, both b,c are positive).

Homework Equations

The Attempt at a Solution

I believe that the question is asking for two different functions. Here's my attempt at the first function:

function simButter(a, b, c, K, x)
syms s
sys = K * (s-a)/((s-b)*(s-c))

dt = 0.01;
t = 0:dt:10; %dt and 10 were arbitrarily picked; what else would I choose?

lsim(sys, x(t), t)

end

For the second function, I have:
function plotXYandTF(x,y)
dt = 0.01;
t = 0:dt:10;

subplot(1, 2, 1);
plot(t, x(t)); hold on;
plot(t, y(t)); hold off;

sys = tf(x,y);
subplot(1,2,2);
bode(sys)
end

Is this even right? I am kind of confused about the way the question is phrased. In general, I know very little about filtering with MATLAB, despite reading a lot of the docs on mathworks.

 

[KataKoniK]

Hello,

Thank you for posting this question on the forum. As a fellow scientist, I understand the importance of being able to accurately simulate and analyze systems in MATLAB. I have reviewed your attempt at the solution and have some suggestions that may help you.

Firstly, your attempt at the first function is on the right track. However, there are a few things that need to be adjusted. Firstly, you do not need to declare the variable "s" as a symbolic variable since you are using the "lsim" function, which is meant for continuous-time systems. Therefore, I would recommend removing the "syms s" line from your code.

Secondly, you have correctly defined the system transfer function, but you have not defined the input signal "x(t)". This can be done by creating a vector of values for the input signal, corresponding to the time vector "t". For example, if you want a sinusoidal input signal, you could define "x" as "sin(t)".

Lastly, the "lsim" function requires the system transfer function to be in the form of a transfer function object. Therefore, I would recommend converting the symbolic expression "sys" to a transfer function object using the "tf" function. The updated code for the first function would look something like this:

function simButter(a, b, c, K, x)

dt = 0.01;
t = 0:dt:10;

sys = tf(K * (s-a)/((s-b)*(s-c))); % convert transfer function to object
x = sin(t); % define input signal
y = lsim(sys, x, t); % simulate system

end

For the second function, you are on the right track as well. However, there are a few things that need to be adjusted. Firstly, you do not need to define the time vector "t" and input signal "x" again, as they are already defined in the first function. Therefore, you can remove those lines from your code. Secondly, you need to define the output signal "y" as well, which is the result of the "lsim" function in the first function. Lastly, the "tf" function requires two arguments, the numerator and denominator of the transfer function. Therefore, you would need to define the numerator and denominator separately before using the "tf" function. The updated code for the second function would look something like this:

function plot