How to Write MATLAB Code for Control Systems with Variable K?

[Badger33]

I have a given system and I need to
A) determine the transfer function
B) find the values of K form Routh-Hurwitz
C) Determine the values of K for the stable region
D) Create the simulink model.

I want to know how to write my MATLAB code so that I can solve what I need to. I DO NOT want the answers! I want to do it my self. Please provide the code entries and how to input them properly, use examples if you can it will help a lot!

This system is a proportional controller. My closed loop transfer function is 4K/s³+13s²+19s+4K

I know the range of my system to be 61.75>K>0 from the Routh-Hurwitz stability conditions.

So I want to be able to sole the C.E. I would like to do this in MATLAB using the roots command. But my issue is that my equation is s³+13s²+19s+4K So I want to have K be a variable change it then resolve for roots. I think i can do it with root locus too but this is how I want to do it, but you can TEACH me both I won't mind. I keep trying to do the following code but it is wrong.
>>K=.001
>>SysP1=[1 13 19s 4K];
>>roots(SysP1)

That is my first solution then the next would be
>>K=.1; roots(SysP1)
Obviously I could just keep changing that last line and getting new solutions.
Help me please.



Next I create the simulink model and want to make a plot of the system response to a step change so I just create my moddel and output to scope and that's the result. If I want an angle input to my step function I can just input that π/4 rad as the step input. Also I want an unstable system and that will be any value of K outside the stable region (or is it were my roots to the CE are positive?)




P.S. This is my first course that I have ever had to use MATLAB for and well have not had a formal introduction to matlab, thus I know very little. I know how to do simulink well though. Seeing as I have no background in MATLAB I have been getting no where and just frustrated and well want to throw my computer out the window!

 

[Valkarie]

To solve the transfer function equation, you can use the symbolic toolbox in MATLAB. The following code will help you to solve the equation for different values of K: % Define symbolic variable syms s K; % Define transfer function SysP1 = 4*K/s^3 + 13*s^2 + 19*s + 4*K; % Solve the equation for different values of K for k = 0:0.1:61.75 SysP1_k = subs(SysP1,K,k); % Substitute value of K rts = roots(SysP1_k); % Solve the equation disp(rts); % Display the roots end To create the Simulink model, you can drag and drop blocks from the Simulink library and connect them accordingly. The step input should be connected to the input port of your system. To change the value of K, you can use a Constant block. For example, if K is 0.1, you can set the value of the Constant block to 0.1. You can then observe the response of the system by connecting the output port of your system to the Scope block.