• Start Matlab.
• We'll look at getting a root locus first.
• Build an m-file.  In that file, type the following Matlab commands
• Num = [1]
• Den = [8 14 7 1]
• Sys = tf(Num,Den)
• rlocus(Sys)
• Let's dissect this m-file.
• Num = [1] defines a numerator array of 1.
• Den = [8 14 7 1] defines a denominator array that represents s³ +  7s² + 14s + 8.
• This is (s + 1)(s + 2)(s + 4) expanded.
• Sys = tf(Num,Den) defines a system representation for a system with Num for the numerator and Den for the denominator.
• rlocus(Sys) generates data and plots the root locus for the system.
• Now, you can save the m-file and run it.  You may need to be sure that the m-file can be found, so you may need to set a path.  Anyhow, we will assume that you save the file as Mymfile.m
• After you have the path set, type Mymfile.  You don't need the ".m" extension, and using it will get you an error message.
• If you check workspace variables by using the whos command, you will find that you have a tf object in the workspace.  That's where the transfer function information is stored.  Once the tf object is defined you can use it in other commands like:
• bode(Sys)
• nyquist(Sys)
• Once you have a tf object defined in your workspace, you can use ltiview (Linear, Time-Invariant View!) to look at a number of system analysis plots, and you can choose from any of the tf objects in your workspace.  Try ltiview and experiment with it.

• Next, we will look at getting the closed loop step response for the same system.  Here's the system we will use.  G(s) will be taken as 1/(s + 1)(s + 2)(s + 4).

• The m-file that will generate a step response is:
• CLNum = [1]
• K = 2
• CLDen = [8 14 7 1+K]
• CLSys = tf(CLNum,CLDen)
• step(CLSys)
• Generate an m-file with these commands and save it with a name of your choice.
• Run the m-file and you will get the closed loop step response.
• Notice what you did in this example.
• You defined a system with a specified numerator and denominator.
• The denominator included a variable term, 1 + K,
• The gain, K, was set in a separate statement.  This statement could be removed as long as the gain was set earlier within the workspace.  If you remove this statement, you can set the gain in the workspace, and re-run the m-file repeatedly to check response for different gains.
• Throughout this example, we used a prefix "CL" to indicate that we have closed loop system variables.
• Once CLSys is defined in the workspace, you can use all of the usual commands available for any tf object, including bode, nyquist, etc.