Control Systems Design in Matlab

(See also page on LTI systems)

Synthesis of More Complex Systems/Working with Systems

• minreal
  Occasionally a model will have poles and zeros that should cancel out in the transfer function.  An example of this is in the system Sys1 defined above. 
                                  
  Matlab doesn't automatically do this simplification, but can with the "minreal" function:
  » Sys1Min=minreal(Sys1)
  Transfer function from input "MyInput" to output "MyOutput":
  2
  -----
  s + 2

• series
  » s3=series(s1,s2);
  Creates a new system which is the same as the series combination of s1 and s2.

• parallel
  » s4=parallel(s1,s2);
  Creates a new system which is the same as the parallel combination of s1 and s2;

• feedback
  » s5=feedback(s1,s2);
  Creates a new system which has s1 in the forward loop and s2 in the feedback loop.   Negative feedback is assumed.  If you want positive feedback use the form:
  » s5=feedback(s1,s2,1);
  
  

System Characterization
    In the following, "sys" is an LTI SISO system.

• Bode Plot
  » bode(sys);
  Plots the bode response of "sys".  If you have given names to the inputs and outputs, these are displayed on the graphs.
  » bode(sys,w);
  Calculates the step response at the frequencies specified by the vector "w".  To specify logarithmically spaced w (link).
  » [m,p,w]=bode(sys);
  Does not plot, but returns with the magnitude and phase of the output,and the frequency vector.

• Nyquist Plot
  » Nyquist(sys);
  Plots the step response of "sys".  If you have given names to the inputs and outputs, these are displayed on the graph.

• LTIViewer
  » LTIView;
  Brings up the LTI viewer which is useful for comparing several different systems.   Will generate any of the plots discussed above.

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