frdemo.m

similer program for matlab

          prompt
        endif
      endwhile
    elseif (j == 2)
      k2 = 0;
      disp("");
      while (k2 != 4)
        disp("\n");
        help nyquist
        prompt;
        disp("")
        clc;

        k2 = menu("Nyquist analysis (Nyquist)",
                  "Continuous system nyquist analysis",
                  "Discrete system nyquist analysis",
                  "Mixed system nyquist analysis",
                  "Return to frdemo menu");

        if( k2 == 1 )
          disp("")
          clc
          disp("\nContinuous system nyquist analysis\n");
          disp("Display Nyquist plots of a SISO system (nyquist)\n")
          disp("Example #1, Consider the following transfer function:\n")
          cmd = "sys1 = tf(1, [1, 0.8, 1]);";
          disp(cmd);
          eval(cmd);
          disp("To examine the transfer function, use the command:");
          cmd = "sysout(sys1);";
          disp(cmd);
          eval(cmd);
          disp("\nTo examine the open loop zeros and poles, use the command:");
          cmd = "sysout(sys1,""zp"");";
          run_cmd;
          disp("\nTo view the system""s nyquist plot, execute the following");
          disp("command:\n")
          cmd = "nyquist(sys1);";
          run_cmd;
          disp("\nIf the real and imaginary parts of the response are desired,");
          disp("use the following command:");
          disp("command: [R,I,w]=nyquist(sys1);\n");
          disp("If the user desires to evaluate the response in a certain");
          disp("frequency range, he may do so by entering the following:");
          disp("command: [M,P,w]=nyquist(num,den,wrange).\n")
          disp("wrange is a vector of frequencies that spans the desired");
          disp("viewing range.\n");
          disp("This will be illustrated in the third nyquist example.\n")
          disp("Variable Description:\n")
          disp("R => real part of response")
          disp("I => imaginary part of response")
          disp("w => frequencies that the transfer function was evaluated at")
          disp("sys1 => system data structure")
          disp("wrange => optional vector of frequencies")
          disp("          if wrange is entered in the argument list, the");
          disp("          system will be evaluated at these specific");
          disp("          frequencies\n")
          prompt

          disp("")
          clc
          disp("Example #2, Consider the following set of poles and zeros:\n")
          cmd = "sys2 = zp([-1;-4],[-2+1.4142i;-2-1.4142i],1);";
          disp(cmd);
          eval(cmd);
          disp("\nTo examine the poles and zeros, use the command:");
          cmd = "sysout(sys2)";
          disp(cmd);
          eval(cmd);
          disp("\nTo view the system""s nyquist plot, execute the following");
          disp("command:\n")
          cmd = "nyquist(sys2);";
          run_cmd;
          prompt

          disp("")
          clc
          disp("\nExample #3, Consider the following state space system:\n")
          cmd = "sys3 = ss([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; 0, 0, -20, -12],[0;0;0;1],[50, 100, 0, 0],0);";
          disp(cmd);
          eval(cmd);
          disp("\nTo examine the state-space system, use the command:");
          cmd = "sysout(sys3)";
          disp(cmd);
          eval(cmd);
          disp("\nTo examine the poles and zeros, use the command:");
          cmd = "sysout(sys3,""zp"")";
          run_cmd;
          disp("\nTo view the system""s nyquist plot, execute the following");
          disp("commands:\n")
          cmd = "nyquist(sys3);";
          run_cmd;
          prompt

          disp("Example #3 (continued), If the user wishes to evaluate the");
          disp("system response over a desired frequency range, he must first");
          disp("create a frequency vector.\n")
          disp("For example, suppose the user is interested in the response");
          disp("of the system defined above over input frequency range of");
          disp("3 - 100 rad/s.\n")
          disp("A frequency vector can be created using the command:\n");
          cmd = "wrange = logspace(log10(3),log10(100),100);";
          disp(cmd);
          eval(cmd);
          disp("\nNyquist can be run again using the frequency vector as");
          disp("follows:\n")
          cmd = "nyquist(sys3,wrange);";
          run_cmd;
          prompt

          disp("")
          clc
          disp("Example #4,  Nyquist can be used for MIMO systems if the system has");
          disp("an equal number of inputs and outputs.  Otherwise, nyquist returns");
          disp("an error.  To examine a MIMO system, systems 2 and 3 will be grouped");
          cmd = "[nn,nz] = sysdimensions(sys2);";
          disp(cmd); eval(cmd);
          cmd = "sys2 = syssetsignals(sys2,\"out\",\"y_sys2\");";
          disp(cmd); eval(cmd);
          cmd = "sys2 = syssetsignals(sys2,\"in\",\"u_sys2\");";
          disp(cmd); eval(cmd);
          cmd = "sys2 = syssetsignals(sys2,\"st\",__sysdefioname__(nn+nz,\"x_sys2\"));";
          disp(cmd); eval(cmd);
          cmd = "sys_mimo = sysgroup(sys2,sys3);";
          disp(cmd); eval(cmd);
          cmd = "sysout(sys_mimo);";
          disp(cmd);
          eval(cmd);
          disp("\nTo view the system's nyquist plot, execute the following command:\n")
          cmd = "nyquist(sys_mimo);";
          run_cmd;
          prompt
          disp("\nTo view the nyquist plots for selected  channels, the command form changes:")
          cmd = "nyquist(sys_mimo,[],1,1);";
          run_cmd;
          disp("\nNotice that this bode plot is the same as the plot from example 2.");
          prompt
          closeplot



        elseif( k2 == 2 )
          disp("")
          clc
          disp("\nDiscrete system nyquist analysis\n");
          disp("Display Nyquist plots of a discrete SISO system (nyquist)\n")
          disp("We will first define a sampling time, T");
          cmd = "T = 0.01;";
          disp(cmd);
          eval(cmd);
          disp("\nExample #1, Consider the following transfer function:\n")
          cmd = "sys1 = tf([2, -3.4, 1.5],[1, -1.6, 0.8],T);";
          disp(cmd);
          eval(cmd);
          disp("To examine the transfer function, use the command:");
          cmd = "sysout(sys1);";
          disp(cmd);
          eval(cmd);
          disp("\nTo examine the open loop zeros and poles, use the command:");
          cmd = "sysout(sys1,""zp"")";
          disp(cmd);
          eval(cmd);
          disp("\nTo view the system""s nyquist plot, execute the following");
          disp("command:")
          cmd = "nyquist(sys1);";
          run_cmd;
          disp("To change the range used for the frequency, a frequency");
          disp("is needed.  Suppose the user would like to examine the");
          disp("nyquist plot in the frequency range of 0.01 - 31.6 rad/s.");
          disp("\nThe frequency vector needed to do this is created with the");
          disp("command:");
          cmd = "wrange = logspace(-2,1.5,200);";
          disp(cmd);
          eval(cmd);
          disp("\nNyquist can be run again with this frequency vector");
          cmd = "nyquist(sys1,wrange);";
          run_cmd;
          disp("\nIf the real and imaginary parts of the response are desired,");
          disp("perform the following command:\n");
          disp("[R,I,w]=nyquist(sys,wrange)\n")
          disp("Variable Description:\n")
          disp("R => real part of response")
          disp("I => imaginary part of response")
          disp("w => frequencies that the transfer function was evaluated at")
          disp("sys => The system data structure");
          disp("wrange => optional vector of frequencies")
          disp("          if wrange is entered in the argument list, the");
          disp("          system will be evaluated at these specific");
          prompt

          disp("")
          clc
          disp("\nExample #2, Consider the following set of poles and zeros:\n")
          cmd = "sys2 = zp([0.98025 + 0.01397i; 0.98025 - 0.01397i],[0.96079;0.99005],1,T);";
          disp(cmd);
          eval(cmd);
          disp("\nTo examine the open loop zeros and poles, use the command:");
          cmd = "sysout(sys2)";
          disp(cmd);
          eval(cmd);
          disp("\nTo view the system's nyquist plot between the frequencies");
          disp("0.01 - 100 rad/s, execute the following commands:\n")
          cmd = "wrange = logspace(-2,2,100);";
          disp(cmd);
          eval(cmd);
          cmd = "nyquist(sys2,wrange);";
          run_cmd;
          prompt;

          disp("")
          clc
          disp("\nExample #3, Consider the following discrete state space");
          disp("system:\n");
          disp("This example will use the same system used in the third");
          disp("example in the continuous nyquist demo.  First, that system");
          disp("will have to be re-entered useing the following commands:\n");
          cmd = "sys3 = ss([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; 0, 0, -20, -12],[0;0;0;1],[50, 100, 0, 0],0);";
          disp(cmd);
          eval(cmd);
          disp("\nTo examine the state-space system, use the command:");
          cmd = "sysout(sys3)";
          disp(cmd);
          eval(cmd);
          disp("\nTo examine the poles and zeros, use the command:");
          cmd = "sysout(sys3,""zp"")";
          disp(cmd);
          eval(cmd);
          disp("\nTo convert the system to discrete time, we need a sampling");
          disp("time which can be entered like this:");
          cmd = "T = 0.01";
          disp(cmd);
          eval(cmd);
          disp("\nNow the command, c2d, is used to convert the system from");
          disp("continuous to discrete time, with the following command");
          cmd = "dsys3 = c2d(sys3,T);";
          run_cmd;
          disp("\nTo examine the new discrete state-space system, use the");
          disp("command");
          cmd = "sysout(dsys3);";
          disp(cmd);
          eval(cmd);
          disp("\nTo examine the new discrete poles and zeros, use the command:");
          cmd = "sysout(dsys3,""zp"")";
          disp(cmd);
          eval(cmd);
          disp("\nTo view the system's nyquist plot, execute the following");
          disp("commands:\n");
          cmd = "axis ([-4, 2, -2.5, 2.5]);";
          disp(cmd); eval(cmd);
          cmd = "nyquist(dsys3);";
          run_cmd;
          disp("Notice that the asymptotes swamp out the behavior of the plot")
          disp("near the origin.  You may use interactive nyquist plots")
          disp("to \"zoom in\" on a plot as follows:")

          cmd = "atol = 1;";
          disp(cmd)
          eval(cmd)
          cmd = "nyquist(dsys3,[],[],[],atol);";
          run_cmd
          prompt


          disp("")
          clc
          disp("MIMO SYSTEM:  Nyquist cannot be used for discrete MIMO systems");
          disp("at this time.");
          ## cmd = "dsys_mimo = sysgroup(sys2,dsys3);";
          ## disp(cmd);
          ## eval(cmd);
          ## cmd = "sysout(dsys_mimo);";
          ## disp(cmd);
          ## eval(cmd);
          ## disp("\nTo view the system's nyquist plot, execute the following command:\n")
          ## cmd = "nyquist(dsys_mimo);";
          ## run_cmd;
          ## prompt
          ## disp("\nTo view the nyquist plots for selected  channels, the command form changes:")
          ## cmd = "nyquist(dsys_mimo,[],1,1);";
          ## run_cmd;
          ## disp("\nNotice that this bode plot is the same as the plot from example 2.");
          prompt
          closeplot


        elseif( k2 == 3 )
          disp("\nMixed system nyquist analysis\n");
          disp("Nyquist exits with an error if it is passed a ""mixed"" system (one")
          disp("with both continuous and discrete states).  Use c2d or d2c to")
          disp("convert the system to either pure digital or pure continuous form");
        endif
      endwhile
    elseif (j == 3)
      help nichols
      prompt
    endif
  endwhile

endfunction