sysrepdemo.m

similer program for matlab

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##               Auburn University. All rights reserved.
##
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## -*- texinfo -*-
## @deftypefn {Function File} {} sysrepdemo
## Tutorial for the use of the system data structure functions.
## @end deftypefn

## Author: A. S. Hodel <[e-mail]>
## Created: June 1995
## Revised Aug 1995 for system data structure format

function sysrepdemo ()

  save_val = page_screen_output ();
  page_screen_output (1);

  disp("System representation demo:")
  num = [5, -1];
  denom = [1, -2, 6];
  a = b = c = [];
  syschoice = -1;
  ch_init = 2;
  ch_extract = ch_init+1;
  ch_update = ch_extract+1;
  ch_view = ch_update+1;
  ch_details = ch_view+1;
  ch_quit = ch_details+1;
  while(syschoice != ch_quit)
   disp(" ")
    syschoice = menu("Octave System Representation Menu", ...
      "General overview of system representation (DO THIS FIRST)", ...
      "Initialize a system (ss, tf, zp)", ...
      "Extract data from a system(sys2ss, sys2tf, sys2zp, etc.)", ...
      "Update internal representation (sysupdate)", ...
      "View the internal contents of a system (sysout)", ...
      "Details of internal representation", ...
      "Return to main menu");
    if(syschoice == 1)  # general overview
      disp("The Octave Control Systems Toolbox (OCST) was designed to")
      disp("provide a simple user interface to a powerful set of tools.")
      disp(" ")
      disp("               ----------")
      disp(" input(s) ---->| System | ---> output(s) ")
      disp("               ----------")
      disp(" ")
      disp("Like other computer-aided control system design tools, the OCST")
      disp("enables users to enter their descriptions of dynamic systems in ")
      disp("their preferred form (state space, transfer function, or ");
      disp("zero-pole format).  ");
      disp("The OCST stores system descriptions in a single variable data ");
      disp("structure that allows for continuous time, discrete-time, or mixed ");
      disp("(sampled-data) systems.  ");
      disp(" ");
      disp("This single variable description of dynamic systems greatly simplifies ");
      disp("both the code of the OCST as well as the user interface, since only")
      disp("one variable is passed per system, regardless of the  internal ")
      disp("representation used in the data structure.  As a result, the ");
      disp("likelihood of user error is greatly reduced when calling OCST")
      disp("functions.  Further, all OCST functions have been written to")
      disp("provide meaningful warning or error message to assist the user")
      disp("in correcting their programming errors while using the OCST.")
      disp("The details of the internal representation can be seen in ");
      disp(["menu option ",num2str(ch_details)]);
      disp("The data structure used in the OCST is called a \"system data structure.\"");
      disp("A system data structure is contstructed with one of:")
      disp("   fir (FIR transfer function to system)")
      disp("   ss (state space matrices to system)")
      disp("   tf (SISO transfer function to system)")
      disp("   zp (SISO zero/pole/leading coefficient to system)")
      disp(" ")
      disp(["These functions are discussed in in menu option ",num2str(ch_init)])
      disp("The data in a system may be extracted using ")
      disp("   sys2fir (FIR transfer function from system")
      disp("   sys2ss (state space matrices from system)")
      disp("   sys2tf (SISO transfer function from system)")
      disp("   sys2zp (SISO zero/pole/leading coefficient from system)")
      disp(" ")
      disp(["These functions are discussed in menu option ", ...
        num2str(ch_extract)]);
      disp("Other options discussed under this menu are updating the internal")
      disp("representation form of a system data structure with sysupdate and printing")
      disp("the description of a dynamic system to the screen with sysout.")
      disp(" ")
      disp("Once the user is familiar with these commands, the rest of the ")
      disp("OCST package will be quite easy to use.")
    elseif(syschoice == ch_init) % Initialize
      disp("Initialization of a system:");
      disp(" ");
      formopt = 0;
      while(formopt != 4)
      disp("Three data formats may be used to initialize a system:")
        formopt = menu("System data structure initialization menu", ...
                "State space form       (ss)", ...
                "Transfer function form (tf)", ...
                "zero-pole form         (zp)", ...
                "Return to System representation menu");
        if(formopt == 1)
          disp("State space representation of a system is based on the usual")
          disp("multi-variable differential equations")
          disp(" ")
          disp("  . ")
          disp("  x = A x + B u      -or -   x(k+1) = A x(k) + B u(k) ")
          disp("  y = C x + D u                y(k) = C x(k) + D u(k) ")
          disp(" ")
          disp("for matrices A, B, C, D of appropriate dimension.")
          disp(" ")
          ssopt = 0;
          ssquit = 5;
          while(ssopt < ssquit)
            ssopt = menu("State space initialization examples", ...
                "Double integrator example", ...
                "Double delay (discrete-time) example", ...
                "Summing junction (D-matrix only) example", ...
                "ss details (help ss)", ...
                "return to system initialization menu", ...
                "return to system representation main menu");
            if(ssopt == 1)
              disp("Example: construct a system representation of a")
              disp("double integrator via state-space form")
              cmd = "a = [0, 1; 0, 0];";
              run_cmd
              cmd = "b = [0; 1];";
              run_cmd
              cmd = "c = [1, 0];";
              run_cmd
              cmd = "sys = ss(a,b,c);";
              run_cmd
              disp("The state space form of the system is seen via sysout:")
              cmd = "sysout(sys)";
              run_cmd
              disp("Notice that the Octave controls  toolbox automatically")
              disp("assigns names to the states, inputs and outputs,")
              disp("and that the D matrix was filled in automatically.")
              disp("We verify that it's a double integrator via sysout:")
              cmd = "sysout(sys,""tf"")";
              run_cmd
              prompt
            elseif(ssopt == 2)
              disp("Example: discrete-time double-delay:")
              disp("This example is identical to the double-integrator,")
              disp("except that it is a discrete-time system, and so has")
              disp("a sampling interval.  We arbitrarily select T=1e-3.");
              cmd = "a = [0, 1; 0, 0];";
              run_cmd
              cmd = "b = [0; 1];";
              run_cmd
              cmd = "c = [1, 0];";
              run_cmd
              cmd = "sys=ss(a,b,c,[],1e-3);";
              run_cmd
              cmd = "sysout(sys)";
              run_cmd
              disp("Notice that the D matrix was filled in automatically.")
              disp("This is done if D is input as the empty matrix.")
              disp(" ")
              disp("Notice also that the output y_1 is labelled as a discrete")
              disp("output.  The OCST data structure keeps track of states")
              disp("and output signals that are produced by the discrete-time")
              disp("portion of a system.  Discrete states and outputs are ")
              disp("implemented as shown in the block diagram below:")
              disp(" ")
              disp(" ")
              disp("       _________   ________ x(kT)  ________________")
              disp("f(t)-->|sampler|-->| delay |----->|zero order hold| -->")
              disp("       ---------   --------        ----------------")
              disp(" ")
              disp("        ___________    _______________")
              disp("f(t)-->| sampler |-->|zero-order hold| --> y(discrete)")
              disp("        -----------    ---------------")
              disp(" ")
              disp("where f(t) is an input signal to either the output or the")
              disp(" discrete state.")
              disp(" ")
              disp("The OCST does not implement samplers on inputs to continuous")
              disp("time states (i.e., there are no samplers implicit in the B")
              disp("or D matrices unless there are corresponding discrete")
              disp("outputs or states.  The OCST provides warning messages when")
              disp("if this convention is violated.")
              prompt
            elseif(ssopt == 3)
              disp("A summing junction that computes e(t) = r(t) - y(t) may be");
              disp("constructed as follows:");
              disp("First, we set the matrix D:")
              cmd = "D = [1, -1];";
              run_cmd
              disp("ss allows the initialization of signal and state names")
              disp("(see option 4), so we initialize these as follows:")
              cmd = "inname = {\"r(t)\",\"y(t)\"};";
              run_cmd;
              cmd = "outname = \"e(t)\";";
              run_cmd
              disp("Since the system is continuous time and without states,")
              disp("the ss inputs tsam, n, and nz are all zero:")
              cmd = "sys = ss([],[],[],D,0,0,0,[],inname,outname);";
              run_cmd
              disp("The resulting system is:")
              cmd = "sysout(sys)";
              run_cmd
              disp("A discrete-time summing block can be implemented by setting")
              disp("the sampling time positive:")
              cmd = "sys = ss([],[],[],D,1e-3,0,0,[],inname,outname);";
              run_cmd
              disp("The resulting system is:")
              cmd = "sysout(sys)";
              run_cmd
              prompt
            elseif(ssopt == 4)
              help ss
              disp(" ")
              disp(" ")
              disp("Notice that state-space form allows a single system to have")
              disp("both continuous and discrete-time states and to have both continuous")
              disp("and discrete-time outputs.  Since it's fairly easy to make an")
              disp("error when mixing systems of this form, the Octave controls")
              disp("toolbox attempts to print warning messages whenever something")
              disp("questionable occurs.")
            elseif(ssopt == 6)
              formopt = 4;              # return to main menu
            endif
          endwhile
        elseif(formopt == 2)
          tfopt = 0;
          while(tfopt < 5)
            tfopt = menu("Transfer function initialization menu", ...
                "Continuous time initialization" , ...
                "Discrete time initialization" , ...
                "User specified signal names" , ...
                "tf details (help tf)", ...
                "Return to system initialization menu", ...
                "Return to system representation main menu");
            if(tfopt == 1) # continuous time
              disp("A transfer function is represented by vectors of the")