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1 ## Copyright (C) 1996, 1998 Auburn University. All rights reserved. |
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2 ## |
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3 ## This file is part of Octave. |
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4 ## |
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5 ## Octave is free software; you can redistribute it and/or modify it |
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6 ## under the terms of the GNU General Public License as published by |
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7 ## the Free Software Foundation; either version 3 of the License, or (at |
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8 ## your option) any later version. |
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9 ## |
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10 ## Octave is distributed in the hope that it will be useful, but |
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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13 ## General Public License for more details. |
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14 ## |
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15 ## You should have received a copy of the GNU General Public License |
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16 ## along with Octave; see the file COPYING. If not, see |
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17 ## <http://www.gnu.org/licenses/>. |
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18 |
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19 ## Undocumented internal function. |
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20 |
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21 ## -*- texinfo -*- |
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22 ## @deftypefn {Function File} {[@var{y}, @var{t}] =} __stepimp__ (@var{sitype}, @var{sys} [, @var{inp}, @var{tstop}, @var{n}]) |
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23 ## Impulse or step response for a linear system. |
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24 ## The system can be discrete or multivariable (or both). |
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25 ## This m-file contains the ``common code'' of step and impulse. |
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26 ## |
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27 ## Produces a plot or the response data for system @var{sys}. |
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28 ## |
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29 ## Limited argument checking; ``do not attempt to do this at home''. |
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30 ## Used internally in @command{impulse}, @command{step}. Use @command{step} |
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31 ## or @command{impulse} instead. |
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32 ## @seealso{step, impulse} |
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33 ## @end deftypefn |
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34 |
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35 ## Author: Kai P. Mueller <mueller@ifr.ing.tu-bs.de> |
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36 ## Created: October 2, 1997 |
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37 ## based on lsim.m of Scottedward Hodel |
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38 |
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39 function [y, t] = __stepimp__ (sitype, sys, inp, tstop, n) |
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40 |
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41 if (sitype == 1) |
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42 IMPULSE = 0; |
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43 elseif (sitype == 2) |
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44 IMPULSE = 1; |
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45 else |
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46 error ("__stepimp__: invalid sitype argument"); |
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47 endif |
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48 sys = sysupdate (sys, "ss"); |
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49 |
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50 USE_DEF = 0; # default tstop and n if we have to give up |
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51 N_MIN = 50; # minimum number of points |
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52 N_MAX = 2000; # maximum number of points |
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53 T_DEF = 10.0; # default simulation time |
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54 |
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55 ## collect useful information about the system |
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56 [ncstates, ndstates, NIN, NOUT] = sysdimensions (sys); |
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57 TSAMPLE = sysgettsam (sys); |
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58 |
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59 if (nargin < 3) |
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60 inp = 1; |
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61 elseif (inp < 1 || inp > NIN) |
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62 error ("__stepimp__: argument inp out of range"); |
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63 endif |
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64 |
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65 DIGITAL = is_digital (sys); |
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66 if (DIGITAL) |
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67 NSTATES = ndstates; |
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68 if (TSAMPLE < eps) |
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69 error ("__stepimp__: sampling time of discrete system too small") |
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70 endif |
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71 else |
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72 NSTATES = ncstates; |
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73 endif |
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74 if (NSTATES < 1) |
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75 error ("__stepimp__: pure gain block (n_states < 1), step response is trivial"); |
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76 endif |
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77 if (nargin < 5) |
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78 ## we have to compute the time when the system reaches steady state |
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79 ## and the step size |
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80 ev = eig (sys2ss (sys)); |
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81 if (DIGITAL) |
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82 ## perform bilinear transformation on poles in z |
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83 for i = 1:NSTATES |
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84 pole = ev(i); |
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85 if (abs(pole + 1) < 1.0e-10) |
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86 ev(i) = 0; |
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87 else |
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88 ev(i) = 2 / TSAMPLE * (pole - 1) / (pole + 1); |
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89 endif |
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90 endfor |
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91 endif |
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92 ## remove poles near zero from eigenvalue array ev |
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93 nk = NSTATES; |
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94 for i = 1:NSTATES |
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95 if (abs (real (ev(i))) < 1.0e-10) |
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96 ev(i) = 0; |
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97 nk = nk - 1; |
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98 endif |
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99 endfor |
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100 if (nk == 0) |
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101 USE_DEF = 1; |
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102 ## printf("##STEPIMP-DEBUG: using defaults.\n"); |
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103 else |
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104 ev = ev(find (ev)); |
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105 x = max (abs (ev)); |
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106 t_step = 0.2 * pi / x; |
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107 x = min (abs (real (ev))); |
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108 t_sim = 5.0 / x; |
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109 ## round up |
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110 yy = 10^(ceil (log10 (t_sim)) - 1); |
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111 t_sim = yy * ceil (t_sim / yy); |
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112 ## printf("##STEPIMP-DEBUG: nk=%d t_step=%f t_sim=%f\n", |
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113 ## nk, t_step, t_sim); |
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114 endif |
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115 endif |
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116 |
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117 if (DIGITAL) |
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118 ## ---- sampled system |
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119 if (nargin == 5) |
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120 n = round (n); |
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121 if (n < 2) |
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122 error ("__stepimp__: n must not be less than 2.") |
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123 endif |
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124 else |
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125 if (nargin == 4) |
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126 ## n is unknown |
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127 elseif (nargin >= 1) |
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128 ## tstop and n are unknown |
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129 if (USE_DEF) |
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130 tstop = (N_MIN - 1) * TSAMPLE; |
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131 else |
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132 tstop = t_sim; |
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133 endif |
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134 endif |
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135 n = floor (tstop / TSAMPLE) + 1; |
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136 if (n < 2) |
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137 n = 2; |
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138 endif |
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139 if (n > N_MAX) |
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140 n = N_MAX; |
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141 printf ("Hint: number of samples limited to %d by default.\n", \ |
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142 N_MAX); |
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143 printf (" ==> increase \"n\" parameter for longer simulations.\n"); |
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144 endif |
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145 endif |
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146 tstop = (n - 1) * TSAMPLE; |
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147 t_step = TSAMPLE; |
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148 else |
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149 ## ---- continuous system |
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150 if (nargin == 5) |
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151 n = round (n); |
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152 if (n < 2) |
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153 error("step: n must not be less than 2.") |
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154 endif |
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155 t_step = tstop / (n - 1); |
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156 else |
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157 if (nargin == 4) |
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158 ## only n in unknown |
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159 if (USE_DEF) |
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160 n = N_MIN; |
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161 t_step = tstop / (n - 1); |
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162 else |
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163 n = floor (tstop / t_step) + 1; |
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164 endif |
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165 else |
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166 ## tstop and n are unknown |
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167 if (USE_DEF) |
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168 tstop = T_DEF; |
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169 n = N_MIN; |
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170 t_step = tstop / (n - 1); |
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171 else |
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172 tstop = t_sim; |
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173 n = floor (tstop / t_step) + 1; |
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174 endif |
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175 endif |
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176 if (n < N_MIN) |
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177 n = N_MIN; |
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178 t_step = tstop / (n - 1); |
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179 endif |
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180 if (n > N_MAX) |
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181 tstop = (n - 1) * t_step; |
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182 t_step = tstop / (N_MAX - 1); |
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183 n = N_MAX; |
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184 endif |
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185 endif |
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186 tstop = (n - 1) * t_step; |
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187 [jnk,B] = sys2ss (sys); |
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188 B = B(:,inp); |
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189 sys = c2d (sys, t_step); |
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190 endif |
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191 ## printf("##STEPIMP-DEBUG: t_step=%f n=%d tstop=%f\n", t_step, n, tstop); |
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192 |
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193 F = sys.a; |
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194 G = sys.b(:,inp); |
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195 C = sys.c; |
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196 D = sys.d(:,inp); |
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197 y = zeros (NOUT, n); |
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198 t = linspace (0, tstop, n); |
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199 |
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200 if (IMPULSE) |
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201 if (! DIGITAL && D'*D > 0) |
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202 error ("impulse: D matrix is nonzero, impulse response infinite.") |
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203 endif |
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204 if (DIGITAL) |
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205 y(:,1) = D / t_step; |
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206 x = G / t_step; |
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207 else |
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208 x = B; |
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209 y(:,1) = C * x; |
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210 x = F * x; |
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211 endif |
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212 for i = 2:n |
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213 y(:,i) = C * x; |
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214 x = F * x; |
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215 endfor |
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216 if (DIGITAL) |
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217 y *= t_step; |
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218 endif |
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219 else |
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220 x = zeros (NSTATES, 1); |
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221 for i = 1:n |
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222 y(:,i) = C * x + D; |
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223 x = F * x + G; |
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224 endfor |
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225 endif |
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226 |
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227 if (nargout == 0) |
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228 if (IMPULSE) |
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229 gm = zeros (NOUT, 1); |
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230 tt = "impulse"; |
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231 else |
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232 ssys = ss (F, G, C, D, t_step); |
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233 gm = dcgain (ssys); |
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234 tt = "step"; |
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235 endif |
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236 ncols = floor (sqrt (NOUT)); |
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237 nrows = ceil (NOUT / ncols); |
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238 for i = 1:NOUT |
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239 subplot (nrows, ncols, i); |
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240 if (DIGITAL) |
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241 [ts, ys] = stairs (t, y(i,:)); |
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242 ts = ts(1:2*n-2)'; |
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243 ys = ys(1:2*n-2)'; |
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244 if (length (gm) > 0) |
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245 yy = [ys; gm(i)*ones(size(ts))]; |
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246 else |
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247 yy = ys; |
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248 endif |
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249 plot (ts, yy); |
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250 grid ("on"); |
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251 xlabel ("time [s]"); |
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252 ylabel ("y(t)"); |
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253 else |
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254 if (length (gm) > 0) |
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255 yy = [y(i,:); gm(i)*ones(size(t))]; |
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256 else |
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257 yy = y(i,:); |
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258 endif |
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259 plot (t, yy); |
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260 grid ("on"); |
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261 xlabel ("time [s]"); |
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262 ylabel ("y(t)"); |
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263 endif |
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264 title (sprintf ("%s: | %s -> %s", tt, |
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265 sysgetsignals (sys, "in", inp, 1), |
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266 sysgetsignals (sys, "out", i, 1))); |
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267 endfor |
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268 y = []; |
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269 t = []; |
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270 endif |
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271 ## printf("##STEPIMP-DEBUG: gratulations, successfull completion.\n"); |
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272 endfunction |
