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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 the |
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7 ## Free Software Foundation; either version 2, or (at your option) any |
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8 ## later version. |
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9 ## |
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10 ## Octave is distributed in the hope that it will be useful, but WITHOUT |
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11 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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12 ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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13 ## 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, write to the Free |
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17 ## Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
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18 ## 02110-1301 USA. |
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19 |
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20 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {[@var{y}, @var{t}] =} __stepimp__ (@var{sitype}, @var{sys} [, @var{inp}, @var{tstop}, @var{n}]) |
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22 ## Impulse or step response for a linear system. |
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23 ## The system can be discrete or multivariable (or both). |
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24 ## This m-file contains the ``common code'' of step and impulse. |
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25 ## |
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26 ## Produces a plot or the response data for system @var{sys}. |
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27 ## |
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28 ## Limited argument checking; ``do not attempt to do this at home''. |
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29 ## Used internally in @command{impulse}, @command{step}. Use @command{step} |
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30 ## or @command{impulse} instead. |
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31 ## @end deftypefn |
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32 ## |
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33 ## @seealso{step, impulse} |
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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) IMPULSE = 0; |
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42 elseif (sitype == 2) IMPULSE = 1; |
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43 else error("__stepimp__: invalid sitype argument.") |
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44 endif |
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45 sys = sysupdate(sys,"ss"); |
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46 |
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47 USE_DEF = 0; # default tstop and n if we have to give up |
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48 N_MIN = 50; # minimum number of points |
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49 N_MAX = 2000; # maximum number of points |
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50 T_DEF = 10.0; # default simulation time |
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51 |
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52 ## collect useful information about the system |
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53 [ncstates,ndstates,NIN,NOUT] = sysdimensions(sys); |
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54 TSAMPLE = sysgettsam(sys); |
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55 |
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56 if (nargin < 3) inp = 1; |
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57 elseif (inp < 1 | inp > NIN) error("Argument inp out of range") |
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58 endif |
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59 |
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60 DIGITAL = is_digital(sys); |
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61 if (DIGITAL) |
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62 NSTATES = ndstates; |
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63 if (TSAMPLE < eps) |
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64 error("__stepimp__: sampling time of discrete system too small.") |
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65 endif |
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66 else NSTATES = ncstates; endif |
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67 if (NSTATES < 1) |
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68 error("step: pure gain block (n_states < 1), step response is trivial"); |
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69 endif |
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70 if (nargin < 5) |
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71 ## we have to compute the time when the system reaches steady state |
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72 ## and the step size |
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73 ev = eig(sys2ss(sys)); |
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74 if (DIGITAL) |
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75 ## perform bilinear transformation on poles in z |
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76 for i = 1:NSTATES |
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77 pole = ev(i); |
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78 if (abs(pole + 1) < 1.0e-10) |
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79 ev(i) = 0; |
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80 else |
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81 ev(i) = 2 / TSAMPLE * (pole - 1) / (pole + 1); |
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82 endif |
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83 endfor |
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84 endif |
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85 ## remove poles near zero from eigenvalue array ev |
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86 nk = NSTATES; |
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87 for i = 1:NSTATES |
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88 if (abs(real(ev(i))) < 1.0e-10) |
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89 ev(i) = 0; |
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90 nk = nk - 1; |
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91 endif |
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92 endfor |
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93 if (nk == 0) |
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94 USE_DEF = 1; |
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95 ## printf("##STEPIMP-DEBUG: using defaults.\n"); |
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96 else |
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97 ev = ev(find(ev)); |
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98 x = max(abs(ev)); |
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99 t_step = 0.2 * pi / x; |
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100 x = min(abs(real(ev))); |
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101 t_sim = 5.0 / x; |
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102 ## round up |
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103 yy = 10^(ceil(log10(t_sim)) - 1); |
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104 t_sim = yy * ceil(t_sim / yy); |
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105 ## printf("##STEPIMP-DEBUG: nk=%d t_step=%f t_sim=%f\n", |
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106 ## nk, t_step, t_sim); |
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107 endif |
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108 endif |
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109 |
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110 if (DIGITAL) |
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111 ## ---- sampled system |
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112 if (nargin == 5) |
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113 n = round(n); |
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114 if (n < 2) |
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115 error("__stepimp__: n must not be less than 2.") |
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116 endif |
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117 else |
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118 if (nargin == 4) |
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119 ## n is unknown |
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120 elseif (nargin >= 1) |
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121 ## tstop and n are unknown |
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122 if (USE_DEF) |
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123 tstop = (N_MIN - 1) * TSAMPLE; |
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124 else |
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125 tstop = t_sim; |
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126 endif |
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127 endif |
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128 n = floor(tstop / TSAMPLE) + 1; |
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129 if (n < 2) n = 2; endif |
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130 if (n > N_MAX) |
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131 n = N_MAX; |
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132 printf("Hint: number of samples limited to %d by default.\n", \ |
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133 N_MAX); |
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134 printf(" ==> increase \"n\" parameter for longer simulations.\n"); |
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135 endif |
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136 endif |
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137 tstop = (n - 1) * TSAMPLE; |
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138 t_step = TSAMPLE; |
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139 else |
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140 ## ---- continuous system |
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141 if (nargin == 5) |
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142 n = round(n); |
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143 if (n < 2) |
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144 error("step: n must not be less than 2.") |
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145 endif |
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146 t_step = tstop / (n - 1); |
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147 else |
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148 if (nargin == 4) |
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149 ## only n in unknown |
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150 if (USE_DEF) |
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151 n = N_MIN; |
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152 t_step = tstop / (n - 1); |
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153 else |
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154 n = floor(tstop / t_step) + 1; |
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155 endif |
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156 else |
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157 ## tstop and n are unknown |
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158 if (USE_DEF) |
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159 tstop = T_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 tstop = t_sim; |
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164 n = floor(tstop / t_step) + 1; |
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165 endif |
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166 endif |
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167 if (n < N_MIN) |
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168 n = N_MIN; |
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169 t_step = tstop / (n - 1); |
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170 endif |
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171 if (n > N_MAX) |
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172 tstop = (n - 1) * t_step; |
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173 t_step = tstop / (N_MAX - 1); |
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174 n = N_MAX; |
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175 endif |
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176 endif |
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177 tstop = (n - 1) * t_step; |
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178 [jnk,B] = sys2ss(sys); |
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179 B = B(:,inp); |
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180 sys = c2d(sys, t_step); |
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181 endif |
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182 ## printf("##STEPIMP-DEBUG: t_step=%f n=%d tstop=%f\n", t_step, n, tstop); |
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183 |
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184 F = sys.a; |
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185 G = sys.b(:,inp); |
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186 C = sys.c; |
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187 D = sys.d(:,inp); |
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188 y = zeros(NOUT, n); |
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189 t = linspace(0, tstop, n); |
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190 |
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191 if (IMPULSE) |
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192 if (!DIGITAL && (D'*D > 0)) |
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193 error("impulse: D matrix is nonzero, impulse response infinite.") |
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194 endif |
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195 if (DIGITAL) |
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196 y(:,1) = D / t_step; |
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197 x = G / t_step; |
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198 else |
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199 x = B; |
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200 y(:,1) = C * x; |
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201 x = F * x; |
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202 endif |
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203 for i = 2:n |
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204 y(:,i) = C * x; |
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205 x = F * x; |
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206 endfor |
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207 if (DIGITAL) |
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208 y *= t_step; |
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209 endif |
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210 else |
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211 x = zeros(NSTATES, 1); |
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212 for i = 1:n |
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213 y(:,i) = C * x + D; |
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214 x = F * x + G; |
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215 endfor |
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216 endif |
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217 |
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218 save_automatic_replot = automatic_replot; |
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219 unwind_protect |
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220 automatic_replot = 0; |
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221 if(nargout == 0) |
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222 ## Plot the information |
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223 oneplot(); |
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224 __gnuplot_set__ nogrid |
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225 __gnuplot_set__ nologscale |
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226 __gnuplot_set__ autoscale |
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227 __gnuplot_set__ nokey |
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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 if (ncols > 1 || nrows > 1) |
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239 clearplot(); |
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240 endif |
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241 for i = 1:NOUT |
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242 subplot(nrows, ncols, i); |
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243 title(sprintf("%s: | %s -> %s", tt,sysgetsignals(sys,"in",inp,1), ... |
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244 sysgetsignals(sys,"out",i,1))); |
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245 if (DIGITAL) |
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246 [ts, ys] = stairs(t, y(i,:)); |
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247 ts = ts(1:2*n-2)'; ys = ys(1:2*n-2)'; |
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248 if (length(gm) > 0) |
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249 yy = [ys; gm(i)*ones(size(ts))]; |
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250 else |
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251 yy = ys; |
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252 endif |
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253 grid("on"); |
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254 xlabel("time [s]"); |
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255 ylabel("y(t)"); |
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256 plot(ts, yy); |
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257 else |
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258 if (length(gm) > 0) |
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259 yy = [y(i,:); gm(i)*ones(size(t))]; |
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260 else |
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261 yy = y(i,:); |
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262 endif |
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263 grid("on"); |
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264 xlabel("time [s]"); |
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265 ylabel("y(t)"); |
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266 plot(t, yy); |
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267 endif |
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268 endfor |
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269 ## leave gnuplot in multiplot mode is bad style |
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270 oneplot(); |
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271 y=[]; |
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272 t=[]; |
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273 endif |
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274 ## printf("##STEPIMP-DEBUG: gratulations, successfull completion.\n"); |
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275 unwind_protect_cleanup |
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276 automatic_replot = save_automatic_replot; |
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277 end_unwind_protect |
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278 endfunction |
