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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, 59 Temple Place, Suite 330, Boston, MA 02111 USA. |
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18 |
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19 ## -*- texinfo -*- |
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20 ## @deftypefn {Function File} {[@var{y}, @var{t}] =} __stepimp__ (@var{sitype}, @var{sys} [, @var{inp}, @var{tstop}, @var{n}]) |
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21 ## Impulse or step response for a linear system. |
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22 ## The system can be discrete or multivariable (or both). |
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23 ## This m-file contains the "common code" of step and impulse. |
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24 ## |
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25 ## Produces a plot or the response data for system sys. |
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26 ## |
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27 ## Limited argument checking; "do not attempt to do this at home". |
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28 ## Used internally in @code{impulse}, @code{step}. Use @code{step} |
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29 ## or @code{impulse} instead. |
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30 ## @end deftypefn |
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31 ## @seealso{step and impulse} |
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32 |
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33 ## Author: Kai P. Mueller <mueller@ifr.ing.tu-bs.de> |
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34 ## Created: October 2, 1997 |
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35 ## based on lsim.m of Scottedward Hodel |
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36 |
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37 function [y, t] = __stepimp__ (sitype, sys, inp, tstop, n) |
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38 |
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39 if (sitype == 1) IMPULSE = 0; |
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40 elseif (sitype == 2) IMPULSE = 1; |
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41 else error("__stepimp__: invalid sitype argument.") |
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42 endif |
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43 sys = sysupdate(sys,"ss"); |
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44 |
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45 USE_DEF = 0; # default tstop and n if we have to give up |
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46 N_MIN = 50; # minimum number of points |
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47 N_MAX = 2000; # maximum number of points |
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48 T_DEF = 10.0; # default simulation time |
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49 |
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50 ## collect useful information about the system |
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51 [ncstates,ndstates,NIN,NOUT] = sysdimensions(sys); |
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52 TSAMPLE = sysgettsam(sys); |
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53 |
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54 if (nargin < 3) inp = 1; |
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55 elseif (inp < 1 | inp > NIN) error("Argument inp out of range") |
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56 endif |
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57 |
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58 DIGITAL = is_digital(sys); |
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59 if (DIGITAL) |
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60 NSTATES = ndstates; |
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61 if (TSAMPLE < eps) |
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62 error("__stepimp__: sampling time of discrete system too small.") |
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63 endif |
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64 else NSTATES = ncstates; endif |
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65 if (NSTATES < 1) |
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66 error("step: pure gain block (n_states < 1), step response is trivial"); |
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67 endif |
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68 if (nargin < 5) |
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69 ## we have to compute the time when the system reaches steady state |
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70 ## and the step size |
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71 ev = eig(sys2ss(sys)); |
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72 if (DIGITAL) |
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73 ## perform bilinear transformation on poles in z |
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74 for i = 1:NSTATES |
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75 pole = ev(i); |
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76 if (abs(pole + 1) < 1.0e-10) |
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77 ev(i) = 0; |
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78 else |
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79 ev(i) = 2 / TSAMPLE * (pole - 1) / (pole + 1); |
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80 endif |
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81 endfor |
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82 endif |
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83 ## remove poles near zero from eigenvalue array ev |
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84 nk = NSTATES; |
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85 for i = 1:NSTATES |
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86 if (abs(real(ev(i))) < 1.0e-10) |
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87 ev(i) = 0; |
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88 nk = nk - 1; |
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89 endif |
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90 endfor |
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91 if (nk == 0) |
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92 USE_DEF = 1; |
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93 ## printf("##STEPIMP-DEBUG: using defaults.\n"); |
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94 else |
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95 ev = ev(find(ev)); |
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96 x = max(abs(ev)); |
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97 t_step = 0.2 * pi / x; |
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98 x = min(abs(real(ev))); |
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99 t_sim = 5.0 / x; |
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100 ## round up |
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101 yy = 10^(ceil(log10(t_sim)) - 1); |
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102 t_sim = yy * ceil(t_sim / yy); |
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103 ## printf("##STEPIMP-DEBUG: nk=%d t_step=%f t_sim=%f\n", |
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104 ## nk, t_step, t_sim); |
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105 endif |
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106 endif |
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107 |
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108 if (DIGITAL) |
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109 ## ---- sampled system |
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110 if (nargin == 5) |
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111 n = round(n); |
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112 if (n < 2) |
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113 error("__stepimp__: n must not be less than 2.") |
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114 endif |
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115 else |
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116 if (nargin == 4) |
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117 ## n is unknown |
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118 elseif (nargin >= 1) |
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119 ## tstop and n are unknown |
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120 if (USE_DEF) |
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121 tstop = (N_MIN - 1) * TSAMPLE; |
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122 else |
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123 tstop = t_sim; |
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124 endif |
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125 endif |
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126 n = floor(tstop / TSAMPLE) + 1; |
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127 if (n < 2) n = 2; endif |
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128 if (n > N_MAX) |
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129 n = N_MAX; |
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130 printf("Hint: number of samples limited to %d by default.\n", \ |
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131 N_MAX); |
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132 printf(" ==> increase \"n\" parameter for longer simulations.\n"); |
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133 endif |
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134 endif |
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135 tstop = (n - 1) * TSAMPLE; |
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136 t_step = TSAMPLE; |
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137 else |
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138 ## ---- continuous system |
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139 if (nargin == 5) |
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140 n = round(n); |
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141 if (n < 2) |
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142 error("step: n must not be less than 2.") |
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143 endif |
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144 t_step = tstop / (n - 1); |
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145 else |
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146 if (nargin == 4) |
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147 ## only n in unknown |
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148 if (USE_DEF) |
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149 n = N_MIN; |
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150 t_step = tstop / (n - 1); |
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151 else |
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152 n = floor(tstop / t_step) + 1; |
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153 endif |
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154 else |
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155 ## tstop and n are unknown |
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156 if (USE_DEF) |
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157 tstop = T_DEF; |
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158 n = N_MIN; |
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159 t_step = tstop / (n - 1); |
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160 else |
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161 tstop = t_sim; |
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162 n = floor(tstop / t_step) + 1; |
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163 endif |
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164 endif |
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165 if (n < N_MIN) |
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166 n = N_MIN; |
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167 t_step = tstop / (n - 1); |
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168 endif |
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169 if (n > N_MAX) |
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170 tstop = (n - 1) * t_step; |
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171 t_step = tstop / (N_MAX - 1); |
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172 n = N_MAX; |
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173 endif |
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174 endif |
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175 tstop = (n - 1) * t_step; |
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176 [jnk,B] = sys2ss(sys); |
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177 B = B(:,inp); |
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178 sys = c2d(sys, t_step); |
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179 endif |
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180 ## printf("##STEPIMP-DEBUG: t_step=%f n=%d tstop=%f\n", t_step, n, tstop); |
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181 |
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182 F = sys.a; |
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183 G = sys.b(:,inp); |
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184 C = sys.c; |
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185 D = sys.d(:,inp); |
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186 y = zeros(NOUT, n); |
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187 t = linspace(0, tstop, n); |
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188 |
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189 if (IMPULSE) |
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190 if (!DIGITAL && (D'*D > 0)) |
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191 error("impulse: D matrix is nonzero, impulse response infinite.") |
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192 endif |
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193 if (DIGITAL) |
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194 y(:,1) = D / t_step; |
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195 x = G / t_step; |
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196 else |
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197 x = B; |
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198 y(:,1) = C * x; |
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199 x = F * x; |
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200 endif |
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201 for i = 2:n |
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202 y(:,i) = C * x; |
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203 x = F * x; |
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204 endfor |
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205 if (DIGITAL) |
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206 y *= t_step; |
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207 endif |
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208 else |
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209 x = zeros(NSTATES, 1); |
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210 for i = 1:n |
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211 y(:,i) = C * x + D; |
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212 x = F * x + G; |
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213 endfor |
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214 endif |
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215 |
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216 save_automatic_replot = automatic_replot; |
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217 unwind_protect |
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218 automatic_replot = 0; |
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219 if(nargout == 0) |
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220 ## Plot the information |
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221 oneplot(); |
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222 gset nogrid |
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223 gset nologscale |
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224 gset autoscale |
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225 gset nokey |
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226 if (IMPULSE) |
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227 gm = zeros(NOUT, 1); |
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228 tt = "impulse"; |
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229 else |
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230 ssys = ss(F, G, C, D, t_step); |
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231 gm = dcgain(ssys); |
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232 tt = "step"; |
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233 endif |
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234 ncols = floor(sqrt(NOUT)); |
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235 nrows = ceil(NOUT / ncols); |
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236 if (ncols > 1 || nrows > 1) |
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237 clearplot(); |
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238 endif |
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239 for i = 1:NOUT |
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240 subplot(nrows, ncols, i); |
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241 title(sprintf("%s: | %s -> %s", tt,sysgetsignals(sys,"in",inp,1), ... |
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242 sysgetsignals(sys,"out",i,1))); |
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243 if (DIGITAL) |
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244 [ts, ys] = stairs(t, y(i,:)); |
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245 ts = ts(1:2*n-2)'; ys = ys(1:2*n-2)'; |
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246 if (length(gm) > 0) |
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247 yy = [ys; gm(i)*ones(size(ts))]; |
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248 else |
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249 yy = ys; |
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250 endif |
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251 grid("on"); |
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252 xlabel("time [s]"); |
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253 ylabel("y(t)"); |
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254 plot(ts, yy); |
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255 else |
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256 if (length(gm) > 0) |
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257 yy = [y(i,:); gm(i)*ones(size(t))]; |
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258 else |
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259 yy = y(i,:); |
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260 endif |
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261 grid("on"); |
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262 xlabel("time [s]"); |
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263 ylabel("y(t)"); |
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264 plot(t, yy); |
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265 endif |
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266 endfor |
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267 ## leave gnuplot in multiplot mode is bad style |
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268 oneplot(); |
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269 y=[]; |
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270 t=[]; |
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271 endif |
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272 ## printf("##STEPIMP-DEBUG: gratulations, successfull completion.\n"); |
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273 unwind_protect_cleanup |
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274 automatic_replot = save_automatic_replot; |
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275 end_unwind_protect |
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276 endfunction |
