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1 # Copyright (C) 1996,1998 A. Scottedward Hodel |
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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, 675 Mass Ave, Cambridge, MA 02139, USA. |
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18 |
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19 function [y, t] = stepimp(sitype, sys, inp, tstop, n) |
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20 # step: Impulse or step response for a linear system. |
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21 # The system can be discrete or multivariable (or both). |
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22 # This m-file contains the "common code" of step and impulse. |
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23 # |
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24 # [y, t] = stepimp(sitype, sys[, inp, tstop, n]) |
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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 # Use step or impulse instead. |
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29 # |
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30 # See also: step, impulse |
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31 |
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32 # Written by Kai P. Mueller October 2, 1997 |
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33 # based on lsim.m of Scottedward Hodel |
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34 # $Revision: 2.0.0.0 $ |
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35 |
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36 if (sitype == 1) IMPULSE = 0; |
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37 elseif (sitype == 2) IMPULSE = 1; |
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38 else error("stepimp: illegal sitype argument.") |
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39 endif |
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40 sys = sysupdate(sys,"ss"); |
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41 |
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42 USE_DEF = 0; # default tstop and n if we have to give up |
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43 N_MIN = 50; # minimum number of points |
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44 N_MAX = 2000; # maximum number of points |
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45 T_DEF = 10.0; # default simulation time |
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46 |
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47 # collect useful information about the system |
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48 [ncstates,ndstates,NIN,NOUT] = sysdimensions(sys); |
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49 TSAMPLE = sysgettsam(sys); |
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50 |
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51 if (nargin < 3) inp = 1; |
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52 elseif (inp < 1 | inp > NIN) error("Argument inp out of range") |
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53 endif |
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54 |
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55 DIGITAL = is_digital(sys); |
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56 if (DIGITAL) |
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57 NSTATES = ndstates; |
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58 if (TSAMPLE < eps) |
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59 error("stepimp: sampling time of discrete system too small.") |
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60 endif |
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61 else NSTATES = ncstates; endif |
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62 if (NSTATES < 1) |
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63 error("step: pure gain block (n_states < 1), step response is trivial"); |
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64 endif |
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65 if (nargin < 5) |
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66 # we have to compute the time when the system reaches steady state |
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67 # and the step size |
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68 ev = eig(sys2ss(sys)); |
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69 if (DIGITAL) |
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70 # perform bilinear transformation on poles in z |
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71 for i = 1:NSTATES |
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72 pole = ev(i); |
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73 if (abs(pole + 1) < 1.0e-10) |
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74 ev(i) = 0; |
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75 else |
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76 ev(i) = 2 / TSAMPLE * (pole - 1) / (pole + 1); |
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77 endif |
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78 endfor |
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79 endif |
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80 # remove poles near zero from eigenvalue array ev |
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81 nk = NSTATES; |
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82 for i = 1:NSTATES |
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83 if (abs(ev(i)) < 1.0e-10) |
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84 ev(i) = 0; |
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85 nk = nk - 1; |
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86 endif |
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87 endfor |
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88 if (nk == 0) |
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89 USE_DEF = 1; |
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90 #printf("##STEPIMP-DEBUG: using defaults.\n"); |
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91 else |
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92 ev = ev(find(ev)); |
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93 x = max(abs(ev)); |
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94 t_step = 0.2 * pi / x; |
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95 x = min(abs(real(ev))); |
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96 t_sim = 5.0 / x; |
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97 # round up |
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98 yy = 10^(ceil(log10(t_sim)) - 1); |
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99 t_sim = yy * ceil(t_sim / yy); |
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100 #printf("##STEPIMP-DEBUG: nk=%d t_step=%f t_sim=%f\n", |
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101 # nk, t_step, t_sim); |
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102 endif |
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103 endif |
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104 |
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105 if (DIGITAL) |
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106 # ---- sampled system |
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107 if (nargin == 5) |
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108 n = round(n); |
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109 if (n < 2) |
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110 error("stepimp: n must not be less than 2.") |
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111 endif |
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112 else |
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113 if (nargin == 4) |
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114 # n is unknown |
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115 elseif (nargin >= 1) |
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116 # tstop and n are unknown |
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117 if (USE_DEF) |
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118 tstop = (N_MIN - 1) * TSAMPLE; |
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119 else |
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120 tstop = t_sim; |
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121 endif |
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122 endif |
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123 n = floor(tstop / TSAMPLE) + 1; |
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124 if (n < 2) n = 2; endif |
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125 if (n > N_MAX) |
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126 n = N_MAX; |
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127 printf("Hint: number of samples limited to %d by default.\n", \ |
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128 N_MAX); |
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129 printf(" ==> increase \"n\" parameter for longer simulations.\n"); |
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130 endif |
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131 endif |
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132 tstop = (n - 1) * TSAMPLE; |
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133 t_step = TSAMPLE; |
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134 else |
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135 # ---- continuous system |
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136 if (nargin == 5) |
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137 n = round(n); |
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138 if (n < 2) |
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139 error("step: n must not be less than 2.") |
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140 endif |
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141 t_step = tstop / (n - 1); |
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142 else |
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143 if (nargin == 4) |
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144 # only n in unknown |
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145 if (USE_DEF) |
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146 n = N_MIN; |
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147 t_step = tstop / (n - 1); |
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148 else |
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149 n = floor(tstop / t_step) + 1; |
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150 endif |
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151 else |
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152 # tstop and n are unknown |
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153 if (USE_DEF) |
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154 tstop = T_DEF; |
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155 n = N_MIN; |
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156 t_step = tstop / (n - 1); |
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157 else |
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158 tstop = t_sim; |
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159 n = floor(tstop / t_step) + 1; |
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160 endif |
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161 endif |
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162 if (n < N_MIN) |
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163 n = N_MIN; |
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164 t_step = tstop / (n - 1); |
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165 endif |
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166 if (n > N_MAX) |
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167 tstop = (n - 1) * t_step; |
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168 t_step = tstop / (N_MAX - 1); |
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169 n = N_MAX; |
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170 endif |
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171 endif |
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172 tstop = (n - 1) * t_step; |
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173 [jnk,B] = sys2ss(sys); |
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174 B = B(:,inp); |
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175 sys = c2d(sys, t_step); |
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176 endif |
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177 #printf("##STEPIMP-DEBUG: t_step=%f n=%d tstop=%f\n", t_step, n, tstop); |
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178 |
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179 F = sys.a; |
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180 G = sys.b(:,inp); |
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181 C = sys.c; |
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182 D = sys.d(:,inp); |
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183 y = zeros(NOUT, n); |
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184 t = linspace(0, tstop, n); |
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185 |
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186 if (IMPULSE) |
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187 if (!DIGITAL && (D'*D > 0)) |
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188 error("impulse: D matrix is nonzero, impulse response infinite.") |
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189 endif |
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190 if (DIGITAL) |
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191 y(:,1) = D; |
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192 x = G / t_step; |
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193 else |
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194 x = B; |
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195 y(:,1) = C * x; |
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196 x = F * x; |
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197 endif |
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198 for i = 2:n |
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199 y(:,i) = C * x; |
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200 x = F * x; |
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201 endfor |
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202 else |
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203 x = zeros(NSTATES, 1); |
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204 for i = 1:n |
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205 y(:,i) = C * x + D; |
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206 x = F * x + G; |
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207 endfor |
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208 endif |
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209 |
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210 if(nargout == 0) |
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211 # Plot the information |
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212 oneplot(); |
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213 gset nogrid |
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214 gset nologscale |
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215 gset autoscale |
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216 gset nokey |
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217 clearplot(); |
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218 if (gnuplot_has_multiplot) |
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219 if (IMPULSE) |
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220 gm = zeros(NOUT, 1); |
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221 tt = "impulse"; |
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222 else |
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223 ssys = ss2sys(F, G, C, D, t_step); |
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224 gm = dcgain(ssys); |
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225 tt = "step"; |
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226 endif |
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227 ncols = floor(sqrt(NOUT)); |
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228 nrows = ceil(NOUT / ncols); |
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229 for i = 1:NOUT |
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230 subplot(nrows, ncols, i); |
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231 title(sprintf("%s: | %s -> %s", tt,sysgetsignals(sys,"in",inp,1), ... |
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232 sysgetsignals(sys,"out",i,1))); |
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233 if (DIGITAL) |
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234 [ts, ys] = stairs(t, y(i,:)); |
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235 ts = ts(1:2*n-2)'; ys = ys(1:2*n-2)'; |
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236 if (length(gm) > 0) |
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237 yy = [ys; gm(i)*ones(size(ts))]; |
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238 else |
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239 yy = ys; |
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240 endif |
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241 grid("on"); |
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242 xlabel("time [s]"); |
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243 ylabel("y(t)"); |
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244 plot(ts, yy); |
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245 else |
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246 if (length(gm) > 0) |
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247 yy = [y(i,:); gm(i)*ones(size(t))]; |
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248 else |
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249 yy = y(i,:); |
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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(t, yy); |
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255 endif |
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256 endfor |
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257 # leave gnuplot in multiplot mode is bad style |
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258 oneplot(); |
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259 else |
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260 # plot everything in one diagram |
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261 title([tt, " response | ", sysgetsignals(sys,"in",inp,1), ... |
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262 " -> all outputs"]); |
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263 if (DIGITAL) |
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264 stairs(t, y(i,:)); |
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265 else |
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266 grid("on"); |
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267 xlabel("time [s]"); |
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268 ylabel("y(t)"); |
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269 plot(t, y(i,:)); |
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270 endif |
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271 endif |
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272 y=[]; |
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273 t=[]; |
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274 endif |
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275 #printf("##STEPIMP-DEBUG: gratulations, successfull completion.\n"); |
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276 endfunction |
