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