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1 @c Copyright (C) 1996, 1997 John W. Eaton |
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2 @c This is part of the Octave manual. |
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3 @c For copying conditions, see the file gpl.texi. |
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4 |
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5 @node Control Theory, Signal Processing, Polynomial Manipulations, Top |
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6 @chapter Control Theory |
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7 |
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8 The Octave Control Systems Toolbox (OCST) was initially developed |
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9 by Dr.@: A. Scottedward Hodel |
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10 @email{a.s.hodel@@eng.auburn.edu} with the assistance |
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11 of his students |
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12 @itemize @bullet |
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13 @item R. Bruce Tenison @email{btenison@@dibbs.net}, |
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14 @item David C. Clem, |
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15 @item John E. Ingram @email{John.Ingram@@sea.siemans.com}, and |
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16 @item Kristi McGowan. |
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17 @end itemize |
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18 This development was supported in part by NASA's Marshall Space Flight |
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19 Center as part of an in-house CACSD environment. Additional important |
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20 contributions were made by Dr. Kai Mueller @email{mueller@@ifr.ing.tu-bs.de} |
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21 and Jose Daniel Munoz Frias (@code{place.m}). |
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22 |
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23 An on-line menu-driven tutorial is available via @code{DEMOcontrol}; |
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24 beginning OCST users should start with this program. |
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25 |
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26 @DOCSTRING(DEMOcontrol) |
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27 |
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28 @menu |
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29 * sysstruct:: |
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30 * sysinterface:: |
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31 * sysdisp:: |
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32 * blockdiag:: |
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33 * numerical:: |
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34 * sysprop:: |
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35 * systime:: |
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36 * sysfreq:: |
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37 * cacsd:: |
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38 * misc:: |
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39 @end menu |
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40 |
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41 @node sysstruct, sysinterface, Control Theory, Control Theory |
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42 @section System Data Structure |
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43 |
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44 @menu |
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45 * sysstructvars:: |
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46 * sysstructtf:: |
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47 * sysstructzp:: |
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48 * sysstructss:: |
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49 @end menu |
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50 |
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51 The OCST stores all dynamic systems in |
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52 a single data structure format that can represent continuous systems, |
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53 discrete-systems, and mixed (hybrid) systems in state-space form, and |
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54 can also represent purely continuous/discrete systems in either |
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55 transfer function or pole-zero form. In order to |
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56 provide more flexibility in treatment of discrete/hybrid systems, the |
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57 OCST also keeps a record of which system outputs are sampled. |
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58 |
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59 Octave structures are accessed with a syntax much like that used |
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60 by the C programming language. For consistency in |
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61 use of the data structure used in the OCST, it is recommended that |
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62 the system structure access m-files be used (@xref{sysinterface}). |
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63 Some elements of the data structure are absent depending on the internal |
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64 system representation(s) used. More than one system representation |
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65 can be used for SISO systems; the OCST m-files ensure that all representations |
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66 used are consistent with one another. |
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67 |
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68 @DOCSTRING(sysrepdemo) |
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69 |
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70 @node sysstructvars, sysstructtf, sysstruct, sysstruct |
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71 @subsection Variables common to all OCST system formats |
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72 |
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73 The data structure elements (and variable types) common to all system |
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74 representations are listed below; examples of the initialization |
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75 and use of the system data structures are given in subsequent sections and |
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76 in the online demo @code{DEMOcontrol}. |
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77 @table @var |
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78 @item n,nz |
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79 The respective number of continuous and discrete states |
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80 in the system (scalar) |
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81 |
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82 @item inname, outname |
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83 list of name(s) of the system input, output signal(s). (list of strings) |
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84 |
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85 @item sys |
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86 System status vector. (vector) |
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87 |
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88 This vector indicates both what representation was used to initialize |
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89 the system data structure (called the primary system type) and which |
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90 other representations are currently up-to-date with the primary system |
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91 type (@xref{structaccess}). |
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92 |
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93 @table @var |
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94 |
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95 @item sys(0) |
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96 primary system type |
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97 |
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98 =0 for tf form (initialized with @code{tf2sys} or @code{fir2sys}) |
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99 |
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100 =1 for zp form (initialized with @code{zp2sys}) |
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101 |
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102 =2 for ss form (initialized with @code{ss2sys}) |
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103 |
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104 @item sys(1:3) |
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105 boolean flags to indicate whether tf, zp, or ss, respectively, |
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106 are ``up to date" (whether it is safe to use the variables |
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107 associated with these representations). |
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108 These flags are changed when calls are made to the @code{sysupdate} command. |
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109 @end table |
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110 |
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111 @item tsam |
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112 Discrete time sampling period (nonnegative scalar). |
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113 @var{tsam} is set to 0 for continuous time systems. |
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114 |
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115 @item yd |
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116 Discrete-time output list (vector) |
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117 |
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118 indicates which outputs are discrete time (i.e., |
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119 produced by D/A converters) and which are continuous time. |
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120 yd(ii) = 0 if output ii is continuous, = 1 if discrete. |
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121 @end table |
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122 |
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123 The remaining variables of the system data structure are only present |
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124 if the corresponding entry of the @code{sys} vector is true (=1). |
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125 |
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126 @node sysstructtf, sysstructzp, sysstructvars, sysstruct |
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127 @subsection @code{tf} format variables |
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128 |
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129 @table @var |
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130 |
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131 @item num |
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132 numerator coefficients (vector) |
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133 |
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134 @item den |
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135 denominator coefficients (vector) |
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136 |
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137 @end table |
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138 |
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139 @node sysstructzp, sysstructss, sysstructtf, sysstruct |
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140 @subsection @code{zp} format variables |
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141 |
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142 @table @var |
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143 @item zer |
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144 system zeros (vector) |
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145 |
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146 @item pol |
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147 system poles (vector) |
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148 |
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149 @item k |
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150 leading coefficient (scalar) |
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151 |
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152 @end table |
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153 |
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154 @node sysstructss, , sysstructzp, sysstruct |
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155 @subsection @code{ss} format variables |
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156 |
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157 @table @var |
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158 @item a,b,c,d |
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159 The usual state-space matrices. If a system has both |
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160 continuous and discrete states, they are sorted so that |
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161 continuous states come first, then discrete states |
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162 |
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163 @strong{Note} some functions (e.g., @code{bode}, @code{hinfsyn}) |
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164 will not accept systems with both discrete and continuous states/outputs |
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165 |
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166 @item stname |
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167 names of system states (list of strings) |
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168 |
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169 @end table |
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170 |
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171 @node sysinterface, sysdisp, sysstruct, Control Theory |
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172 @section System Construction and Interface Functions |
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173 |
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174 Construction and manipulations of the OCST system data structure |
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175 (@xref{sysstruct}) requires attention to many details in order |
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176 to ensure that data structure contents remain consistent. Users |
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177 are strongly encouraged to use the system interface functions |
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178 in this section. Functions for the formatted display in of system |
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179 data structures are given in @ref{sysdisp}. |
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180 |
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181 @menu |
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182 * fir2sys:: |
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183 * ss2sys:: |
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184 * tf2sys:: |
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185 * zp2sys:: |
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186 * structaccess:: |
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187 * structintern:: |
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188 @end menu |
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189 |
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190 @node fir2sys, ss2sys, sysinterface, sysinterface |
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191 @subsection Finite impulse response system interface functions |
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192 |
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193 @DOCSTRING(fir2sys) |
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194 |
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195 @DOCSTRING(sys2fir) |
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196 |
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197 @node ss2sys, tf2sys, fir2sys, sysinterface |
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198 @subsection State space system interface functions |
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199 |
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200 @DOCSTRING(ss2sys) |
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201 |
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202 @DOCSTRING(sys2ss) |
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203 |
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204 @node tf2sys, zp2sys, ss2sys, sysinterface |
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205 @subsection Transfer function system interface functions |
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206 |
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207 @DOCSTRING(tf2sys) |
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208 |
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209 @DOCSTRING(sys2tf) |
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210 |
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211 @node zp2sys, structaccess, tf2sys, sysinterface |
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212 @subsection Zero-pole system interface functions |
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213 |
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214 @DOCSTRING(zp2sys) |
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215 |
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216 @DOCSTRING(sys2zp) |
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217 |
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218 @node structaccess, structintern, zp2sys, sysinterface |
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219 @subsection Data structure access functions |
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220 |
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221 @DOCSTRING(syschnames) |
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222 |
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223 @DOCSTRING(syschtsam) |
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224 |
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225 @DOCSTRING(sysdimensions) |
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226 |
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227 @DOCSTRING(sysgetsignals) |
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228 |
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229 @DOCSTRING(sysgettype) |
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230 |
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231 @DOCSTRING(syssetsignals) |
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232 |
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233 @DOCSTRING(sysupdate) |
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234 |
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235 @node structintern, , structaccess, sysinterface |
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236 @subsection Data structure internal functions |
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237 |
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238 @DOCSTRING(syschnamesl) |
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239 |
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240 @DOCSTRING(sysdefioname) |
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241 |
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242 @DOCSTRING(sysdefstname) |
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243 |
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244 @DOCSTRING(tf2sysl) |
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245 |
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246 @node sysdisp, blockdiag, sysinterface, Control Theory |
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247 @section System display functions |
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248 |
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249 @DOCSTRING(sysout) |
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250 |
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251 @DOCSTRING(polyout) |
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252 |
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253 @DOCSTRING(tfout) |
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254 |
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255 @DOCSTRING(zpout) |
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256 |
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257 @DOCSTRING(outlist) |
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258 |
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259 @node blockdiag, numerical, sysdisp, Control Theory |
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260 @section Block Diagram Manipulations |
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261 |
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262 @xref{systime} |
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263 |
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264 Unless otherwise noted, all parameters (input,output) are |
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265 system data structures. |
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266 |
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267 @DOCSTRING(bddemo) |
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268 |
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269 @DOCSTRING(buildssic) |
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270 |
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271 @DOCSTRING(jet707) |
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272 |
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273 @DOCSTRING(ord2) |
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274 |
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275 @DOCSTRING(sysadd) |
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276 |
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277 @DOCSTRING(sysappend) |
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278 |
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279 @DOCSTRING(sysconnect) |
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280 |
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281 @DOCSTRING(syscont) |
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282 |
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283 @DOCSTRING(syscont_disc) |
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284 |
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285 @DOCSTRING(sysdisc) |
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286 |
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287 @DOCSTRING(sysdup) |
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288 |
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289 @DOCSTRING(sysgroup) |
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290 |
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291 @DOCSTRING(sysgroupn) |
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292 |
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293 @DOCSTRING(sysmult) |
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294 |
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295 @DOCSTRING(sysprune) |
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296 |
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297 @DOCSTRING(sysreorder) |
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298 |
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299 @DOCSTRING(sysscale) |
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300 |
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301 @DOCSTRING(syssub) |
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302 |
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303 @DOCSTRING(ugain) |
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304 |
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305 @DOCSTRING(wgt1o) |
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306 |
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307 @node numerical, sysprop, blockdiag, Control Theory |
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308 @section Numerical Functions |
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309 |
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310 @DOCSTRING(are) |
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311 |
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312 @DOCSTRING(dare) |
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313 |
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314 @DOCSTRING(dgram) |
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315 |
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316 @DOCSTRING(dlyap) |
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317 |
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318 @DOCSTRING(gram) |
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319 |
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320 @DOCSTRING(lyap) |
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321 |
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322 @DOCSTRING(pinv) |
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323 |
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324 @DOCSTRING(qzval) |
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325 |
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326 @DOCSTRING(zgfmul) |
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327 |
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328 @DOCSTRING(zgfslv) |
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329 |
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330 @DOCSTRING(zginit) |
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331 |
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332 @DOCSTRING(zgpbal) |
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333 |
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334 @DOCSTRING(zgreduce) |
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335 |
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336 @DOCSTRING(zgrownorm) |
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337 |
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338 @DOCSTRING(zgscal) |
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339 |
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340 @DOCSTRING(zgsgiv) |
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341 |
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342 @DOCSTRING(zgshsr) |
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343 |
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344 References: |
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345 @table @strong |
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346 @item ZGEP |
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347 Hodel, "Computation of Zeros with Balancing," 1992, Linear Algebra |
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348 and its Applications |
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349 @item @strong{Generalized CG} |
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350 Golub and Van Loan, "Matrix Computations, 2nd ed" 1989 |
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351 @end table |
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352 |
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353 @node sysprop, systime, numerical, Control Theory |
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354 @section System Analysis-Properties |
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355 |
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356 @DOCSTRING(analdemo) |
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357 |
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358 @DOCSTRING(abcddim) |
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359 |
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360 @DOCSTRING(abcddims) |
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361 |
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362 @DOCSTRING(ctrb) |
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363 |
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364 @DOCSTRING(h2norm) |
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365 |
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366 @DOCSTRING(hinfnorm) |
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367 |
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368 @DOCSTRING(obsv) |
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369 |
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370 @DOCSTRING(pzmap) |
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371 |
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372 @DOCSTRING(is_abcd) |
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373 |
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374 @DOCSTRING(is_controllable) |
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375 |
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376 @DOCSTRING(is_detectable) |
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377 |
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378 @DOCSTRING(is_dgkf) |
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379 |
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380 @DOCSTRING(is_digital) |
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381 |
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382 @DOCSTRING(is_observable) |
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383 |
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384 @DOCSTRING(is_sample) |
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385 |
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386 @DOCSTRING(is_siso) |
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387 |
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388 @DOCSTRING(is_stabilizable) |
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389 |
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390 @DOCSTRING(is_signal_list) |
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391 |
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392 @DOCSTRING(is_stable) |
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393 |
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394 @node systime, sysfreq, sysprop, Control Theory |
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395 @section System Analysis-Time Domain |
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396 |
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397 @DOCSTRING(c2d) |
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398 |
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399 @DOCSTRING(d2c) |
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400 |
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401 @DOCSTRING(dmr2d) |
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402 |
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403 @DOCSTRING(damp) |
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404 |
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405 @DOCSTRING(dcgain) |
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406 |
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407 @DOCSTRING(impulse) |
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408 |
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409 @DOCSTRING(step) |
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410 |
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411 @DOCSTRING(stepimp) |
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412 |
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413 @node sysfreq, cacsd, systime, Control Theory |
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414 @section System Analysis-Frequency Domain |
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415 |
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416 @strong{Demonstration/tutorial script} |
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417 @DOCSTRING(frdemo) |
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418 |
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419 @DOCSTRING(bode) |
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420 |
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421 @DOCSTRING(bode_bounds) |
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422 |
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423 @DOCSTRING(bodquist) |
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424 |
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425 @DOCSTRING(freqchkw) |
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426 |
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427 @DOCSTRING(freqresp) |
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428 |
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429 @DOCSTRING(ltifr) |
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430 |
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431 @DOCSTRING(nyquist) |
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432 |
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433 @DOCSTRING(tzero) |
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434 |
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435 @DOCSTRING(tzero2) |
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436 |
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437 @node cacsd, misc, sysfreq, Control Theory |
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438 @section Controller Design |
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439 |
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440 @DOCSTRING(dgkfdemo) |
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441 |
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442 @DOCSTRING(hinfdemo) |
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443 |
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444 @DOCSTRING(dlqe) |
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445 |
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446 @DOCSTRING(dlqr) |
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447 |
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448 @DOCSTRING(h2syn) |
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449 |
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450 @DOCSTRING(hinf_ctr) |
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451 |
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452 @DOCSTRING(hinfsyn) |
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453 |
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454 @DOCSTRING(hinfsyn_chk) |
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455 |
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456 @DOCSTRING(lqe) |
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457 |
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|
458 @DOCSTRING(lqg) |
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|
459 |
|
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|
460 @DOCSTRING(lqr) |
|
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|
461 |
|
3346
|
462 @DOCSTRING(lsim) |
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|
463 |
|
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|
464 @DOCSTRING(place) |
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|
465 |
|
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|
466 @node misc, , cacsd, Control Theory |
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|
467 @section Miscellaneous Functions (Not yet properly filed/documented) |
|
|
468 |
|
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|
469 @DOCSTRING(axis2dlim) |
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|
470 |
|
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|
471 @DOCSTRING(moddemo) |
|
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|
472 |
|
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|
473 @DOCSTRING(prompt) |
|
3294
|
474 |
|
3346
|
475 @DOCSTRING(rldemo) |
|
3294
|
476 |
|
3346
|
477 @DOCSTRING(rlocus) |
|
3294
|
478 |
|
3346
|
479 @DOCSTRING(sortcom) |
|
3294
|
480 |
|
3346
|
481 @DOCSTRING(ss2tf) |
|
3294
|
482 |
|
3346
|
483 @DOCSTRING(ss2zp) |
|
3294
|
484 |
|
3346
|
485 @DOCSTRING(starp) |
|
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|
486 |
|
3346
|
487 @DOCSTRING(susball) |
|
3294
|
488 |
|
3346
|
489 @DOCSTRING(tf2ss) |
|
3294
|
490 |
|
3346
|
491 @DOCSTRING(tf2zp) |
|
3294
|
492 |
|
3346
|
493 @DOCSTRING(zp2ss) |
|
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|
494 |
|
3346
|
495 @DOCSTRING(zp2ssg2) |
|
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|
496 |
|
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497 @DOCSTRING(zp2tf) |
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|
498 |
