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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 |
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6 @chapter Control Theory |
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7 |
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8 The Octave Control Systems Toolbox (@acronym{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 @acronym{NASA}'s Marshall Space Flight |
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19 Center as part of an in-house @acronym{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 @acronym{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 |
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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 @acronym{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 @acronym{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 @acronym{OCST}, it is recommended that |
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62 the system structure access m-files be used (@pxref{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 @acronym{SISO} systems; the @acronym{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 |
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71 @subsection Variables common to all @acronym{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 |
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79 @itemx nz |
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80 The respective number of continuous and discrete states |
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81 in the system (scalar) |
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82 |
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83 @item inname |
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84 @itemx outname |
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85 list of name(s) of the system input, output signal(s). (list of strings) |
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86 |
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87 @item sys |
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88 System status vector. (vector) |
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89 |
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90 This vector indicates both what representation was used to initialize |
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91 the system data structure (called the primary system type) and which |
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92 other representations are currently up-to-date with the primary system |
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93 type (@pxref{structaccess}). |
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94 |
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95 The value of the first element of the vector indicates the primary |
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96 system type. |
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97 |
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98 @table @asis |
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99 @item 0 |
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100 for tf form (initialized with @code{tf2sys} or @code{fir2sys}) |
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101 |
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102 @item 1 |
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103 for zp form (initialized with @code{zp2sys}) |
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104 |
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105 @item 2 |
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106 for ss form (initialized with @code{ss2sys}) |
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107 @end table |
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108 |
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109 The next three elements are boolean flags that indicate whether tf, zp, |
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110 or ss, respectively, are ``up to date" (whether it is safe to use the |
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111 variables associated with these representations). These flags are |
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112 changed when calls are made to the @code{sysupdate} command. |
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113 |
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114 @item tsam |
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115 Discrete time sampling period (nonnegative scalar). |
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116 @var{tsam} is set to 0 for continuous time systems. |
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117 |
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118 @item yd |
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119 Discrete-time output list (vector) |
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120 |
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121 indicates which outputs are discrete time (i.e., |
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122 produced by D/A converters) and which are continuous time. |
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123 yd(ii) = 0 if output ii is continuous, = 1 if discrete. |
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124 @end table |
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125 |
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126 The remaining variables of the system data structure are only present |
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127 if the corresponding entry of the @code{sys} vector is true (=1). |
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128 |
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129 @node sysstructtf |
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130 @subsection @code{tf} format variables |
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131 |
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132 @table @var |
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133 @item num |
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134 numerator coefficients (vector) |
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135 |
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136 @item den |
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137 denominator coefficients (vector) |
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138 |
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139 @end table |
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140 |
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141 @node sysstructzp |
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142 @subsection @code{zp} format variables |
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143 |
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144 @table @var |
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145 @item zer |
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146 system zeros (vector) |
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147 |
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148 @item pol |
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149 system poles (vector) |
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150 |
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151 @item k |
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152 leading coefficient (scalar) |
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153 |
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154 @end table |
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155 |
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156 @node sysstructss |
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157 @subsection @code{ss} format variables |
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158 |
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159 @table @var |
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160 @item a |
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161 @itemx b |
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162 @itemx c |
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163 @itemx d |
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164 The usual state-space matrices. If a system has both |
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165 continuous and discrete states, they are sorted so that |
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166 continuous states come first, then discrete states |
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167 |
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168 @strong{Note} some functions (e.g., @code{bode}, @code{hinfsyn}) |
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169 will not accept systems with both discrete and continuous states/outputs |
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170 |
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171 @item stname |
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172 names of system states (list of strings) |
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173 |
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174 @end table |
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175 |
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176 @node sysinterface |
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177 @section System Construction and Interface Functions |
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178 |
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179 Construction and manipulations of the @acronym{OCST} system data structure |
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180 (@pxref{sysstruct}) requires attention to many details in order |
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181 to ensure that data structure contents remain consistent. Users |
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182 are strongly encouraged to use the system interface functions |
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183 in this section. Functions for the formatted display in of system |
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184 data structures are given in @ref{sysdisp}. |
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185 |
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186 @menu |
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187 * fir2sys:: |
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188 * ss2sys:: |
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189 * tf2sys:: |
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190 * zp2sys:: |
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191 * structaccess:: |
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192 @end menu |
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193 |
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194 @node fir2sys |
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195 @subsection Finite impulse response system interface functions |
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196 |
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197 @DOCSTRING(fir2sys) |
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198 |
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199 @DOCSTRING(sys2fir) |
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200 |
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201 @node ss2sys |
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202 @subsection State space system interface functions |
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203 |
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204 @DOCSTRING(ss) |
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205 |
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206 @DOCSTRING(ss2sys) |
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207 |
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208 @DOCSTRING(sys2ss) |
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209 |
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210 @node tf2sys |
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211 @subsection Transfer function system interface functions |
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212 |
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213 @DOCSTRING(tf) |
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214 |
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215 @DOCSTRING(tf2sys) |
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216 |
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217 @DOCSTRING(sys2tf) |
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218 |
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219 @node zp2sys |
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220 @subsection Zero-pole system interface functions |
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221 |
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222 @DOCSTRING(zp) |
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223 |
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224 @DOCSTRING(zp2sys) |
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225 |
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226 @DOCSTRING(sys2zp) |
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227 |
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228 @node structaccess |
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229 @subsection Data structure access functions |
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230 |
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231 @DOCSTRING(syschnames) |
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232 |
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233 @DOCSTRING(syschtsam) |
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234 |
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235 @DOCSTRING(sysdimensions) |
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236 |
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237 @DOCSTRING(sysgetsignals) |
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238 |
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239 @DOCSTRING(sysgettype) |
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240 |
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241 @DOCSTRING(syssetsignals) |
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242 |
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243 @DOCSTRING(sysupdate) |
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244 |
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245 @DOCSTRING(minfo) |
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246 |
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247 @DOCSTRING(sysgettsam) |
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248 |
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249 @node sysdisp |
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250 @section System display functions |
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251 |
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252 @DOCSTRING(sysout) |
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253 |
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254 @DOCSTRING(tfout) |
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255 |
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256 @DOCSTRING(zpout) |
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257 |
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258 @node blockdiag |
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259 @section Block Diagram Manipulations |
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260 |
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261 @xref{systime}. |
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262 |
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263 Unless otherwise noted, all parameters (input,output) are |
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264 system data structures. |
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265 |
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266 @DOCSTRING(bddemo) |
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267 |
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268 @DOCSTRING(buildssic) |
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269 |
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270 @DOCSTRING(jet707) |
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271 |
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272 @DOCSTRING(ord2) |
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273 |
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274 @DOCSTRING(sysadd) |
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275 |
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276 @DOCSTRING(sysappend) |
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277 |
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278 @DOCSTRING(sysconnect) |
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279 |
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280 @DOCSTRING(syscont) |
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281 |
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282 @DOCSTRING(sysdisc) |
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283 |
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284 @DOCSTRING(sysdup) |
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285 |
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286 @DOCSTRING(sysgroup) |
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287 |
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288 @DOCSTRING(sysmult) |
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289 |
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290 @DOCSTRING(sysprune) |
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291 |
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292 @DOCSTRING(sysreorder) |
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293 |
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294 @DOCSTRING(sysscale) |
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295 |
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296 @DOCSTRING(syssub) |
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297 |
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298 @DOCSTRING(ugain) |
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299 |
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300 @DOCSTRING(wgt1o) |
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301 |
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302 @DOCSTRING(parallel) |
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303 |
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304 @DOCSTRING(sysmin) |
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305 |
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306 @node numerical |
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307 @section Numerical Functions |
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308 |
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309 @DOCSTRING(are) |
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310 |
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311 @DOCSTRING(dare) |
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312 |
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313 @DOCSTRING(dre) |
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314 |
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315 @DOCSTRING(dgram) |
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316 |
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317 @DOCSTRING(dlyap) |
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318 |
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319 @DOCSTRING(gram) |
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320 |
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321 @DOCSTRING(lyap) |
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322 |
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323 @DOCSTRING(qzval) |
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324 |
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325 @DOCSTRING(zgfmul) |
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326 |
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327 @DOCSTRING(zgfslv) |
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328 |
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329 @DOCSTRING(zginit) |
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330 |
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331 @DOCSTRING(zgreduce) |
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332 |
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333 @DOCSTRING(zgrownorm) |
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334 |
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335 @DOCSTRING(zgscal) |
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336 |
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337 @DOCSTRING(zgsgiv) |
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338 |
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339 @DOCSTRING(zgshsr) |
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340 |
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341 @strong{References} |
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342 @table @strong |
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343 @item ZGEP |
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344 Hodel, @cite{Computation of Zeros with Balancing}, 1992, Linear Algebra |
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345 and its Applications |
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346 @item @strong{Generalized CG} |
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347 Golub and Van Loan, @cite{Matrix Computations, 2nd ed} 1989. |
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348 @end table |
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349 |
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350 @node sysprop |
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351 @section System Analysis-Properties |
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352 |
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353 @DOCSTRING(analdemo) |
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354 |
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355 @DOCSTRING(abcddim) |
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356 |
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357 @DOCSTRING(ctrb) |
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358 |
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359 @DOCSTRING(h2norm) |
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360 |
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361 @DOCSTRING(hinfnorm) |
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362 |
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363 @DOCSTRING(obsv) |
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364 |
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365 @DOCSTRING(pzmap) |
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366 |
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367 @DOCSTRING(is_abcd) |
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368 |
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369 @DOCSTRING(is_controllable) |
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370 |
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371 @DOCSTRING(is_detectable) |
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372 |
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373 @DOCSTRING(is_dgkf) |
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374 |
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375 @DOCSTRING(is_digital) |
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376 |
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377 @DOCSTRING(is_observable) |
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378 |
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379 @DOCSTRING(is_sample) |
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380 |
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381 @DOCSTRING(is_siso) |
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382 |
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383 @DOCSTRING(is_stabilizable) |
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384 |
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385 @DOCSTRING(is_signal_list) |
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386 |
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387 @DOCSTRING(is_stable) |
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388 |
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389 @node systime |
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390 @section System Analysis-Time Domain |
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391 |
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392 @DOCSTRING(c2d) |
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393 |
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394 @DOCSTRING(d2c) |
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395 |
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396 @DOCSTRING(dmr2d) |
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397 |
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398 @DOCSTRING(damp) |
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399 |
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400 @DOCSTRING(dcgain) |
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401 |
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402 @DOCSTRING(impulse) |
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403 |
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404 @DOCSTRING(step) |
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405 |
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406 @node sysfreq |
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407 @section System Analysis-Frequency Domain |
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408 |
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409 @strong{Demonstration/tutorial script} |
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410 @DOCSTRING(frdemo) |
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411 |
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412 @DOCSTRING(bode) |
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413 |
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414 @DOCSTRING(bode_bounds) |
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415 |
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416 @DOCSTRING(freqchkw) |
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417 |
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418 @DOCSTRING(ltifr) |
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419 |
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420 @DOCSTRING(nyquist) |
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421 |
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422 @DOCSTRING(nichols) |
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423 |
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424 @DOCSTRING(tzero) |
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425 |
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426 @DOCSTRING(tzero2) |
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427 |
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428 @node cacsd |
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429 @section Controller Design |
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430 |
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431 @DOCSTRING(dgkfdemo) |
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432 |
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433 @DOCSTRING(hinfdemo) |
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434 |
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435 @DOCSTRING(dlqe) |
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436 |
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437 @DOCSTRING(dlqr) |
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438 |
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439 @DOCSTRING(dkalman) |
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440 |
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441 @DOCSTRING(h2syn) |
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442 |
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443 @DOCSTRING(hinf_ctr) |
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444 |
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445 @DOCSTRING(hinfsyn) |
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446 |
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447 @DOCSTRING(hinfsyn_chk) |
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448 |
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449 @DOCSTRING(hinfsyn_ric) |
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450 |
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451 @DOCSTRING(lqe) |
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452 |
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453 @DOCSTRING(lqg) |
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454 |
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455 @DOCSTRING(lqr) |
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|
456 |
|
3346
|
457 @DOCSTRING(lsim) |
|
3294
|
458 |
|
3346
|
459 @DOCSTRING(place) |
|
3294
|
460 |
|
4167
|
461 @node misc |
|
3294
|
462 @section Miscellaneous Functions (Not yet properly filed/documented) |
|
|
463 |
|
3346
|
464 @DOCSTRING(axis2dlim) |
|
3294
|
465 |
|
3346
|
466 @DOCSTRING(moddemo) |
|
3294
|
467 |
|
3346
|
468 @DOCSTRING(prompt) |
|
3294
|
469 |
|
3346
|
470 @DOCSTRING(rldemo) |
|
3294
|
471 |
|
3346
|
472 @DOCSTRING(rlocus) |
|
3294
|
473 |
|
3346
|
474 @DOCSTRING(sortcom) |
|
3294
|
475 |
|
3346
|
476 @DOCSTRING(ss2tf) |
|
3294
|
477 |
|
3346
|
478 @DOCSTRING(ss2zp) |
|
3294
|
479 |
|
3346
|
480 @DOCSTRING(starp) |
|
3294
|
481 |
|
3346
|
482 @DOCSTRING(tf2ss) |
|
3294
|
483 |
|
3346
|
484 @DOCSTRING(tf2zp) |
|
3294
|
485 |
|
3346
|
486 @DOCSTRING(zp2ss) |
|
3294
|
487 |
|
3346
|
488 @DOCSTRING(zp2tf) |
|
3294
|
489 |
