1 | #*------------------------------------------------------------------- |
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2 | * EMSO Model Library (EML) Copyright (C) 2004 - 2007 ALSOC. |
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3 | * |
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4 | * This LIBRARY is free software; you can distribute it and/or modify |
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5 | * it under the therms of the ALSOC FREE LICENSE as available at |
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6 | * http://www.enq.ufrgs.br/alsoc. |
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7 | * |
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8 | * EMSO Copyright (C) 2004 - 2007 ALSOC, original code |
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9 | * from http://www.rps.eng.br Copyright (C) 2002-2004. |
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10 | * All rights reserved. |
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11 | * |
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12 | * EMSO is distributed under the therms of the ALSOC LICENSE as |
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13 | * available at http://www.enq.ufrgs.br/alsoc. |
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14 | * |
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15 | *------------------------------------------------------------------- |
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16 | * Model of PIDs |
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17 | *-------------------------------------------------------------------- |
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18 | * - Inputs |
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19 | * - a scaled processs variable |
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20 | * - a scaled bias |
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21 | * - a scaled setpoint |
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22 | * |
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23 | * - Outputs |
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24 | * - a scaled output |
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25 | * |
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26 | * |
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27 | *-------------------------------------------------------------------- |
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28 | * Author: Tiago Osório |
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29 | * $Id: PIDs.mso 74 2006-12-08 18:43:02Z paula $ |
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30 | *-------------------------------------------------------------------*# |
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31 | using "types"; |
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32 | |
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33 | Model MParameters |
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34 | |
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35 | VARIABLES |
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36 | |
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37 | alpha as positive (Brief="Derivative term filter constant", Default=1); |
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38 | beta as positive (Brief="Proportional term setPoint change filter"); |
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39 | bias as control_signal (Brief="Previous scaled bias", Default=0.5); |
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40 | derivTime as time_sec (Brief="Derivative time constant"); |
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41 | intTime as time_sec (Brief="Integral time constant"); |
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42 | gain as positive (Brief="Controller gain", Default=0.5); |
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43 | gamma as positive (Brief="Derivative term SP change filter"); |
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44 | tau as time_sec (Brief="Input filter time constant"); |
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45 | tauSet as time_sec (Brief="Input filter time constant"); |
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46 | |
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47 | end |
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48 | |
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49 | Model MOptions |
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50 | |
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51 | VARIABLES |
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52 | |
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53 | action as Real (Brief="Controller action: (-1) Direct,(1) Reverse", Default=-1); |
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54 | autoMan as Real (Brief="Controller option: (0) Automatic, (1) Manual", Default=0); |
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55 | clip as Real (Brief="Controller option: (1) output clipped, (0) output unclipped", Default=1); |
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56 | |
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57 | end |
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58 | |
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59 | Model MPorts |
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60 | |
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61 | VARIABLES |
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62 | |
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63 | input as control_signal (Brief="Previous scaled input signal", Default=0.5); |
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64 | output as control_signal (Brief="Scaled output signal", Default=0.5); |
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65 | setPoint as control_signal (Brief="Scaled setPoint",Default=0.5); |
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66 | |
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67 | end |
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68 | |
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69 | Model MInternal_Variables |
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70 | |
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71 | VARIABLES |
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72 | |
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73 | derivTerm as control_signal (Brief="Derivative term", Default=0); |
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74 | dFilt as control_signal (Brief="Derivative term filtered", Default=0.5); |
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75 | error as control_signal (Brief="Error definition for proportional term"); |
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76 | errorD as control_signal (Brief="Error definition for derivative term"); |
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77 | errorI as control_signal (Brief="Error definition for integral term"); |
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78 | inputFilt as control_signal (Brief="Filtered input"); |
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79 | intTerm as control_signal (Brief="Integral term", Default=0); |
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80 | outp as control_signal (Brief="Sum of proportional, integral and derivative terms"); |
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81 | outps as control_signal (Brief="Variable outp scaled between -1 and 1"); |
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82 | propTerm as control_signal (Brief="Proportional term", Default=0); |
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83 | setPointFilt as control_signal (Brief="Filtered setPoint", Default=0); |
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84 | |
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85 | end |
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86 | |
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87 | Model PID_basic |
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88 | |
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89 | VARIABLES |
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90 | Parameters as MParameters; |
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91 | Options as MOptions; |
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92 | Internal as MInternal_Variables; |
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93 | Ports as MPorts; |
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94 | |
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95 | EQUATIONS |
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96 | |
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97 | if (Parameters.tau equal 0) then |
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98 | "Input first order filter" |
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99 | (Parameters.tau + 1e-3*"s")*diff(Internal.inputFilt)= Ports.input - Internal.inputFilt; |
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100 | else |
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101 | "Input first order filter" |
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102 | Parameters.tau*diff(Internal.inputFilt)= Ports.input - Internal.inputFilt; |
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103 | end |
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104 | |
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105 | if (Parameters.tauSet equal 0) then |
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106 | "setPoint first order filter" |
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107 | (Parameters.tauSet + 1e-3*"s")*diff(Internal.setPointFilt)= Ports.setPoint - Internal.setPointFilt; |
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108 | else |
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109 | "setPoint first order filter" |
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110 | Parameters.tauSet*diff(Internal.setPointFilt)= Ports.setPoint - Internal.setPointFilt; |
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111 | end |
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112 | |
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113 | if Options.autoMan equal 1 then |
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114 | "Error definition for proportional term" |
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115 | Internal.error = Internal.inputFilt*(Parameters.beta-1.0); |
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116 | "Error definition for derivative term" |
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117 | Internal.errorD= Internal.inputFilt*(Parameters.gamma-1.0); |
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118 | "Error definition for integral term" |
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119 | Internal.errorI= 0; |
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120 | else |
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121 | "Error definition for proportional term" |
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122 | Internal.error = Parameters.beta*Internal.setPointFilt - Internal.inputFilt; |
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123 | "Error definition for derivative term" |
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124 | Internal.errorD = Parameters.gamma*Internal.setPointFilt - Internal.inputFilt; |
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125 | "Error definition for integral term" |
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126 | Internal.errorI = Internal.setPointFilt-Internal.inputFilt; |
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127 | end |
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128 | |
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129 | "Calculate proportional term" |
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130 | Internal.propTerm=Internal.error; |
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131 | |
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132 | if (Parameters.derivTime equal 0) then |
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133 | "Derivative term filter" |
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134 | Parameters.alpha*(Parameters.derivTime + 1e-3*"s")*diff(Internal.dFilt) = Internal.errorD - Internal.dFilt; |
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135 | else |
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136 | "Derivative term filter" |
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137 | Parameters.alpha*(Parameters.derivTime)*diff(Internal.dFilt) = Internal.errorD - Internal.dFilt; |
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138 | end |
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139 | |
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140 | "Calculate derivative term" |
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141 | Internal.derivTerm = Parameters.derivTime*diff(Internal.dFilt); |
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142 | |
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143 | "Scale outp" |
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144 | Internal.outps=2*Internal.outp-1; |
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145 | |
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146 | if Options.clip equal 1 then |
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147 | if abs(Internal.outps)>1 then |
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148 | "Calculate clipped output when it´s saturated" |
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149 | Ports.output=(sign(Internal.outps)*1+1)/2; |
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150 | else |
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151 | "Calculate clipped output when it´s not saturated" |
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152 | Ports.output=Internal.outp; |
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153 | end |
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154 | else |
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155 | "Calculate unclipped output" |
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156 | Ports.output=Internal.outp; |
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157 | end |
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158 | |
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159 | INITIAL |
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160 | Internal.intTerm = 0; |
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161 | diff(Internal.dFilt) = 0*"1/s"; |
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162 | diff(Internal.inputFilt) = 0*"1/s"; |
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163 | diff(Internal.setPointFilt) = 0*"1/s"; |
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164 | end |
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165 | |
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166 | |
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167 | Model PID_Ideal_AW as PID_basic |
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168 | |
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169 | VARIABLES |
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170 | AWFactor as Real (Brief="Integral term multiplier used in anti-reset windup"); |
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171 | |
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172 | EQUATIONS |
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173 | |
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174 | "Calculate integral term with anti-windup" |
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175 | Parameters.intTime*diff(Internal.intTerm) = AWFactor*Internal.errorI; |
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176 | |
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177 | "Sum of proportional, integral and derivative terms" |
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178 | Internal.outp = Parameters.bias + Options.action*Parameters.gain*(Internal.propTerm + Internal.intTerm + Internal.derivTerm); |
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179 | |
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180 | if abs(Internal.outps)>1 and (Options.action*sign(Internal.outps)*Internal.errorI)>0 then |
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181 | "Calculate AWFactor" |
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182 | AWFactor=-tanh(sign(Internal.outps)*Internal.outps*100-102); |
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183 | else |
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184 | "Calculate AWFactor" |
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185 | AWFactor=1; |
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186 | end |
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187 | end |
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188 | |
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189 | Model PID_Parallel_AW as PID_basic |
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190 | |
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191 | VARIABLES |
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192 | AWFactor as Real (Brief="Integral term multiplier used in anti-reset windup"); |
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193 | |
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194 | EQUATIONS |
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195 | |
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196 | "Calculate integral term with anti-windup" |
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197 | Parameters.intTime*diff(Internal.intTerm) = AWFactor*Internal.errorI; |
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198 | |
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199 | "Sum of proportional, integral and derivative terms" |
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200 | Internal.outp = Parameters.bias + Options.action*(Parameters.gain*Internal.propTerm + Internal.intTerm + Internal.derivTerm); |
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201 | |
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202 | if abs(Internal.outps)>1 and (Options.action*sign(Internal.outps)*Internal.errorI)>0 then |
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203 | "Calculate AWFactor" |
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204 | AWFactor=-tanh(sign(Internal.outps)*Internal.outps*100-102); |
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205 | else |
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206 | "Calculate AWFactor" |
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207 | AWFactor=1; |
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208 | end |
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209 | end |
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210 | |
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211 | Model PID_Series_AW as PID_basic |
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212 | |
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213 | VARIABLES |
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214 | AWFactor as Real (Brief="Integral term multiplier used in anti-reset windup"); |
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215 | |
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216 | EQUATIONS |
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217 | |
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218 | "Calculate integral term with anti-windup" |
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219 | Parameters.intTime*diff(Internal.intTerm) = AWFactor*Internal.errorI; |
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220 | |
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221 | "Sum of proportional, integral and derivative terms" |
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222 | Internal.outp = Parameters.bias + Options.action*(Parameters.gain*(Internal.propTerm + Internal.intTerm)*(1 + Internal.derivTerm)); |
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223 | |
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224 | if abs(Internal.outps)>1 and (Options.action*sign(Internal.outps)*Internal.errorI)>0 then |
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225 | "Calculate AWFactor" |
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226 | AWFactor=-tanh(sign(Internal.outps)*Internal.outps*100-102); |
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227 | else |
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228 | "Calculate AWFactor" |
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229 | AWFactor=1; |
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230 | end |
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231 | end |
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232 | |
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233 | Model PID_Ideal as PID_basic |
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234 | |
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235 | EQUATIONS |
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236 | |
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237 | "Calculate integral term" |
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238 | Parameters.intTime*diff(Internal.intTerm) = Internal.errorI; |
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239 | |
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240 | "Sum of proportional, integral and derivative terms" |
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241 | Internal.outp = Parameters.bias + Options.action*Parameters.gain*(Internal.propTerm + Internal.intTerm + Internal.derivTerm); |
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242 | |
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243 | end |
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244 | |
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245 | Model PID_Parallel as PID_basic |
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246 | |
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247 | EQUATIONS |
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248 | |
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249 | "Calculate integral term" |
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250 | Parameters.intTime*diff(Internal.intTerm) = Internal.errorI; |
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251 | |
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252 | "Sum of proportional, integral and derivative terms" |
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253 | Internal.outp = Parameters.bias + Options.action*(Parameters.gain*Internal.propTerm + Internal.intTerm + Internal.derivTerm); |
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254 | |
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255 | end |
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256 | |
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257 | Model PID_Series as PID_basic |
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258 | |
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259 | EQUATIONS |
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260 | |
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261 | "Calculate integral term" |
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262 | Parameters.intTime*diff(Internal.intTerm) = Internal.errorI; |
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263 | |
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264 | "Sum of proportional, integral and derivative terms" |
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265 | Internal.outp = Parameters.bias + Options.action*(Parameters.gain*(Internal.propTerm + Internal.intTerm)*(1 + Internal.derivTerm)); |
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266 | |
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267 | end |
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268 | |
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269 | Model PID_Ideal_AWBT as PID_basic |
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270 | |
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271 | EQUATIONS |
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272 | |
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273 | "Calculate integral term with anti-windup and bumpless transfer" |
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274 | Options.action*Parameters.gain*(Parameters.intTime*diff(Internal.intTerm)-Internal.errorI) = Ports.output-Internal.outp; |
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275 | |
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276 | "Sum of proportional, integral and derivative terms" |
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277 | Internal.outp = Parameters.bias + Options.action*Parameters.gain*(Internal.propTerm + Internal.intTerm + Internal.derivTerm); |
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278 | |
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279 | end |
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280 | |
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281 | Model PID_Parallel_AWBT as PID_basic |
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282 | |
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283 | EQUATIONS |
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284 | |
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285 | "Calculate integral term with anti-windup and bumpless transfer" |
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286 | Options.action*Parameters.gain*(Parameters.intTime*diff(Internal.intTerm)-Internal.errorI) = Ports.output-Internal.outp; |
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287 | |
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288 | "Sum of proportional, integral and derivative terms" |
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289 | Internal.outp = Parameters.bias + Options.action*(Parameters.gain*Internal.propTerm + Internal.intTerm + Internal.derivTerm); |
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290 | |
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291 | end |
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292 | |
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293 | Model PID_Series_AWBT as PID_basic |
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294 | |
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295 | EQUATIONS |
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296 | |
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297 | "Calculate integral term with anti-windup and bumpless transfer" |
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298 | Options.action*Parameters.gain*(Parameters.intTime*diff(Internal.intTerm)-Internal.errorI) = Ports.output-Internal.outp; |
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299 | |
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300 | "Sum of proportional, integral and derivative terms" |
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301 | Internal.outp = Parameters.bias + Options.action*(Parameters.gain*(Internal.propTerm + Internal.intTerm)*(1 + Internal.derivTerm)); |
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302 | |
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303 | end |
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