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{| class="wikitable"  
{| class="wikitable"  
|-
|-
! Chapter !! Function !! Implemented !! File
! Chapter !! Function !! Implemented !! File !! Number of Tests !! Status !! SLICOT functions !! Priority (0-2)
|-
|-
| rowspan="11" | Basic Models || tf    || style="background: green;" | yes || @tf/tf.m
| rowspan="11" | Basic Models || tf    || style="background: green;" | yes || @tf/tf.m   || || || ||
|-
|-
|                                zpk    || style="background: green;" | yes || zpk.m
|                                zpk    || style="background: green;" | yes || zpk.m     || || || ||
|-
|-
|                                ss    || style="background: green;" | yes || @ss/ss.m
|                                ss    || style="background: green;" | yes || @ss/ss.m   || || || ||
|-
|-
|                                frd    || style="background: green;" | yes || @frd/frd.m
|                                frd    || style="background: green;" | yes || @frd/frd.m || || || ||
|-  
|-  
|                                pid    || style="background: green;" | yes || pid.m
|                                pid    || style="background: red;"   | no  ||            || || || ||
|-
|-
|                                pidstd || style="background: green;" | yes || pidstd.m
|                                pidstd || style="background: red;"   | no  ||            || || || ||
|-
|-
|                                pid2  || style="background: red;"  | no  ||
|                                pid2  || style="background: red;"  | no  ||            || || || ||
|-
|-
|                                dss    || style="background: green;" | yes || @lti/dss.m
|                                dss    || style="background: green;" | yes || @lti/dss.m || || || ||
|-
|-
|                                drss  || style="background: red;"  | no  ||
|                                drss  || style="background: red;"  | no  ||            || || || ||
|-
|-
|                                filt  || style="background: green;" | yes || filt.m
|                                filt  || style="background: green;" | yes || filt.m     || || || ||
|-
|-
|                                rss    || style="background: red;"  | no  ||
|                                rss    || style="background: red;"  | no  ||            || || || ||
|-
|-
| rowspan="24" | Tunable Models || ltiblock.gain      || style="background: red;" | no ||
| rowspan="24" | Tunable Models || ltiblock.gain      || style="background: red;" | no || || || || ||
|-
|-
|                                  ltiblock.pid      || style="background: red;" | no ||
|                                  ltiblock.pid      || style="background: red;" | no || || || || ||
|-
|-
|                                  ltiblock.pid2      || style="background: red;" | no ||
|                                  ltiblock.pid2      || style="background: red;" | no || || || || ||
|-
|-
|                                  ltiblock.ss        || style="background: red;" | no ||
|                                  ltiblock.ss        || style="background: red;" | no || || || || ||
|-
|-
|                                  ltiblock.tf        || style="background: red;" | no ||
|                                  ltiblock.tf        || style="background: red;" | no || || || || ||
|-
|-
|                                  realp              || style="background: red;" | no ||
|                                  realp              || style="background: red;" | no || || || || ||
|-
|-
|                                  AnalysisPoint      || style="background: red;" | no ||
|                                  AnalysisPoint      || style="background: red;" | no || || || || ||
|-
|-
|                                  genss              || style="background: red;" | no ||
|                                  genss              || style="background: red;" | no || || || || ||
|-
|-
|                                  genfrd            || style="background: red;" | no ||
|                                  genfrd            || style="background: red;" | no || || || || ||
|-
|-
|                                  genmat            || style="background: red;" | no ||
|                                  genmat            || style="background: red;" | no || || || || ||
|-
|-
|                                  getLoopTransfer    || style="background: red;" | no ||
|                                  getLoopTransfer    || style="background: red;" | no || || || || ||
|-
|-
|                                  getIOTransfer      || style="background: red;" | no ||
|                                  getIOTransfer      || style="background: red;" | no || || || || ||
|-
|-
|                                  getSensitivity    || style="background: red;" | no ||
|                                  getSensitivity    || style="background: red;" | no || || || || ||
|-
|-
|                                  getCompSensitivity || style="background: red;" | no ||
|                                  getCompSensitivity || style="background: red;" | no || || || || ||
|-
|-
|                                  getPoints          || style="background: red;" | no ||
|                                  getPoints          || style="background: red;" | no || || || || ||
|-
|-
|                                  replaceBlock      || style="background: red;" | no ||
|                                  replaceBlock      || style="background: red;" | no || || || || ||
|-
|-
|                                  getValue          || style="background: red;" | no ||
|                                  getValue          || style="background: red;" | no || || || || ||
|-
|-
|                                  setValue          || style="background: red;" | no ||
|                                  setValue          || style="background: red;" | no || || || || ||
|-
|-
|                                  getBlockValue      || style="background: red;" | no ||
|                                  getBlockValue      || style="background: red;" | no || || || || ||
|-
|-
|                                  setBlockValue      || style="background: red;" | no ||
|                                  setBlockValue      || style="background: red;" | no || || || || ||
|-
|-
|                                  showBlockValue    || style="background: red;" | no ||
|                                  showBlockValue    || style="background: red;" | no || || || || ||
|-
|-
|                                  showTunable        || style="background: red;" | no ||
|                                  showTunable        || style="background: red;" | no || || || || ||
|-
|-
|                                  nblocks            || style="background: red;" | no ||
|                                  nblocks            || style="background: red;" | no || || || || ||
|-
|-
|                                  getLFTModel        || style="background: red;" | no ||
|                                  getLFTModel        || style="background: red;" | no || || || || ||
|-
|-
| rowspan="9" | Model with Time Delays || pade            || style="background: red;"  | no  ||
| rowspan="9" | Model with Time Delays || pade            || style="background: red;"  | no  ||          || || || ||
|-
|-
|                                        absorbDelay      || style="background: red;"  | no  ||
|                                        absorbDelay      || style="background: red;"  | no  ||          || || || ||
|-
|-
|                                        thiran          || style="background: green;" | yes || thiran.m
|                                        thiran          || style="background: green;" | yes || thiran.m || || || ||
|-
|-
|                                        hasdelay        || style="background: red;"  | no  ||
|                                        hasdelay        || style="background: red;"  | no  ||          || || || ||
|-
|-
|                                        hasInternalDelay || style="background: red;"  | no  ||
|                                        hasInternalDelay || style="background: red;"  | no  ||          || || || ||
|-
|-
|                                        totaldelay      || style="background: red;"  | no  ||
|                                        totaldelay      || style="background: red;"  | no  ||          || || || ||
|-
|-
|                                        delayss          || style="background: red;"  | no  ||
|                                        delayss          || style="background: red;"  | no  ||          || || || ||
|-
|-
|                                        setDelayModel    || style="background: red;"  | no  ||
|                                        setDelayModel    || style="background: red;"  | no  ||          || || || ||
|-
|-
|                                        getDelayModel    || style="background: red;"  | no  ||
|                                        getDelayModel    || style="background: red;"  | no  ||          || || || ||
|-
|-
| rowspan="26" | Model Attributes || get          || style="background: green;" | yes || @iddata/get.m
| rowspan="26" | Model Attributes || get          || style="background: green;" | yes || @iddata/get.m     || || || ||
|-
|-
|                                    set          || style="background: green;" | yes || @iddata/set.m
|                                    set          || style="background: green;" | yes || @iddata/set.m     || || || ||
|-
|-
|                                    tfdata      || style="background: green;" | yes || @lti/tfdata.m
|                                    tfdata      || style="background: green;" | yes || @lti/tfdata.m     || || || ||
|-
|-
|                                    zpkdata      || style="background: green;" | yes || @lti/zpkdata.m
|                                    zpkdata      || style="background: green;" | yes || @lti/zpkdata.m   || || || ||
|-
|-
|                                    ssdata      || style="background: green;" | yes || @lti/ssdata.m
|                                    ssdata      || style="background: green;" | yes || @lti/ssdata.m     || || || ||
|-
|-
|                                    frdata      || style="background: green;" | yes || @lti/frdata.m
|                                    frdata      || style="background: green;" | yes || @lti/frdata.m     || || || ||
|-
|-
|                                    piddata      || style="background: red;"  | no  ||
|                                    piddata      || style="background: red;"  | no  ||                  || || || ||
|-
|-
|                                    pidstddata  || style="background: red;"  | no  ||
|                                    pidstddata  || style="background: red;"  | no  ||                  || || || ||
|-
|-
|                                    piddata2    || style="background: red;"  | no  ||
|                                    piddata2    || style="background: red;"  | no  ||                  || || || ||
|-
|-
|                                    pidstddata2  || style="background: red;"  | no  ||
|                                    pidstddata2  || style="background: red;"  | no  ||                  || || || ||
|-
|-
|                                    dssdata      || style="background: green;" | yes || @lti/dssdata.m
|                                    dssdata      || style="background: green;" | yes || @lti/dssdata.m   || || || ||
|-
|-
|                                    chgFreqUnit  || style="background: red;"  | no  ||
|                                    chgFreqUnit  || style="background: red;"  | no  ||                  || || || ||
|-
|-
|                                    chgTimeUnit  || style="background: red;"  | no  ||
|                                    chgTimeUnit  || style="background: red;"  | no  ||                  || || || ||
|-
|-
|                                    isct        || style="background: green;" | yes || @lti/isct.m
|                                    isct        || style="background: green;" | yes || @lti/isct.m       || || || ||
|-
|-
|                                    isdt        || style="background: green;" | yes || @lti/isdt.m
|                                    isdt        || style="background: green;" | yes || @lti/isdt.m       || || || ||
|-
|-
|                                    isempty      || style="background: green;" | yes || built-in function
|                                    isempty      || style="background: green;" | yes || built-in function || || || ||
|-
|-
|                                    isfinite    || style="background: green;" | yes || built-in function
|                                    isfinite    || style="background: green;" | yes || built-in function || || || ||
|-
|-
|                                    isParametric || style="background: red;"  | no  ||
|                                    isParametric || style="background: red;"  | no  ||                  || || || ||
|-
|-
|                                    isproper    || style="background: red;"  | no  ||
|                                    isproper    || style="background: red;"  | no  ||                  || || || ||
|-
|-
|                                    isreal      || style="background: green;" | yes || built-in function
|                                    isreal      || style="background: green;" | yes || built-in function || || || ||
|-
|-
|                                    isiso        || style="background: red;"  | no  ||
|                                    isiso        || style="background: red;"  | no  ||                  || || || ||
|-
|-
|                                    isstable    || style="background: green;" | yes || @lti/isstable.m
|                                    isstable    || style="background: green;" | yes || @lti/isstable.m   || || || ||
|-
|-
|                                    isstatic    || style="background: red;"  | no  ||
|                                    isstatic    || style="background: red;"  | no  ||                  || || || ||
|-
|-
|                                    order        || style="background: red;"  | no  ||
|                                    order        || style="background: red;"  | no  ||                  || || || ||
|-
|-
|                                    ndims        || style="background: green;" | yes || built-in function
|                                    ndims        || style="background: green;" | yes || built-in function || || || ||
|-
|-
|                                    size        || style="background: green;" | yes || built-in function
|                                    size        || style="background: green;" | yes || built-in function || || || ||
|-
|-
| rowspan="5" | Model Arrays || stack  || style="background: red;"  | no  ||
| rowspan="5" | Model Arrays || stack  || style="background: red;"  | no  ||                  || || || ||
|-
|-
|                              nmodels || style="background: red;"  | no  ||
|                              nmodels || style="background: red;"  | no  ||                  || || || ||
|-
|-
|                              permute || style="background: green;" | yes || built-in function
|                              permute || style="background: green;" | yes || built-in function || || || ||
|-
|-
|                              reshape || style="background: green;" | yes || built-in function
|                              reshape || style="background: green;" | yes || built-in function || || || ||
|-
|-
|                              repsys  || style="background: green;" | yes || repsys.m
|                              repsys  || style="background: green;" | yes || repsys.m         || || || ||
|-
|-
|}
|}
Line 165: Line 165:
{| class="wikitable"  
{| class="wikitable"  
|-
|-
! Function !! Implemented !! File
! Function !! Implemented !! File !! Number of Tests !! Status !! SLICOT functions !! Priority
|-
|-
| feedback || style="background: green;" | yes || @lti/feedback.m
| feedback || style="background: green;" | yes || @lti/feedback.m ||  || || ||
|-
|-
| connect || style="background: green;" | yes || @lti/connect.m
| connect || style="background: green;" | yes || @lti/connect.m ||  || || ||
|-
|-
| sumblk || style="background: green;" | yes || sumblk.m
| sumblk || style="background: green;" | yes || sumblk.m ||  || || ||
|-
|-
| series || style="background: green;" | yes || @lti/series.m
| series || style="background: red;" | no ||  ||  || || ||
|-
|-
| parallel || style="background: green;" | yes || @lti/parallel.m
| parallel || style="background: red;" | no ||  ||  || || ||
|-
|-
| append || style="background: green;" | yes || append.m
| append || style="background: green;" | yes || append.m ||  || || ||
|-
|-
| blkdiag || style="background: green;" | yes || @lti/blkdiag.m
| blkdiag || style="background: green;" | yes || @lti/blkdiag.m ||  || || ||
|-
|-
| imp2exp || style="background: red;" | no ||
| imp2exp || style="background: red;" | no ||  ||  || || ||
|-
|-
| inv || style="background: green;" | yes || built-in function
| inv || style="background: green;" | yes || built-in function ||  || || ||
|-
|-
| lft || style="background: red;" | no ||
| lft || style="background: red;" | no ||  ||  || || ||
|-
|-
| connectOptions || style="background: red;" | no ||
| connectOptions || style="background: red;" | no ||  ||  || || ||
|-
|-
|}
|}
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{| class="wikitable"  
{| class="wikitable"  
|-
|-
! Chapter !! Function !! Implemented !! File !! Number of Tests !! Status !! SLICOT functions !! Priority (0-2)
! Chapter !! Function !! Implemented !! File !! Number of Tests !! Status !! SLICOT functions !! Priority
|-
|-
| rowspan="4" | Model Type Conversion || pidstd2 || style="background: red;" | no ||  ||  || || ||
| rowspan="4" | Model Type Conversion || pidstd2 || style="background: red;" | no ||  ||  || || ||
Line 261: Line 261:
{| class="wikitable"  
{| class="wikitable"  
|-
|-
! Chapter !! Function !! Implemented !! File !! Number of Tests !! Status !! SLICOT functions !! Priority (0-2)
! Chapter !! Function !! Implemented !! File !! Status !! SLICOT functions !! Priority
|-
|-
| rowspan="13" | Time-Domain Analysis || linearSystemAnalyzer || style="background: red;" | no ||  ||  || || ||
| rowspan="13" | Time-Domain Analysis || linearSystemAnalyzer || style="background: red;" | no ||  ||  || ||
|-
|-
| impulseplot || style="background: red;" | no ||  ||  || || ||
| impulseplot || style="background: red;" | no ||  ||  || ||
|-
|-
| initialplot || style="background: red;" | no ||  ||  || || ||
| initialplot || style="background: red;" | no ||  ||  || ||
|-
|-
| lsimplot || style="background: red;" | no ||  ||  || || ||
| lsimplot || style="background: red;" | no ||  ||  || ||
|-
|-
| stepplot || style="background: red;" | no ||  ||  || || ||
| stepplot || style="background: red;" | no ||  ||  || ||
|-
|-
| covar || style="background: green;" | yes || covar.m ||  || || ||
| covar || style="background: green;" | yes || covar.m ||  || ||
|-
|-
| impulse || style="background: green;" | yes || impulse.m ||  || || ||
| impulse || style="background: green;" | yes || impulse.m ||  || ||
|-
|-
| initial || style="background: green;" | yes || initial.m ||  || || ||
| initial || style="background: green;" | yes || initial.m ||  || ||
|-
|-
| lsim || style="background: green;" | yes || lsim.m ||  || || ||
| lsim || style="background: green;" | yes || lsim.m ||  || ||
|-
|-
| step || style="background: green;" | yes || step.m ||  || || ||
| step || style="background: green;" | yes || step.m ||  || ||
|-
|-
| lsiminfo || style="background: red;" | no ||  ||  || || ||
| lsiminfo || style="background: red;" | no ||  ||  || ||
|-
|-
| stepinfo || style="background: red;" | no ||  ||  || || ||
| stepinfo || style="background: red;" | no ||  ||  || ||
|-
|-
| stepDataOptions || style="background: red;" | no ||  ||  || || ||
| stepDataOptions || style="background: red;" | no ||  ||  || ||
|-
|-
| rowspan="14" | Frequency-Domain Analysis || bodeplot || style="background: red;" | no ||  ||  || || ||
| rowspan="14" | Frequency-Domain Analysis || bodeplot || style="background: red;" | no ||  ||  || ||
|-
|-
| nicholsplot || style="background: red;" | no ||  ||  || || ||
| nicholsplot || style="background: red;" | no ||  ||  || ||
|-
|-
| nyquistplot || style="background: red;" | no ||  ||  || || ||
| nyquistplot || style="background: red;" | no ||  ||  || ||
|-
|-
| sigmaplot || style="background: red;" | no ||  ||  || || ||
| sigmaplot || style="background: red;" | no ||  ||  || ||
|-
|-
| bode || style="background: green;" | yes || bode.m ||  || || ||
| bode || style="background: green;" | yes || bode.m ||  || ||
|-
|-
| nichols || style="background: green;" | yes || nichols.m ||  || || ||
| nichols || style="background: green;" | yes || nichols.m ||  || ||
|-
|-
| nyquist || style="background: green;" | yes || nyquist.m ||  || || ||
| nyquist || style="background: green;" | yes || nyquist.m ||  || ||
|-
|-
| sigma || style="background: green;" | yes || sigma.m ||  || || ||
| sigma || style="background: green;" | yes || sigma.m ||  || ||
|-
|-
| evalfr || style="background: red;" | no ||  ||  || || ||
| evalfr || style="background: red;" | no ||  ||  || ||
|-
|-
| freqresp || style="background: green;" | yes || @lti/freqresp.m ||  || || ||
| freqresp || style="background: green;" | yes || @lti/freqresp.m ||  || ||
|-
|-
| bandwidth || style="background: green;" | yes || built-in function ||  || || ||
| bandwidth || style="background: green;" | yes || built-in function ||  || ||
|-
|-
| dcgain || style="background: green;" | yes || @lti/dcgain.m ||  || || ||
| dcgain || style="background: green;" | yes || @lti/dcgain.m ||  || ||
|-
|-
| getGainCrossover || style="background: red;" | no ||  ||  || || ||
| getGainCrossover || style="background: red;" | no ||  ||  || ||
|-
|-
| getPeakGain || style="background: red;" | no ||  ||  || || ||
| getPeakGain || style="background: red;" | no ||  ||  || ||
|-
|-
| rowspan="11" | Stability Analysis || pole || style="background: green;" | yes || @lti/pole.m ||  || || ||
| rowspan="10" | Stability Analysis || pole || style="background: green;" | yes || @lti/pole.m ||  || ||
|-
|-
| zero || style="background: green;" | yes || @lti/zero.m ||  || || ||
| zero || style="background: green;" | yes || @lti/zero.m ||  || ||
|-
|-
| damp || style="background: green;" | yes || damp.m ||  || || ||
| damp || style="background: red;" | no || ||  || ||
|-
|-
| dsort || style="background: green;" | yes || dsort.m ||  || || ||
| dsort || style="background: red;" | no || ||  || ||
|-
|-
| esort || style="background: green;" | yes || esort.m ||  || || ||
| esort || style="background: red;" | no || ||  || ||
|-
|-
| tzero || style="background: red;" | no ||  ||  || || ||
| tzero || style="background: red;" | no ||  ||  || ||
|-
|-
| pzmap || style="background: green;" | yes || pzmap.m ||  || || ||
| pzplot || style="background: red;" | no || ||  || ||
|-
|-
| pzplot || style="background: red;" | no ||  ||  || || ||
| iopzplot || style="background: red;" | no ||  ||  || ||
|-
|-
| iopzplot || style="background: red;" | no ||  ||  || || ||
| allmargin || style="background: red;" | no ||  ||  || ||
|-
|-
| allmargin || style="background: red;" | no || ||  || || ||
| margin || style="background: green;" | yes || margin.m ||  || ||
|-
|-
| margin || style="background: green;" | yes || margin.m ||  || || ||
| rowspan="11" | Plot Customization || bodeoptions || style="background: red;" | no || ||  || ||
|-
|-
| rowspan="11" | Plot Customization || bodeoptions || style="background: red;" | no ||  ||  || || ||
| hsvoptions || style="background: red;" | no ||  ||  || ||
|-
|-
| hsvoptions || style="background: red;" | no ||  ||  || || ||
| nicholsoptions || style="background: red;" | no ||  ||  || ||
|-
|-
| nicholsoptions || style="background: red;" | no ||  ||  || || ||
| nyquistoptions || style="background: red;" | no ||  ||  || ||
|-
|-
| nyquistoptions || style="background: red;" | no ||  ||  || || ||
| pzoptions || style="background: red;" | no ||  ||  || ||
|-
|-
| pzoptions || style="background: red;" | no ||  ||  || || ||
| sigmaoptions || style="background: red;" | no ||  ||  || ||
|-
|-
| sigmaoptions || style="background: red;" | no ||  ||  || || ||
| timeoptions || style="background: red;" | no ||  ||  || ||
|-
|-
| timeoptions || style="background: red;" | no ||  ||  || || ||
| setoptions || style="background: red;" | no ||  ||  || ||
|-
|-
| setoptions || style="background: red;" | no ||  ||  || || ||
| getoptions || style="background: red;" | no ||  ||  || ||
|-
|-
| getoptions || style="background: red;" | no ||  ||  || || ||
| ctrlpref || style="background: red;" | no ||  ||  || ||
|-
|-
| ctrlpref || style="background: red;" | no ||  ||  || || ||
| updateSystem || style="background: red;" | no ||  ||  || ||
|-
| updateSystem || style="background: red;" | no ||  ||  || || ||
|-
|-
|}
|}
Line 367: Line 365:
{| class="wikitable"  
{| class="wikitable"  
|-
|-
! Chapter !! Function !! Implemented !! File !! Number of Tests !! Status !! SLICOT functions !! Priority (0-2)
! Chapter !! Function !! Implemented !! File !! Status !! SLICOT functions !! Priority
|-
|-
| rowspan="3" | PID Controller Tuning || pidTuner || style="background: red;" | no ||  ||  || || ||
| rowspan="3" | PID Controller Tuning || pidTuner || style="background: red;" | no ||  ||  || ||
|-
|-
| pidtune || style="background: red;" | no ||  ||  || || ||
| pidtune || style="background: red;" | no ||  ||  || ||
|-
|-
| pidtuneOptions || style="background: red;" | no ||  ||  || || ||
| pidtuneOptions || style="background: red;" | no ||  ||  || ||
|-
|-
| rowspan="5" | SISO Feedback Loops || rlocus || style="background: green;" | yes || rlocus.m  ||  || || ||
| rowspan="4" | SISO Feedback Loops || rlocus || style="background: green;" | yes || rlocus.m  ||  || ||
|-
|-
| sgrid || style="background: red;" | no ||  ||  || || ||
| rlocusplot || style="background: red;" | no ||  ||  || ||
|-
|-
| rlocusplot || style="background: red;" | no ||  ||  || || ||
| controlSystemDesigner || style="background: red;" | no ||  ||  || ||
|-
|-
| controlSystemDesigner || style="background: red;" | no ||  ||  || || ||
| sisoinit || style="background: red;" | no ||  ||  || ||
|-
|-
| sisoinit || style="background: red;" | no ||  ||  || || ||
| rowspan="12" | Linear-Quadratic-Gaussian Control || lqr || style="background: green;" | yes || lqr.m ||  || ||
|-
|-
| rowspan="12" | Linear-Quadratic-Gaussian Control || lqr || style="background: green;" | yes || lqr.m ||  || || ||
| lqry || style="background: red;" | no ||  ||  || ||
|-
|-
| lqry || style="background: red;" | no ||  ||  || || ||
| lqi || style="background: red;" | no ||  ||  || ||
|-
|-
| lqi || style="background: red;" | no ||  ||  || || ||
| dlqr || style="background: green;" | yes || dlqr.m ||  || ||
|-
|-
| dlqr || style="background: green;" | yes || dlqr.m ||  || || ||
| lqrd || style="background: red;" | no ||  ||  || ||
|-
|-
| lqrd || style="background: red;" | no ||  ||  || || ||
| kalman || style="background: green;" | yes || kalman.m ||  || ||
|-
|-
| kalman || style="background: green;" | yes || kalman.m ||  || || ||
| kalmd || style="background: red;" | no ||  ||  || ||
|-
|-
| kalmd || style="background: red;" | no ||  ||  || || ||
| lqg || style="background: red;" | no ||  ||  || ||
|-
|-
| lqg || style="background: red;" | no ||  ||  || || ||
| lqgreg || style="background: red;" | no ||  ||  || ||
|-
|-
| lqgreg || style="background: red;" | no ||  ||  || || ||
| lqgtrack || style="background: red;" | no ||  ||  || ||
|-
|-
| lqgtrack || style="background: red;" | no ||  ||  || || ||
| augstate || style="background: red;" | no ||  ||  || ||
|-
|-
| augstate || style="background: red;" | no ||  ||  || || ||
| norm || style="background: green;" | yes || @lti/norm.m ||  || ||
|-
|-
| norm || style="background: green;" | yes || @lti/norm.m  ||  || || ||
| rowspan="3" | Pole Placement || estim || style="background: green;" | yes || estim.m  ||  || ||
|-
|-
| rowspan="4" | Pole Placement || estim || style="background: green;" | yes || estim.m  ||  || || ||
| place || style="background: green;" | yes || place.m  ||  || ||
|-
|-
| place || style="background: green;" | yes || place.m  ||  || || ||
| reg || style="background: red;" | no ||  ||  || ||
|-
| acker || style="background: green;" | yes || acker.m  ||  || || ||
|-
| reg || style="background: red;" | no ||  ||  || ||  
|-
|-
|}
|}
Line 423: Line 417:
{| class="wikitable"  
{| class="wikitable"  
|-
|-
! Function !! Implemented !! File !! Number of Tests !! Status !! SLICOT functions !! Priority (0-2)
! Function !! Implemented !! File !! Status !! SLICOT functions !! Priority
|-
| lyap || style="background: green;" | yes || lyap.m ||  || || ||
|-
|-
| lyapchol || style="background: green;" | yes || lyapchol.m ||  || || ||
| lyap || style="background: green;" | yes || lyap.m ||  || ||
|-
|-
| dlyap || style="background: green;" | yes || dlyap.m ||  || || ||
| lyapchol || style="background: green;" | yes || lyapchol.m ||  || ||
|-
|-
| dlyapchol || style="background: green;" | yes || dlyapchol.m ||  || || ||
| dlyap || style="background: green;" | yes || dlyap.m ||  || ||
|-
|-
| care || style="background: green;" | yes || care.m ||  || || ||
| dlyapchol || style="background: green;" | yes || dlyapchol.m ||  || ||
|-
|-
| dare || style="background: green;" | yes || dare.m ||  || || ||
| care || style="background: green;" | yes || care.m ||  || ||
|-
|-
| gcare || style="background: red;" | no || ||  || || ||
| dare || style="background: green;" | yes || dare.m ||  || ||
|-
|-
| gdare || style="background: red;" | no || ||  || || ||
| gcare || style="background: red;" | no || ||  || ||
|-
|-
| icare || style="background: red;" | no || ||  || || ||
| gdare || style="background: red;" | no || ||  || ||
|-
|-
| idare || style="background: red;" | no || ||  || || ||
| ctrb || style="background: green;" | yes || ctrb.m ||  || ||
|-
|-
| ctrb || style="background: green;" | yes || ctrb.m ||  || || ||
| obsv || style="background: green;" | yes || obsv.m ||  || ||
|-
|-
| obsv || style="background: green;" | yes || obsv.m ||  || || ||
| ctrbf || style="background: green;" | yes || ctrbf.m ||  || ||
|-
|-
| ctrbf || style="background: green;" | yes || ctrbf.m ||  || || ||
| obsvf || style="background: green;" | yes || obsvf.m ||  || ||
|-
|-
| obsvf || style="background: green;" | yes || obsvf.m ||  || || ||
| gram || style="background: green;" | yes || gram.m ||  || ||
|-
|-
| gram || style="background: green;" | yes || gram.m ||  || || ||
| bdschur || style="background: red;" | no ||  ||  || ||
|-
| bdschur || style="background: red;" | no ||  ||  || || ||
|-
|-
|}
|}


== Examples ==
== Some very basic examples ==
 
=== PT1 / Low-pass filter step response ===


=== PT1/low-pass filter step response ===
<!-- {{SyntaxHighlight| -->
<!-- {{SyntaxHighlight| -->
{{Code|Creating a transfer function and plotting its response|<syntaxhighlight lang="octave" style="font-size:14px">
{{Code|Creating a transfer function and plotting its response|<syntaxhighlight lang="octave" style="font-size:13px">
  T1 = 0.4;             # time constant
  T1=0.4;               # time constant
  P = tf([1], [T1 1]);  # create transfer function model
  P=tf([1], [T1 1])     # create transfer function model
  step(P, 2)            # plot step response
  step(P,2)            # plot step response


  #add some common markers like the tangent line at the origin, which crosses lim(n->inf) f(t) at t=T1
  #add some common markers like the tangent line at the origin, which crosses lim(n->inf) f(t) at t=T1
  hold on
  hold on
  plot ([0 T1], [0 1], "--", 'color', [.75 .75 .75])
  plot ([0 T1], [0 1],"g")
  plot ([T1 T1], [0 1], "--", 'color', [.75 .75 .75])
  plot ([T1 T1], [0 1],"k")
plot ([0 T1], [1-1/e 1-1/e],"m")
  hold off
  hold off
</syntaxhighlight>}}
</syntaxhighlight>}}
Line 478: Line 468:
[[File:Pt1.png|600px]]
[[File:Pt1.png|600px]]


==== Bode Diagram with TikZ/PGFplots ====
Try also bode(P)!  
 
(a first order low-pass filter has -3db magnitude at f=1/T1)  
We use the same system as before but we draw now with <code style="font-size:14px; border:solid lightgray 1px; padding: 2px">bode(P)</code> a bode diagram.
The output is written to a .csv file.
 
<!-- {{SyntaxHighlight| -->
{{Code|Creating a transfer function and calculating its bode diagram|<syntaxhighlight lang="octave" style="font-size:14px">
T1 = 0.4;              # time constant
P = tf([1], [T1 1]);
 
[mag, pha, w] = bode(P);
 
csvwrite("dat/bode_p.csv", [w', 20*log10(mag), pha]);
</syntaxhighlight>}}
 
We can then invoke LaTeX with the following .tex file
 
<!-- {{SyntaxHighlight| -->
{{Code|Creating a bode diagram with pgfplots|<syntaxhighlight lang="latex" style="font-size:14px">
\documentclass[tikz]{standalone}
\usepackage{pgfplotstable}
\usepackage{siunitx}
\usetikzlibrary{pgfplots.groupplots}
 
\begin{document}
\pgfplotstableread[col sep=comma]{\detokenize{/path/to/csv/file/dat/bode_p.csv}}\datatable
\begin{tikzpicture}
\begin{groupplot}[
  group style={rows=2},
  width=0.8\textwidth,
  height=0.4\textwidth,
  xmajorgrids,
  ymajorgrids,
  enlarge x limits=false,
  xmode=log,
]
  \nextgroupplot[
    title={Bode Diagram of $P$},
    ylabel={Magnitude / \si{\decibel}},
  ]
  \addplot[blue,line width=1pt] table[x index=0,y index=1]{\datatable};
  \nextgroupplot[
    xlabel={Frequency / \si{\radian\per\second}},
    ylabel={Phase / \si{\degree}},
  ]
  \addplot[red,line width=1pt] table[x index=0,y index=2]{\datatable};
\end{groupplot}
\end{tikzpicture}
\end{document}
</syntaxhighlight>}}
 
to generate a beautiful bode diagram
 
[[File:bode_p.png]]
 
It can be seen that a first order low-pass filter has <math display="inline">-3\,dB</math> magnitude at <math display="inline">f=1/T_1=2.5\,rad/s</math>.
 
=== Inverted Pendulum ===
 
==== Model ====
 
A nonlinear model of the inverted pendulum can be derived by
 
<math>
\begin{cases}
  (M+m)\ddot{x}+c\dot{x}-ml\cos{\theta}\ddot{\theta}+ml\sin{\theta}\dot{\theta}^2&=f(t)\\
  -ml\ddot{x}\cos{\theta}+(ml^2+I)\ddot{\theta}+b\dot{\theta}+mgl\sin{\theta}&=0
\end{cases}\text{,}
</math>
 
where the variables are defined as
 
{|
! align="left" | Name
! align="left" | Definition
|-
|<math display="inline">M</math>
|Mass of the cart
|-
|<math display="inline">m</math>
|Mass of the pendulum
|-
|<math display="inline">c</math>
|Translational damping coefficient
|-
|<math display="inline">l</math>
|Length of the pendulum
|-
|<math display="inline">I</math>
|Inertia of the pendulum
|-
|<math display="inline">b</math>
|Rotational damping coefficient
|}
 
[[File:inverted_pendulum_new.png|frame|Schematic drawing of the inverted pendulum.]]
 
Linearization around the point <math display="inline">\theta=\pi</math> and substitution of <math display="inline">\theta'=\theta-\pi</math> (from here on in the analysis, <math display="inline">\theta'</math> will be written as <math display="inline">\theta</math>, but it should be noted that <math display="inline">\theta</math> now
measures from a new reference) leads to
 
<math>
\begin{cases}
(M+m)\ddot{x}+c\dot{x}+ml\ddot{\theta}&=f(t)\\
ml\dot{x}+(ml^2+I)\ddot{\theta}+b\dot{\theta}-mgl\theta&=0
\end{cases}\text{.}
</math>
 
This can be expressed in the frequency domain like
 
<math>
\begin{cases}
(M+m)s^2X(s)+csX(s)+mls^2\Theta(s)&=F(s)\\
mlsX(s)+(ml^2+I)s^2\Theta(s)+bs\Theta(s)-mgl\Theta(s)&=0
\end{cases}
</math>
 
==== Transfer functions ====
 
By dividing the state variables by the input one obtains the transfer functions
 
<math>
\begin{align}
G_1(s)&=\frac{X(s)}{F(s)}=\frac{\alpha_2s^2+\alpha_1s+\alpha_0}{\beta_4s^4+\beta_3s^3+\beta_2s^2+\beta_1s}\\
G_2(s)&=\frac{\Theta(s)}{F(s)}=\frac{\gamma_1s}{\beta_4s^3+\beta_3s^2+\beta_2s+\beta_1}
\end{align}
</math>
 
with
 
{|
|<math display="inline">\alpha_2=ml^2+I</math>
|-
|<math display="inline">\alpha_1=b</math>
|-
|<math display="inline">\alpha_0=-mgl</math>
|-
|<math display="inline">\beta_4=(M+m)(ml^2+I)-m^2l^2</math>
|-
|<math display="inline">\beta_3=(M+m)b+(ml^2+I)c</math>
|-
|<math display="inline">\beta_2=-(M+m)mgl+bc</math>
|-
|<math display="inline">\beta_1=-mglc</math>
|-
|<math display="inline">\gamma_1=-ml</math>
|}
 
This can be expressed in Octave
 
<!-- {{SyntaxHighlight| -->
{{Code|Creating the transfer functions for the inverted pendulum|<syntaxhighlight lang="octave" style="font-size:14px">
m = 0.15;
l = 0.314;
M = 1.3;
I = 0;
g = 9.80665;
b = 20;
c = 20;
 
G1 = tf([m*l^2+I b -m*g*l],
        [(M+m)*(m*l^2+I)-m^2*l^2 (M+m)*b+(m*l^2+I)*c -(M+m)*m*g*l+b*c -m*g*l*c 0]);
G2 = tf([-m*l],
        [(M+m)*(m*l^2+I)-m^2*l^2 (M+m)*b+(m*l^2+I)*c -(M+m)*m*g*l+b*c -m*g*l*c]);
</syntaxhighlight>}}
 
and by invoking the <code style="font-size:14px; border:solid lightgray 1px; padding: 2px">bode</code> command
 
<!-- {{SyntaxHighlight| -->
{{Code|Creating Bode plots for the inverted pendulum|<syntaxhighlight lang="octave" style="font-size:14px">
bode(G1);
bode(G2);
</syntaxhighlight>}}
 
one obtains the bode diagrams of the two transfer functions.
 
<div><ul>
<li style="display: inline-block;"> [[File:bode_g1.png|frame|Bode diagram of the cart movement transfer function.]] </li>
<li style="display: inline-block;"> [[File:bode_g2.png|frame|Bode diagram of the pendulums rotation transfer function.]] </li>
</ul></div>


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