~ubuntu-branches/ubuntu/hoary/scilab/hoary

<SP>: the t-by-m input-data sequence matrix (input when jobx0 = 1 and comuse = 2, or comuse = 1). Column j of U contains the t values of the j-th input component for consecutive time increments.</SP>

118

</PARAM_DESCRIPTION>

119

</PARAM_ITEM>

120

<PARAM_ITEM>

121

<PARAM_NAME>tol</PARAM_NAME>

122

<PARAM_DESCRIPTION>

123

<SP>: optionnal, tolerance used for estimating the rank of

124

matrices. If tol > 0, then the given value of tol is used as

125

a lower bound for the reciprocal condition number; an m-by-n matrix

126

whose estimated condition number is less than 1/tol is considered

127

to be of full rank. Default: m*n*epsilon_machine where

128

epsilon_machine is the relative machine precision.</SP>

129

</PARAM_DESCRIPTION>

130

</PARAM_ITEM>

131

<PARAM_ITEM>

132

<PARAM_NAME>printw</PARAM_NAME>

133

<PARAM_DESCRIPTION>

134

<SP>:optionnal, switch for printing the warning messages.</SP>

135

<PARAM_INDENT>

136

<PARAM_ITEM>

137

<PARAM_NAME>= </PARAM_NAME>

138

<PARAM_DESCRIPTION>

139

<SP>1: print warning messages;</SP>

140

</PARAM_DESCRIPTION>

141

</PARAM_ITEM>

142

<PARAM_ITEM>

143

<PARAM_NAME>= </PARAM_NAME>

144

<PARAM_DESCRIPTION>

145

<SP>0: do not print warning messages.</SP>

146

</PARAM_DESCRIPTION>

147

</PARAM_ITEM>

148

</PARAM_INDENT>

149

150

Default: printw = 0.

151

152

</PARAM_DESCRIPTION>

153

</PARAM_ITEM>

154

<PARAM_ITEM>

155

<PARAM_NAME>ldwork</PARAM_NAME>

156

<PARAM_DESCRIPTION>

157

<SP>: (optional) the workspace size. Default : computed by the formula LDWORK = MAX( minimum workspace size needed, 2*CSIZE/3, CSIZE - ( m + l )*t - 2*n*( n + m + l ) - l*m ) where CSIZE is the cache size in double precision words.</SP>

158

</PARAM_DESCRIPTION>

159

</PARAM_ITEM>

160

<PARAM_ITEM>

161

<PARAM_NAME>x0</PARAM_NAME>

162

<PARAM_DESCRIPTION>

163

<SP>: initial state vector</SP>

164

</PARAM_DESCRIPTION>

165

</PARAM_ITEM>

166

<PARAM_ITEM>

167

<PARAM_NAME>Br</PARAM_NAME>

168

<PARAM_DESCRIPTION>

169

<SP>: system input matrix</SP>

170

</PARAM_DESCRIPTION>

171

</PARAM_ITEM>

172

<PARAM_ITEM>

173

<PARAM_NAME>Dr</PARAM_NAME>

174

<PARAM_DESCRIPTION>

175

<SP>: system direct feedthrough matrix</SP>

176

</PARAM_DESCRIPTION>

177

</PARAM_ITEM>

178

<PARAM_ITEM>

179

<PARAM_NAME>V</PARAM_NAME>

180

<PARAM_DESCRIPTION>

181

<SP>: the n-by-n orthogonal matrix which reduces A to a real Schur form (output when jobx0 = 1 or comuse = 1).</SP>

182

</PARAM_DESCRIPTION>

183

</PARAM_ITEM>

184

<PARAM_ITEM>

185

<PARAM_NAME>rcnd</PARAM_NAME>

186

<PARAM_DESCRIPTION>

187

<SP>: (optional) the reciprocal condition numbers of the matrices involved in rank decisions.</SP>

188

</PARAM_DESCRIPTION>

189

</PARAM_ITEM>

190

</PARAM_INDENT>

191

</PARAM>

192

193

194

findBD function for estimating the initial state and the system

195

matrices B and D of a discrete-time system, using SLICOT routine

196

IB01CD.

197

198

199

<![CDATA[

200

201

[x0,Br,V,rcnd] = findBD(1,1,1,A,C,Y,U)

202

[x0,Br,Dr,V,rcnd] = findBD(1,1,2,A,C,Y,U)

203

[Br,V,rcnd] = findBD(2,1,1,A,C,Y,U)

204

[B,Dr,V,rcnd] = findBD(2,1,2,A,C,Y,U)

205

[x0,V,rcnd] = findBD(1,2,1,A,B,C,Y,U)

206

[x0,V,rcnd] = findBD(1,2,2,A,B,C,D,Y,U)

207

[x0,rcnd] = findBD(2,2) // (Set x0 = 0, rcnd = 1)

208

[x0,V,rcnd] = findBD(1,3,A,C,Y)

209

]]>

210

</VERBATIM>

211

212

Note: the example lines above may contain at the end the parameters

213

tol, printw, ldwork.

214

215

216

FINDBD estimates the initial state and/or the system matrices Br and Dr

217

of a discrete-time system, given the system matrices A, C, and possibly

218

B, D, and the input and output trajectories of the system.

219

220

221

The model structure is :

222

223

224

<![CDATA[

225

x(k+1) = Ax(k) + Bu(k), k >= 1,

226

y(k) = Cx(k) + Du(k),

227

]]>

228

</VERBATIM>

229

230

where

231

232

x(k) is the n-dimensional state vector (at time k),

233

234

235

u(k) is the m-dimensional input vector,

236

237

238

y(k) is the l-dimensional output vector,

239

240

241

and A, B, C, and D are real matrices of appropriate dimensions.

242

243

</DESCRIPTION>

244

245

246

247

<SP>The n-by-m system input matrix B is an input parameter when jobx0 = 1 and comuse = 2, and it is an output parameter when comuse = 1.</SP>

248

</ITEM>

249

250

<SP>The l-by-m system matrix D is an input parameter when jobx0 = 1, comuse = 2 and job = 2, and it is an output parameter when comuse = 1 and job = 2.</SP>

251

</ITEM>

252

253

<SP>The n-vector of estimated initial state x(0) is an output parameter when jobx0 = 1, but also when jobx0 = 2 and comuse <= 2, in which case it is set to 0.</SP>

254

</ITEM>

255

256

<SP>If ldwork is specified, but it is less than the minimum workspace size needed, that minimum value is used instead.</SP>

257

</ITEM>

258

</ITEMIZE>

259

</SECTION>

260

261

<![CDATA[

262

//generate data from a given linear system

263

A = [ 0.5, 0.1,-0.1, 0.2;

264

0.1, 0, -0.1,-0.1;

265

-0.4,-0.6,-0.7,-0.1;

266

0.8, 0, -0.6,-0.6];

267

B = [0.8;0.1;1;-1];

268

C = [1 2 -1 0];

269

SYS=syslin(0.1,A,B,C);

270

nsmp=100;

271

U=prbs_a(nsmp,nsmp/5);

272

Y=(flts(U,SYS)+0.3*rand(1,nsmp,'normal'));

273

274

// Compute R

275

S=15;L=1;

276

[R,N,SVAL] = findR(S,Y',U');

277

278

N=3;

279

METH=3;TOL=-1;

280

[A,C] = findAC(S,N,L,R,METH,TOL);

281

[X0,B,D] = findBD(1,1,2,A,C,Y',U')

282

SYS1=syslin(1,A,B,C,D,X0);

283

284

Y1=flts(U,SYS1);

285

xbasc();plot2d((1:nsmp)',[Y',Y1'])

286

]]>

287

</EXAMPLE>

288

<SEE_ALSO>

289

<SEE_ALSO_ITEM>

290

<LINK>inistate</LINK>

291

</SEE_ALSO_ITEM>

292

<SEE_ALSO_ITEM>

293

<LINK>findx0BD</LINK>

294

</SEE_ALSO_ITEM>

295

<SEE_ALSO_ITEM>

296

<LINK>findABCD</LINK>

297

</SEE_ALSO_ITEM>

298

<SEE_ALSO_ITEM>

299

<LINK>findAC</LINK>

300

</SEE_ALSO_ITEM>

301

<SEE_ALSO_ITEM>

302

<LINK>findBD</LINK>

303

</SEE_ALSO_ITEM>

304

</SEE_ALSO>

305

<AUTHOR>V. Sima, Katholieke Univ. Leuven, Belgium, May 2000.

306

(Revisions: V. Sima, July 2000)</AUTHOR>

307

</MAN>

Older »