www.pudn.com > Closid30.rar > Sysid97.ps, change:1997-07-18,size:81424b


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E end 
%%EndProlog 
%%BeginSetup 
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TeXDict begin 
%%PaperSize: A4 
 
%%EndSetup 
%%Page: 1 1 
1 0 bop 179 516 a Ft(CLOSID)16 b(-)f(A)h(CLOSED-LOOP)f(SYSTEM)h 
(IDENTIFICA)l(TION)i(TOOLBO)o(X)772 565 y(F)o(OR)e(MA)l(TLAB)372 
648 y(P)o(aul)e(M.J.)j(V)l(an)e(den)g(Hof)p Fs(,)f Ft(Ra)o(ymond)g(A.)i 
(de)g(Callafon)1409 633 y Fr(1)1441 648 y Fs(and)672 
698 y Ft(Edwin)f(T.)h(v)m(an)h(Donk)o(elaar)1190 683 
y Fr(2)460 848 y Fq(Me)n(chanic)n(al)e(Engine)n(ering)h(Systems)f(and)g 
(Contr)n(ol)f(Gr)n(oup,)240 898 y(Delft)g(University)h(of)f(T)m(e)n 
(chnolo)n(gy,)h(Mekelwe)n(g)g(2,)g(2628)g(CD)g(Delft,)f(The)h 
(Netherlands)567 947 y(E-mail:)f(p.m.j.vandenhof@wbmt.tudelft.nl)172 
1142 y Ft(Abstract.)i Fs(A)e(closed-lo)q(op)g(system)g(iden)o 
(ti\014cation)f(to)q(olb)q(o)o(x)g(for)h Fp(Ma)m(tlab)i 
Fs(is)e(presen)o(ted,)h(in-)172 1192 y(cluding)e(a)f(user-friendly)h 
(graphical)f(user)i(in)o(terface,)f(that)g(comm)o(unicates)d(with)j 
(MathW)m(ork's)172 1242 y(System)k(Iden)o(ti\014cation)f(T)m(o)q(olb)q 
(o)o(x)g(\(SITB\),)h(v)o(ersion)g(4.0.)e(With)h(the)i(CLOSID)f(to)q 
(olb)q(o)o(x)e(it)i(is)172 1291 y(p)q(ossible)e(to)f(iden)o(tify)f 
(linear)g(\(parametric\))h(mo)q(dels)f(on)g(the)i(basis)f(of)f(exp)q 
(erimen)o(tal)h(data)f(ob-)172 1341 y(tained)h(from)e(a)h(plan)o(t)g 
(that)g(is)h(op)q(erating)f(under)i(the)f(presence)i(of)d(a)g(con)o 
(troller.)g(The)h(to)q(olb)q(o)o(x)172 1391 y(is)e(designed)f(as)h(an)f 
(add-on)g(to)g(the)g(SITB,)h(and)f(has)g(b)q(een)h(giv)o(en)f(a)g 
(similar)e(setup.)j(It)f(comprises)172 1441 y(sev)o(eral)k(closed-lo)q 
(op)e(iden)o(ti\014cation)g(metho)q(ds)h(\(b)q(oth)g(classical)f(and)h 
(more)f(recen)o(t)i(ones\),)f(and)172 1491 y(includes)h(to)q(ols)e(for) 
h(ev)n(aluation)e(of)i(closed-lo)q(op)f(mo)q(del)g(prop)q(erties.)172 
1619 y Ft(Keyw)o(ords.)h Fs(Matlab)f(to)q(olb)q(o)o(x;)g(system)g(iden) 
o(ti\014cation;)g(closed-lo)q(op)h(iden)o(ti\014cation;)172 
1669 y(soft)o(w)o(are)g(to)q(ols.)195 1838 y(1.)20 b(INTR)o(ODUCTION) 
-111 1938 y(No)o(w)o(ada)o(ys)h(there)i(are)f(w)o(ell-supp)q(orted)g 
(and)g(user)g(friendly)-111 1988 y(to)q(ols)15 b(a)o(v)n(ailable)f(for) 
h(the)h(iden)o(ti\014cation)f(of)g(\(linear\))h(systems)-111 
2037 y(on)e(the)g(basis)g(of)f(exp)q(erimen)o(tal)g(data.)g(See)i(in)f 
(particular)f(the)-111 2087 y(Math)o(w)o(ork's)19 b(System)g(Iden)o 
(ti\014cation)g(T)m(o)q(olb)q(o)o(x)e(SITB,)j(v)o(er-)-111 
2137 y(sion)g(4.0,)e(whic)o(h)i(is)g(equipp)q(ed)h(with)f(a)g 
(graphical)f(user)i(in-)-111 2187 y(terface.)e(This)f(enables)g(the)h 
(user)g(to)f(iden)o(tify)f(and)h(v)n(alidate)-111 2237 
y(mo)q(dels)12 b(in)g(di\013eren)o(t)i(t)o(yp)q(es)g(of)e(mo)q(del)g 
(structures)j(b)o(y)e(mouse-)-111 2287 y(clic)o(king,)g(rather)j(than)e 
(b)o(y)h(en)o(tering)g(\(complex\))f(commands.)-111 2336 
y(Additionally)f(there)j(is)e(users')i(supp)q(ort)f(in)f(terms)h(of)f 
(graphi-)-111 2386 y(cal)e(to)q(ols)g(for)h(mo)q(del)e(ev)n(aluation)g 
(as)i(w)o(ell)e(as)i(supp)q(ort)g(for)g(e.g.)-111 2436 
y(b)q(o)q(okk)o(eeping)h(of)f(iden)o(ti\014ed)h(mo)q(dels.)-111 
2486 y(In)h(the)g(to)q(ols)g(that)f(are)i(curren)o(tly)f(a)o(v)n 
(ailable,)d(there)k(are)g(only)-111 2536 y(limited)g(p)q(ossibilities)h 
(to)h(iden)o(tify)g(mo)q(dels)f(on)h(the)g(basis)g(of)-111 
2585 y(data)i(that)h(is)g(obtained)g(under)g(closed-lo)q(op)g(exp)q 
(erimen)o(tal)p -111 2633 600 2 v -111 2698 a Fo(1)-76 
2710 y Fn(The)9 b(researc)o(h)d(of)i(Ra)o(ymond)e(de)h(Callafon)g(is)i 
(supp)q(orted)c(b)o(y)j(the)f(Dutc)o(h)-111 2752 y(Institute)i(of)i 
(Systems)f(and)h(Con)o(trol)f(\(DISC\).)-111 2780 y Fo(2)-76 
2792 y Fn(The)f(researc)o(h)d(of)i(Edwin)h(v)n(an)e(Donk)o(elaar)f(is)j 
(supp)q(orted)d(b)o(y)i(the)f(Dutc)o(h)-111 2833 y(T)m(ec)o(hnology)i 
(F)m(oundation)g(\(STW\))i(under)f(con)o(tract)g(D)o(WT55.3618)987 
1839 y Fs(conditions.)f(This)g(particular)g(exp)q(erimen)o(tal)f 
(situation)h(-)g(whic)o(h)987 1888 y(often)17 b(o)q(ccurs)h(in)e 
(practical)h(situations)f(-)h(requires)h(a)e(sp)q(ecial)987 
1938 y(treatmen)o(t,)h(in)g(the)h(sense)h(that)e(b)q(esides)i(input)e 
(and)g(output)987 1988 y(signals)e(of)g(a)g(plan)o(t,)f(measured)i 
(external)g(excitation)f(signals)987 2038 y(can)g(b)q(e)h(in)o(v)o(olv) 
o(ed,)d(as)h(w)o(ell)h(as)f(some)g(\(p)q(ossibly)h(kno)o(wn\))f(con-) 
987 2088 y(troller)g(that)g(is)g(implemen)o(ted)d(on)j(the)h(system.) 
987 2162 y(The)d(curren)o(t)i(to)q(olb)q(o)o(x)c(CLOSID)i(o\013ers)g 
(the)h(follo)o(wing)8 b(exten-)987 2212 y(sion)14 b(to)g(the)g(iden)o 
(ti\014cation)f(to)q(olb)q(o)o(x)g(SITB:)1034 2287 y 
Fm(\017)20 b Fs(It)10 b(pro)o(vides)g(a)f(graphical)g(user)i(in)o 
(terface)f(supp)q(orted)h(to)q(ol)1075 2337 y(for)i(iden)o 
(ti\014cation)f(of)h(mo)q(dels)f(from)f(closed-lo)q(op)i(obser-)1075 
2387 y(v)n(ations;)1034 2436 y Fm(\017)20 b Fs(It)15 
b(enables)h(the)g(use)g(of)f(external)h(excitation)f(signals)f(as)1075 
2486 y(w)o(ell)f(as)h(a)g(\(p)q(ossibly\))g(kno)o(wn)f(con)o(troller)h 
(in)f(the)i(lo)q(op;)1034 2536 y Fm(\017)20 b Fs(It)15 
b(comm)o(unicates)e(with)i(the)g(SITB,)g(meaning)f(that)h(for)1075 
2586 y(the)g(actual)f(estimation)f(part)i(of)f(the)h(closed-lo)q(op)f 
(iden-)1075 2636 y(ti\014cation)j(metho)q(ds,)g(SITB)h(is)g 
(automatically)c(op)q(ened)1075 2685 y(and)19 b(applied,)f(while)h(in)g 
(the)g(CLOSID)g(to)q(ol)g(the)h(data)1075 2735 y(pro)q(cessing)d(and)e 
(the)h(\(closed-lo)q(op\))g(mo)q(del)e(pro)q(cessing)1075 
2785 y(is)h(p)q(erformed.)g(Therefore)h(full)e(p)q(erformance)h(and)g 
(\015ex-)p eop 
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2 1 bop -111 1115 a Fs(Fig.)13 b(1.)g(CLOSID)h(main)d(windo)o(w)-23 
1202 y(ibilit)o(y)19 b(of)h(the)i(estimation)d(metho)q(ds)i(in)f(SITB)h 
(is)g(re-)-23 1252 y(tained.)-65 1301 y Fm(\017)g Fs(It)c(pro)o(vides)g 
(ev)n(aluation)e(of)h(mo)q(dels)g(in)h(terms)f(of)g(their)-23 
1351 y(closed-lo)q(op)c(prop)q(erties,)i(as)f(e.g.)f(sensitivit)o(y)g 
(functions,)-23 1401 y(complemen)o(tary)e(sensitivities,)j(closed-lo)q 
(op)g(p)q(oles,)f(etc.)-111 1476 y(In)19 b(the)h(curren)o(t)h(v)o 
(ersion,)d(the)i(graphical)e(user)j(in)o(terface)e(of)-111 
1526 y(CLOSID)13 b(is)g(able)g(to)f(deal)h(with)g(SISO)g 
(\(single-input,)f(single-)-111 1575 y(output\))i(mo)q(dels)f(only)m(.) 
117 1783 y(2.)20 b(MAIN)14 b(CLOSID-WINDO)o(W)-111 1882 
y(The)i(graphical)f(user)h(in)o(terface)h(of)e(the)h(CLOSID)f(to)q(olb) 
q(o)o(x)g(is)-111 1932 y(op)q(ened)k(b)o(y)f(en)o(tering)h 
Fl(closid)e Fs(in)h(the)h Fp(Ma)m(tlab)h Fs(command)-111 
1982 y(windo)o(w.)8 b(This)i(op)q(ens)g(the)g(main)e(windo)o(w)g(as)i 
(sho)o(wn)g(in)f(Figure)-111 2032 y(1.)k(The)h(main)e(windo)o(w)h(sho)o 
(ws)h(the)h(follo)o(wing)c(basic)j(parts:)-65 2106 y 
Fm(\017)21 b Fs(a)c Ft(data)j(b)q(oard)d Fs(on)h(the)h(left)e(upp)q(er) 
i(part,)f(where)h(im-)-23 2156 y(p)q(orted)h(data)f(sets)i(are)e 
(represen)o(ted)k(b)o(y)c(colored)h(line-)-23 2206 y(icons,)13 
b(that)h(can)g(b)q(e)h(selected)g(b)o(y)f(a)g(mouse)f(action.)-65 
2256 y Fm(\017)21 b Fs(a)15 b Ft(con)o(trolle)o(r)g(b)q(oard)f 
Fs(on)h(the)h(left)g(lo)o(w)o(er)f(part,)g(where)-23 
2306 y(imp)q(orted)8 b(con)o(trollers)h(are)h(represen)o(ted)i(b)o(y)d 
(colored)h(line-)-23 2355 y(icons,)j(with)h(similar)d(selection)k 
(options.)-65 2405 y Fm(\017)21 b Fs(an)9 b Ft(iden)o(ti)o(\014cati)o 
(on)e(men)o(u)h Fs(in)h(the)h(middle;)d(this)i(p)q(op-up)-23 
2455 y(men)o(u)j(pro)o(vides)i(the)h(user)f(with)g(a)f(list)g(of)h 
(iden)o(ti\014cation)-23 2505 y(metho)q(ds)f(that)h(can)g(b)q(e)h 
(applied.)-65 2555 y Fm(\017)21 b Fs(a)14 b Ft(mo)q(del)i(b)q(oard)e 
Fs(on)h(the)h(righ)o(t)f(upp)q(er)h(part,)f(sho)o(wing)-23 
2604 y(iden)o(ti\014ed)k(or)h(imp)q(orted)f(mo)q(dels)f(of)h(the)i 
(plan)o(t)e(to)g(b)q(e)-23 2654 y(iden)o(ti\014ed.)-65 
2704 y Fm(\017)i Fs(a)13 b Ft(mo)q(del)h(ev)m(aluation)d 
Fs(area,)i(con)o(taining)f(c)o(hec)o(k)i(b)q(o)o(xes)-23 
2754 y(for)h(the)h(application)e(of)h(sev)o(eral)h(\(closed-lo)q(op\))f 
(ev)n(alua-)-23 2804 y(tion)10 b(pro)q(cedures)k(for)c(the)i(mo)q(dels) 
e(on)h(the)h(mo)q(del)d(b)q(oard.)987 1202 y(Besides)24 
b(the)g(con)o(troller)e(b)q(oard,)g(the)h(comp)q(osition)e(of)h(the)987 
1252 y(CLOSID)15 b(main)d(windo)o(w)h(is)h(v)o(ery)h(similar)d(to)i 
(the)h(main)d(win-)987 1301 y(do)o(w)k(of)g(the)h(SITB.)g(This)f(con)o 
(troller)h(b)q(oard)f(is)g(required,)h(as)987 1351 y(some)c(of)f(the)i 
(closed-lo)q(op)f(iden)o(ti\014cation)g(metho)q(ds)f(need)j(the)987 
1401 y(a)f(priori)f(kno)o(wledge)h(of)f(the)i(con)o(troller.)987 
1451 y(Additionally)m(,)10 b(this)j(enables)h(the)f(user)h(to)f(ev)n 
(aluate)f(the)i(mo)q(d-)987 1501 y(els)d(in)e(the)i(presence)i(of)c(a)h 
(\(user-c)o(hosen\))i(feedbac)o(k)f(con)o(troller.)987 
1550 y(Data)h(sets,)i(con)o(trollers)f(and)f(mo)q(dels)g(can)g(b)q(e)i 
(imp)q(orted)d(from)987 1600 y(the)19 b Fp(Ma)m(tlab)h 
Fs(w)o(orkspace,)e(through)g(selecting)h(the)g(resp)q(ec-)987 
1650 y(tiv)o(e)14 b(p)q(op-up)g(men)o(us)f(for)h(data,)f(con)o(troller) 
h(and)f(mo)q(del.)987 1700 y(The)27 b(closed-lo)q(op)f(con\014guration) 
g(that)h(is)f(considered)i(all)987 1750 y(through)18 
b(the)g(to)q(olb)q(o)o(x)f(is)g(depicted)i(in)e(Figure)g(2.)g(It)h(is)f 
(also)987 1800 y(displa)o(y)o(ed)d(in)f(the)i Ft(data)g(imp)q(ort)d 
Fs(windo)o(w.)p 1265 1910 118 4 v 1265 2020 4 111 v 1307 
1979 a Fk(C)p 1379 2020 V 1265 2023 118 4 v 1596 1910 
V 1596 2020 4 111 v 302 w(G)p 1710 2020 V 1596 2023 118 
4 v 1158 1965 a Fj(d)1103 1993 y Fr(+)1124 2013 y Fi(\000)1489 
1965 y Fj(d)1456 1935 y Fr(+)1434 1955 y(+)1821 1965 
y Fj(d)1788 1935 y Fr(+)1765 1955 y(+)p 1048 1966 100 
2 v 1105 1965 a Fh(-)p 1489 1954 2 100 v 1489 1954 a(?)p 
1169 1966 100 2 v 1227 1965 a(-)p 1157 2076 2 100 v 1158 
2018 a(6)p 1379 1966 100 2 v 1437 1965 a(-)p 1500 1966 
V 79 w(-)p 1158 2077 663 2 v 1710 1966 100 2 v 168 w(-)p 
1832 1966 V 80 w(-)p 1875 2076 2 111 v 1820 1954 2 78 
v 1821 1954 a(?)p 1545 2077 332 2 v 1511 1873 a Fk(r)1530 
1879 y Fr(1)1048 1939 y Fk(r)1067 1945 y Fr(2)1522 1950 
y Fk(u)1832 1895 y(v)1898 1939 y(y)987 2159 y Fs(Fig.)h(2.)g(Closed-lo) 
q(op)g(system)h(con\014guration)987 2256 y(A)e(data)g(set)h(is)f(comp)q 
(osed)g(of)f(exp)q(erimen)o(tal)g(data)h Fm(f)p Fk(u;)7 
b(y)q Fm(g)k Fs(o)o(v)o(er)987 2306 y(a)20 b(giv)o(en)e(time)h 
(horizon,)f(together)j(with)e(either)h(one)g(of)f(the)987 
2355 y(external)10 b(excitation)g(signals)f Fk(r)1481 
2361 y Fr(1)1509 2355 y Fs(and/or)g Fk(r)1662 2361 y 
Fr(2)1680 2355 y Fs(.)g(Data)g(sets)i(can)f(b)q(e)987 
2405 y(view)o(ed)15 b(on)f(screen)i(in)e(terms)g(of)f(time)g(sequences) 
k(and)d(p)q(o)o(w)o(er)987 2455 y(sp)q(ectra,)20 b(b)o(y)e(clic)o(king) 
g(on)g(the)h(corresp)q(onding)g(c)o(hec)o(k)h(b)q(o)o(xes)987 
2505 y(under)15 b(the)g(data)e(b)q(oard.)987 2580 y(Mo)q(dels,)21 
b(as)g(w)o(ell)e(as)i(con)o(trollers,)g(can)f(b)q(e)i(imp)q(orted)d 
(from)987 2629 y(and)i(exp)q(orted)g(to)g(the)g Fp(Ma)m(tlab)g 
Fs(w)o(orkspace,)g(in)f(di\013eren)o(t)987 2679 y(formats:)1034 
2754 y Fm(\017)g Fs([)p Fk(num)p Fs(;)7 b Fk(den)p Fs(]:)g(p)q 
(olynomial)f(co)q(e\016cien)o(ts)11 b(of)d(n)o(umerator)h(and)1075 
2804 y(denominator,)i(in)h(descending)i(p)q(o)o(w)o(ers)f(of)f 
Fk(z)r Fs(,)g(stac)o(k)o(ed)i(in)p eop 
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3 2 bop -23 116 a Fs(a)13 b(matrix)f(with)i(heigh)o(t)f(2.)-65 
166 y Fm(\017)21 b Fs([)p Fk(A)11 b(B)r Fs(;)c Fk(C)14 
b(D)q Fs(]:)f(state)h(space)g(matrices)e(\(A,B,C,D\))h(placed)-23 
216 y(in)g(a)h(system)f(matrix.)-65 265 y Fm(\017)21 
b Fk(theta)p Fs(:)13 b Fk(theta)p Fs(-format)f(as)i(used)h(in)e(the)i 
(SITB.)-111 340 y(The)e(particular)e(mo)q(del)g(imp)q(ort)g(windo)o(w)g 
(is)h(depicted)h(in)f(Fig-)-111 390 y(ure)j(3.)-111 1034 
y(Fig.)e(3.)g(Mo)q(del)h(imp)q(ort)e(windo)o(w)26 1160 
y(3.)20 b(CLOSED-LOOP)15 b(IDENTIFICA)m(TION)-111 1259 
y(The)g(CLOSID)f(to)q(olb)q(o)o(x)f(con)o(tains)h(\014v)o(e)g(iden)o 
(ti\014cation)g(meth-)-111 1309 y(o)q(ds)19 b(for)f(parametric)g(mo)q 
(del)f(iden)o(ti\014cation,)g(and)h(one)h(non-)-111 1359 
y(parametric)13 b(metho)q(d.)g(The)h(metho)q(ds)f(are)i(denoted)g(b)o 
(y)-97 1434 y(\(1\))21 b Ft(t)o(w)o(o-stage)12 b Fs(metho)q(d,)-97 
1484 y(\(2\))21 b Ft(indirect)10 b Fs(iden)o(ti\014cation,)-97 
1533 y(\(3\))21 b(iden)o(ti\014cation)9 b(with)g(a)h 
Ft(tailor-made)d Fs(parametrization,)-97 1583 y(\(4\))21 
b Ft(coprime)14 b(factor)f Fs(iden)o(ti\014cation,)-97 
1633 y(\(5\))21 b(iden)o(ti\014cation)14 b(in)h(the)g 
Ft(dual-Y)l(oula/Kucera)e Fs(param-)-23 1683 y(etrization,)-97 
1733 y(\(6\))21 b Ft(non-parametri)o(c)11 b Fs(\(sp)q(ectral\))16 
b(estimation.)-111 1807 y(F)m(or)f(details)h(on)g(the)g(di\013eren)o(t) 
h(metho)q(ds,)e(one)h(is)f(referred)j(to)-111 1857 y(the)c(references,) 
j(in)c(particular)h(to)g(V)m(an)f(den)h(Hof)g(\(1997\).)-111 
1932 y(The)20 b(metho)q(ds)f(are)h(all)e(c)o(haracterized)j(b)o(y)f 
(three)g(steps,)h(fo-)-111 1982 y(cussed)d(on)e(a)f(sp)q(eci\014c)j 
(closed-lo)q(op)d(ob)r(ject)i(that)f(is)g(going)f(to)-111 
2032 y(b)q(e)c(iden)o(ti\014ed.)g(The)g(three)h(steps)g(are)f(clearly)f 
(indicated)h(in)f(the)-111 2081 y(sev)o(eral)16 b(iden)o(ti\014cation)f 
(windo)o(ws)g(and)g(are)h(c)o(haracterized)i(as)-111 
2131 y(follo)o(ws.)-65 2206 y Fm(\017)j Ft(Construction)12 
b(of)k(auxiliary)d(i/o)i(signals)p Fs(.)-23 2256 y(A)k(\014rst)h(step)g 
(of)f(c)o(ho)q(osing/constructing)h(appropriate)-23 2306 
y(auxiliary)14 b(input)h(and)h(output)g(signals,)f(that)h(are)g(going) 
-23 2355 y(to)11 b(b)q(e)i(used)g(to)e(iden)o(tify)g(a)h(particular)f 
(transfer)i(function)-23 2405 y(ob)r(ject.)-65 2455 y 
Fm(\017)21 b Ft(Iden)o(ti\014cati)o(on)o Fs(.)-23 2505 
y(A)d(second)h(step)g(of)e(actual)h(iden)o(ti\014cation)f(of)g(the)i 
(con-)-23 2555 y(sidered)f(ob)r(ject,)h(b)o(y)e(estimating)f 
(parameters)i(through)-23 2604 y(a)13 b(least-squares)i(iden)o 
(ti\014cation)f(criterion.)-65 2654 y Fm(\017)21 b Ft(Calculate)14 
b(plan)o(t)g(mo)q(del)p Fs(.)-23 2704 y(F)m(rom)j(the)k(iden)o 
(ti\014ed)e(ob)r(ject)i(a)e(plan)o(t)g(mo)q(del)f(is)i(con-)-23 
2754 y(structed)26 b(and)e(this)g(plan)o(t)g(mo)q(del)f(is)h(copied)g 
(to)g(the)-23 2804 y(CLOSID)13 b(mo)q(del)g(b)q(oard.)987 
1021 y(Fig.)g(4.)g(Windo)o(w)g(for)h(coprime)e(factor)i(iden)o 
(ti\014cation)987 1262 y(By)h(c)o(ho)q(osing)f(one)g(of)f(the)i(iden)o 
(ti\014cation)f(metho)q(ds)f(from)g(the)987 1312 y Ft(iden)o 
(ti\014cati)o(on)18 b Fs(p)q(op-up)k(men)o(u,)e(a)i(particular)f(windo) 
o(w)g(is)987 1362 y(op)q(ened,)15 b(displa)o(ying)d(the)j(three)g 
(steps)g(men)o(tioned)e(ab)q(o)o(v)o(e.)987 1436 y(The)g(\014rst)f 
(step)h(is)f(trivial)f(for)g(some)g(metho)q(ds,)g(but)h(requires)i(a) 
987 1486 y(separate)h(iden)o(ti\014cation)e(for)g(some)g(others,)h(as)g 
(e.g.)e(the)i(iden-)987 1536 y(ti\014cation)20 b(of)f(the)i(sensitivit) 
o(y)f(function)g(for)g(the)g(t)o(w)o(o-stage)987 1586 
y(metho)q(d.)d(In)g(these)i(latter)f(cases,)g(quic)o(k-start)g(options) 
f(pro-)987 1636 y(vide)h(a)g(simple)f(means)g(to)h(construct)h(the)g 
(appropriate)f(sig-)987 1685 y(nals.)987 1735 y(Apart)g(from)f(the)h 
(\\tailor-made")d(approac)o(h,)i(all)g(iden)o(ti\014ca-)987 
1785 y(tion)g(metho)q(ds)f(will)f(p)q(erform)h(the)h(second)h(step)g(b) 
o(y)f(op)q(ening)987 1835 y Fp(Ma)m(tlab)n Fs('s)c(SITB)g 
(automatically)l(,)8 b(cop)o(ying)k(the)g(appropriate)987 
1885 y(signals)j(from)e(the)i(CLOSID)g(to)q(olb)q(o)o(x)f(to)h(the)g 
(data)g(b)q(oard)g(of)987 1934 y(SITB,)h(allo)o(wing)e(the)i(user)i(to) 
d(iden)o(tify)g(the)i(required)g(trans-)987 1984 y(fer)j(function)f(ob) 
r(ject)i(in)e(the)h(\\op)q(en-lo)q(op")e(to)q(olb)q(o)o(x.)g(In)i(all) 
987 2034 y(of)c(these)i(situations,)e(the)h(second)g(step)h(is)e(an)g 
(iden)o(ti\014cation)987 2084 y(problem)11 b(that)h(can)g(b)q(e)h 
(handled)f(b)o(y)g(the)g(algorithms)e(that)i(are)987 
2134 y(a)o(v)n(ailable)g(in)h(SITB.)987 2208 y(When)j(an)f(appropriate) 
g(mo)q(del)f(is)h(iden)o(ti\014ed)g(and)g(v)n(alidated)987 
2258 y(in)i(SITB,)f(it)h(can)g(b)q(e)g(copied)g(to)g(the)g(CLOSID)g 
(windo)o(w,)f(b)o(y)987 2308 y(pushing)23 b(the)g Ft(Calculate)h(and)h 
(cop)o(y)g(plan)o(t)f(mo)q(del)d Fs(in)987 2358 y(the)12 
b(CLOSID)f(iden)o(ti\014cation)g(windo)o(w.)e(This)i(third)h(step)g 
(then)987 2408 y(transfers)j(the)f(plan)o(t)f(mo)q(del)g(to)g(the)h 
(CLOSID)g(mo)q(del)e(b)q(oard,)987 2457 y(where)j(closed-lo)q(op)d 
(prop)q(erties)j(of)d(the)i(mo)q(del)d(can)i(b)q(e)h(ev)n(alu-)987 
2507 y(ated.)987 2557 y(As)22 b(an)g(illustration)e(the)i 
Ft(coprime)h(factor)e Fs(iden)o(ti\014cation)987 2607 
y(windo)o(w)13 b(is)h(sho)o(wn)g(in)g(Figure)g(4)987 
2682 y(The)c(nonparametric)e(iden)o(ti\014cation)h(metho)q(d)g(iden)o 
(ti\014es)g(sp)q(ec-)987 2731 y(tral)14 b(mo)q(dels)f(for)g(the)i(one)f 
(input,)f(t)o(w)o(o)g(output)h(transfer)h(from)987 2781 
y Fk(r)j Fs(to)f Fk(col)q Fs(\()p Fk(y)q(;)7 b(u)p Fs(\),)18 
b(and)f(constructs)i(a)e(plan)o(t)g(mo)q(del)e(b)o(y)i(taking)987 
2831 y(the)d(quotien)o(t)g(of)e(the)i(t)o(w)o(o)f(scalar)h 
(nonparametric)e(estimates.)p eop 
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4 3 bop 130 89 1622 2 v 129 130 2 42 v 138 130 V 163 
118 a Fn(Iden)o(ti\014cati)o(on)p 433 130 V 441 130 V 
595 130 V 285 w(Auxiliary)p 857 130 V 128 w(Signals)10 
b(for)p 1161 130 V 133 w(Estimated)p 1445 130 V 137 w(Exp)q(orted)p 
1742 130 V 1750 130 V 129 172 V 137 172 V 163 159 a(metho)q(d)p 
433 172 V 441 172 V 199 w(Data)p 595 172 V 79 w(information)p 
857 172 V 110 w(estimation)p 1161 172 V 162 w(ob)r(ject)p 
1445 172 V 195 w(mo)q(del)p 1742 172 V 1750 172 V 129 
213 V 137 213 V 433 213 V 441 213 V 595 213 V 857 213 
V 970 201 a(\()p Fg(x;)5 b(z)q Fn(\))p 1161 213 V 208 
w Fg(x)k Ff(!)h Fg(z)p 1445 213 V 1742 213 V 1750 213 
V 130 215 1622 2 v 130 223 V 129 307 2 84 v 137 307 V 
163 294 a Fn(Tw)o(o-step)p 433 307 V 441 307 V 161 w 
Fg(r)483 299 y Fo(1)500 294 y Fg(;)c(u;)g(y)p 595 307 
V 721 286 a Fn(^)715 294 y Fg(S)p 857 307 V 221 w(x)j 
Fn(=)1029 286 y(^)1023 294 y Fg(S)s(r)p 1161 307 V 218 
w(G)1308 298 y Fe(o)p 1445 307 V 1588 286 a Fn(^)1580 
294 y Fg(G)p 1742 307 V 1750 307 V 129 348 2 42 v 137 
348 V 433 348 V 441 348 V 595 348 V 857 348 V 968 336 
a(z)j Fn(=)e Fg(y)p 1161 348 V 1445 348 V 1742 348 V 
1750 348 V 130 350 1622 2 v 129 477 2 127 v 137 477 V 
163 444 a Fn(Indirect)p 433 477 V 441 477 V 199 w Fg(r)501 
449 y Fo(1)518 444 y Fg(;)c(y)p 595 477 V 857 477 V 417 
w(x)k Fn(=)g Fg(r)p 1161 477 V 136 w(R)1214 448 y Fe(o)1241 
444 y Fn(=)1327 421 y Fg(G)1354 425 y Fe(o)p 1283 437 
134 2 v 1283 469 a Fn(1)d(+)i Fg(C)r(G)1398 473 y Fe(o)p 
1445 477 2 127 v 1502 436 a Fn(^)1494 444 y Fg(G)i Fn(=)1625 
413 y(^)1618 421 y Fg(R)p 1574 437 116 2 v 1574 473 a 
Fn(1)c Ff(\000)i Fg(C)1670 465 y Fn(^)1662 473 y Fg(R)p 
1742 477 2 127 v 1750 477 V 129 518 2 42 v 137 518 V 
433 518 V 441 518 V 505 506 a(C)p 595 518 V 857 518 V 
438 w(z)j Fn(=)e Fg(y)p 1161 518 V 1445 518 V 1742 518 
V 1750 518 V 130 520 1622 2 v 129 603 2 84 v 137 603 
V 163 591 a Fn(T)m(ailor-made)p 433 603 V 441 603 V 134 
w Fg(r)501 596 y Fo(1)518 591 y Fg(;)c(y)p 595 603 V 
857 603 V 383 w(x)k Fn(=)g Fg(S)r Fn(\()p Fg(\022)q Fn(\))p 
Fg(r)p 1161 603 V 196 w(G)1308 595 y Fe(o)p 1445 603 
V 1588 582 a Fn(^)1580 591 y Fg(G)p 1742 603 V 1750 603 
V 129 645 2 42 v 137 645 V 433 645 V 441 645 V 505 632 
a(C)p 595 645 V 857 645 V 438 w(z)i Fn(=)e Fg(y)p 1161 
645 V 1445 645 V 1742 645 V 1750 645 V 130 646 1622 2 
v 129 746 2 100 v 137 746 V 163 717 a Fn(Coprime)g(factors)p 
433 746 V 441 746 V 65 w Fg(r)o(;)c(u;)g(y)p 595 746 
V 61 w(G)648 721 y Fe(x)677 717 y Fn(=)11 b Fg(N)743 
721 y Fe(x)762 717 y Fg(D)792 702 y Fd(\000)p Fo(1)791 
723 y Fe(x)p 857 746 V 888 717 a Fg(x)f Fn(=)1035 694 
y Fg(r)p 960 710 167 2 v 960 742 a(D)989 746 y Fe(x)1017 
742 y Fn(+)e Fg(C)r(N)1107 746 y Fe(x)p 1161 746 2 100 
v 1236 717 a Fn(\()p Fg(N)1278 721 y Fe(o)1296 717 y 
Fg(;)d(D)1340 721 y Fe(o)1357 717 y Fn(\))p 1445 746 
V 1513 709 a(^)1505 717 y Fg(G)11 b Fn(=)1590 709 y(^)1580 
717 y Fg(N)1620 709 y Fn(^)1612 717 y Fg(D)1642 706 y 
Fd(\000)p Fo(1)p 1742 746 V 1750 746 V 129 841 2 95 v 
137 841 V 433 841 V 441 841 V 505 805 a Fg(C)p 595 841 
V 857 841 V 407 w(z)g Fn(=)f(\()p Fg(y)q(;)c(u)p Fn(\))p 
1161 841 V 1445 841 V 1742 841 V 1750 841 V 130 842 1622 
2 v 129 942 2 100 v 137 942 V 163 913 a(Dual)11 b(Y)m(oula/K)p 
433 942 V 441 942 V 93 w Fg(r)o(;)6 b(u;)g(y)p 595 942 
V 72 w(C)12 b Fn(=)f Fg(N)735 917 y Fe(c)751 913 y Fg(D)781 
898 y Fd(\000)p Fo(1)780 919 y Fe(c)p 857 942 V 888 913 
a Fg(x)f Fn(=)1035 890 y Fg(r)p 960 906 167 2 v 960 938 
a(D)989 942 y Fe(x)1017 938 y Fn(+)e Fg(C)r(N)1107 942 
y Fe(x)p 1161 942 2 100 v 1445 942 V 1742 942 V 1750 
942 V 129 1096 2 154 v 137 1096 V 433 1096 V 441 1096 
V 505 1025 a Fg(C)p 595 1096 V 91 w(G)648 1029 y Fe(x)677 
1025 y Fn(=)j Fg(N)743 1029 y Fe(x)762 1025 y Fg(D)792 
1010 y Fd(\000)p Fo(1)791 1031 y Fe(x)p 857 1096 V 883 
1025 a Fg(z)h Fn(=)978 1002 y Fg(y)d Ff(\000)g Fg(G)1067 
1006 y Fe(x)1087 1002 y Fg(u)p 953 1018 180 2 v 953 1050 
a(D)982 1054 y Fe(c)1006 1050 y Fn(+)f Fg(G)1068 1054 
y Fe(x)1088 1050 y Fg(N)1116 1054 y Fe(c)p 1161 1096 
2 154 v 1282 1025 a Fg(R)1309 1029 y Fe(o)p 1445 1096 
V 1479 1017 a Fn(^)1471 1025 y Fg(G)i Fn(=)1550 1002 
y Fg(N)1578 1006 y Fe(x)1605 1002 y Fn(+)f Fg(D)1670 
1006 y Fe(c)1693 993 y Fn(^)1686 1002 y Fg(R)p 1550 1018 
163 2 v 1550 1054 a(D)1579 1058 y Fe(x)1606 1054 y Ff(\000)g 
Fg(N)1670 1058 y Fe(c)1693 1046 y Fn(^)1686 1054 y Fg(R)p 
1742 1096 2 154 v 1750 1096 V 130 1098 1622 2 v 443 1164 
a Fs(T)m(able)k(1.)g(Synopsis)h(of)f(closed-lo)q(op)h(iden)o 
(ti\014cation)f(metho)q(ds)106 1283 y(4.)20 b(P)m(ARAMETRIC)13 
b(METHODS)-111 1383 y(A)19 b(brief)g(o)o(v)o(erview)g(is)g(giv)o(en)g 
(of)f(the)i(c)o(haracteristics)h(of)d(the)-111 1433 y(di\013eren)o(t)g 
(parametric)f(metho)q(ds,)f(and)h(the)h(main)d(issues)j(are)-111 
1482 y(summarized)d(in)h(T)m(able)g(1.)g(In)h(the)g(descriptions)h(it)e 
(is)h(sp)q(eci-)-111 1532 y(\014ed)11 b(whic)o(h)g(data)g(and)g(priors) 
g(are)g(required)h(\(measured)f(signal)-111 1582 y(and/or)f(kno)o 
(wledge)g(of)f(the)i(con)o(troller\),)f(and)g(whic)o(h)g(auxiliary)-111 
1632 y(information)f(needs)j(to)g(b)q(e)g(sp)q(eci\014ed)h(b)q(efore)f 
(the)g(actual)f(iden-)-111 1682 y(ti\014cation)k(in)h(step)h(2)f(can)g 
(b)q(e)h(p)q(erformed.)e(Throughout)h(this)-111 1732 
y(section,)d(signal)e Fk(r)j Fs(is)e(used)i(as)e(an)h(abbreviation)e 
(for)i Fk(r)748 1738 y Fr(1)773 1732 y Fs(+)7 b Fk(C)s(r)864 
1738 y Fr(2)881 1732 y Fs(.)-111 2025 y(4.1)20 b Fq(Two-stage)14 
b(metho)n(d)-111 2125 y Fs(In)d(the)h(\014rst)g(stage)g(the)g(transfer) 
h(function)e(b)q(et)o(w)o(een)h(reference)-111 2175 y(signal)h 
Fk(r)q Fs(1)h(and)g(input)g(signal)f Fk(u)g Fs(\(sensitivit)o(y)h 
(function\))g(is)g(es-)-111 2225 y(timated,)k(p)q(ossibly)h(with)g(a)g 
(high-order)h(mo)q(del.)d(With)i(this)-111 2274 y(estimate)14 
b(a)g(noise-free)h(input)f(signal)f(is)h(sim)o(ulated,)e(whic)o(h)i(is) 
-111 2324 y(used)21 b(in)e(the)i(second)g(stage)f(together)h(with)e 
(the)i(measured)-111 2374 y(output)14 b(signal,)e(to)i(iden)o(tify)f(a) 
h(plan)o(t)f(mo)q(del.)-111 2424 y(First)h(stage:)61 
2526 y(^)55 2537 y Fk(\014)78 2543 y Fc(N)122 2537 y 
Fs(=)d(arg)d(min)320 2509 y(1)p 312 2527 38 2 v 312 2565 
a Fk(N)377 2485 y Fc(N)361 2498 y Fb(X)364 2585 y Fc(t)p 
Fr(=1)421 2537 y Fs([)p Fk(u)p Fs(\()p Fk(t)p Fs(\))h 
Fm(\000)h Fk(S)r Fs(\()p Fk(q)q(;)d(\014)r Fs(\))p Fk(r)697 
2543 y Fr(1)716 2537 y Fs(\()p Fk(t)p Fs(\)])775 2520 
y Fr(2)-111 2650 y Fs(An)k(accurate)h(\(high-order\))f(mo)q(del)e(is)h 
(obtained)g(and)h(denoted)-111 2704 y(as)-46 2694 y(^)-53 
2704 y Fk(S)s Fs(\()p Fk(q)q Fs(\))23 b(=)g Fk(S)r Fs(\()p 
Fk(q)q(;)193 2693 y Fs(^)187 2704 y Fk(\014)210 2710 
y Fc(N)242 2704 y Fs(\),)e(and)f(an)h(auxiliary)e(input)h(signal)g(is) 
-111 2754 y(constructed)g(as)e Fk(x)p Fs(\()p Fk(t)p 
Fs(\))f(:=)329 2743 y(^)322 2754 y Fk(S)s Fs(\()p Fk(q)q 
Fs(\))p Fk(r)421 2760 y Fr(1)440 2754 y Fs(\()p Fk(t)p 
Fs(\).)g(A)h(quic)o(k-start)g(option)-111 2804 y(for)c(this)f 
(estimation)g(is)g(a)o(v)n(ailable.)987 1286 y Ft(Estimation)e 
Fs(\(in)j(SITB\))987 1336 y(In)h(the)f(second)i(stage)e(parameters)g 
(are)h(iden)o(ti\014ed)f(according)987 1386 y(to)g(\(e.g.\))1169 
1477 y(^)1166 1488 y Fk(\022)1185 1494 y Fc(N)1228 1488 
y Fs(=)e(arg)7 b(min)1363 1515 y Fc(\022)1427 1460 y 
Fs(1)p 1418 1479 V 1418 1517 a Fk(N)1483 1436 y Fc(N)1468 
1449 y Fb(X)1471 1537 y Fc(t)p Fr(=1)1528 1488 y Fs([)p 
Fk(y)q Fs(\()p Fk(t)p Fs(\))j Fm(\000)f Fk(G)p Fs(\()p 
Fk(q)q(;)e(\022)q Fs(\))p Fk(x)p Fs(\()p Fk(t)p Fs(\)])1866 
1471 y Fr(2)1885 1488 y Fk(:)987 1629 y Fs(This)17 b(metho)q(d)f(will)g 
(generally)g(not)h(b)q(e)g(able)g(to)g(pro)o(vide)f(un-)987 
1678 y(stable)f(mo)q(dels)d(of)i(an)f(unstable)i(plan)o(t.)987 
1792 y(4.2)20 b Fq(Indir)n(e)n(ct)15 b(metho)n(d)987 
1892 y Fs(The)k(closed-lo)q(op)f(transfer)g(function)g(b)q(et)o(w)o 
(een)i Fk(r)1803 1898 y Fr(1)1839 1892 y Fs(and)e Fk(y)h 
Fs(is)987 1942 y(estimated,)9 b(and)g(b)o(y)h(using)f(information)e(on) 
i(the)i(implem)o(en)o(ted)987 1992 y(con)o(troller)i 
Fk(C)s Fs(,)f(an)h(op)q(en-lo)q(op)g(plan)o(t)f(mo)q(del)g(is)g 
(reconstructed)987 2042 y(from)h(this)g(estimate.)987 
2116 y Ft(Estimation)e Fs(\(in)j(SITB\))987 2166 y(P)o(arameters)g(are) 
h(estimated)e(according)h(to)g(e.g.)1163 2273 y(^)1159 
2284 y Fk(\022)1178 2290 y Fc(N)1222 2284 y Fs(=)e(arg)7 
b(min)1357 2311 y Fc(\022)1420 2256 y Fs(1)p 1412 2275 
V 1412 2313 a Fk(N)1477 2232 y Fc(N)1462 2245 y Fb(X)1464 
2333 y Fc(t)p Fr(=1)1522 2284 y Fs([)p Fk(y)q Fs(\()p 
Fk(t)p Fs(\))i Fm(\000)h Fk(R)p Fs(\()p Fk(q)q(;)d(\022)q 
Fs(\))p Fk(r)1795 2290 y Fr(1)1814 2284 y Fs(\()p Fk(t)p 
Fs(\)])1873 2267 y Fr(2)1891 2284 y Fk(;)987 2436 y Fs(leading)12 
b(to)f(the)i(iden)o(ti\014ed)f(transfer)h(function)1748 
2425 y(^)1739 2436 y Fk(R)e Fs(=)h Fk(R)p Fs(\()p Fk(q)q(;)1916 
2425 y Fs(^)1913 2436 y Fk(\022)1932 2442 y Fc(N)1964 
2436 y Fs(\).)987 2485 y(Next)j(a)e(plan)o(t)h(mo)q(del)e(is)i 
(calculated)g(according)g(to)1391 2584 y(^)1382 2595 
y Fk(G)p Fs(\()p Fk(q)q Fs(\))d(=)1588 2556 y(^)1579 
2567 y Fk(R)p 1527 2585 136 2 v 1527 2630 a Fs(1)e Fm(\000)h 
Fk(C)1640 2619 y Fs(^)1632 2630 y Fk(R)1668 2595 y(:)987 
2731 y Fs(If)18 b(the)h(con)o(troller)f(is)g(stable,)g(then)1589 
2721 y(^)1579 2731 y Fk(G)g Fs(is)g(guaran)o(teed)h(to)f(b)q(e)987 
2781 y(stabilized)f(b)o(y)f Fk(C)s Fs(.)f(The)i(mo)q(del)d(order)j(of) 
1678 2771 y(^)1669 2781 y Fk(G)f Fs(will)f(generically)987 
2831 y(b)q(e)g(equal)e(to)h(the)h(sum)e(mo)q(del)f(of)h(orders)i(of) 
1715 2821 y(^)1706 2831 y Fk(R)f Fs(and)g Fk(C)s Fs(.)p 
eop 
%%Page: 5 5 
5 4 bop -111 116 a Fs(4.3)20 b Fq(Identi\014c)n(ation)15 
b(with)g(tailor-made)f(p)n(ar)n(ametrization)-111 216 
y Fs(The)k(closed-lo)q(op)g(transfer)h(function)f(b)q(et)o(w)o(een)h 
Fk(r)704 222 y Fr(1)740 216 y Fs(and)f Fk(y)i Fs(is)-111 
265 y(estimated,)c(using)h(a)g(dedicated)i(parametrization)c(in)i 
(terms)-111 315 y(of)12 b(the)i(parameters)f(of)f(the)h(op)q(en-lo)q 
(op)g(plan)o(t)f(mo)q(del)g(and)g(the)-111 365 y(kno)o(wn)h(con)o 
(troller)h Fk(C)s Fs(.)-111 440 y Ft(Estimation)d Fs(\(in)j(CLOSID\)) 
-111 490 y(P)o(arameters)g(are)g(estimated)g(according)f(to)-19 
602 y(^)-23 613 y Fk(\022)-4 619 y Fc(N)40 613 y Fs(=)f(arg)7 
b(min)175 640 y Fc(\022)238 585 y Fs(1)p 230 604 38 2 
v 230 642 a Fk(N)295 562 y Fc(N)280 574 y Fb(X)282 662 
y Fc(t)p Fr(=1)340 613 y Fs([)p Fk(y)q Fs(\()p Fk(t)p 
Fs(\))i Fm(\000)554 585 y Fk(G)p Fs(\()p Fk(q)q(;)e(\022)q 
Fs(\))p 476 604 281 2 v 476 642 a(1)i(+)g Fk(C)s Fs(\()p 
Fk(q)q Fs(\))p Fk(G)p Fs(\()p Fk(q)q(;)e(\022)q Fs(\))761 
613 y Fk(r)780 619 y Fr(1)799 613 y Fs(\()p Fk(t)p Fs(\)])858 
596 y Fr(2)876 613 y Fk(;)-111 771 y Fs(leading)13 b(to)h(the)g(iden)o 
(ti\014ed)g(plan)o(t)f(mo)q(del)575 760 y(^)566 771 y 
Fk(G)o Fs(\()p Fk(q)q Fs(\))f(=)g Fk(G)p Fs(\()p Fk(q)q(;)797 
760 y Fs(^)794 771 y Fk(\022)813 777 y Fc(N)844 771 y 
Fs(\).)-111 845 y(The)21 b(parameter)e(set)j(that)e(corresp)q(onds)i 
(to)e(stable)g(closed-)-111 895 y(lo)q(op)14 b(systems)i(ma)o(y)d(b)q 
(e)j(disconnected)h(in)e(the)h(case)g(that)f(the)-111 
945 y(mo)q(del)c(order)i(of)e Fk(G)p Fs(\()p Fk(q)q(;)c(\022)q 
Fs(\))12 b(is)g(smaller)f(than)h(the)h(order)g(of)f Fk(C)s 
Fs(.)f(In)-111 995 y(this)j(case)h(inaccurate)g(mo)q(dels)d(can)i 
(result.)-111 1124 y(4.4)20 b Fq(Coprime)14 b(factor)g(metho)n(d)-111 
1223 y Fs(The)23 b(closed-lo)q(op)f(transfer)h(functions)f(b)q(et)o(w)o 
(een)i(a)e(\014ltered)-111 1273 y(v)o(ersion)14 b(of)g 
Fk(r)h Fs(\(as)f(input\))g(and)g(\()p Fk(y)q(;)7 b(u)p 
Fs(\))14 b(are)h(estimated,)e(and)h(an)-111 1323 y(op)q(en-lo)q(op)j 
(plan)o(t)h(mo)q(del)e(is)i(obtained)g(b)o(y)g(taking)f(the)h(quo-)-111 
1373 y(tien)o(t)c(of)f(the)i(t)o(w)o(o)e(estimates.)-111 
1447 y Ft(Estimation)e Fs(\(in)j(SITB\))-111 1497 y(P)o(arameters)g 
(are)g(estimated)g(according)f(to)-72 1610 y(^)-75 1621 
y Fk(\022)-56 1627 y Fc(N)-13 1621 y Fs(=)f(arg)7 b(min)123 
1648 y Fc(\022)186 1593 y Fs(1)p 177 1611 38 2 v 177 
1649 a Fk(N)242 1569 y Fc(N)227 1581 y Fb(X)230 1669 
y Fc(t)p Fr(=1)308 1621 y Fs(tr)14 b([)366 1562 y Fb(\024)397 
1596 y Fk(y)q Fs(\()p Fk(t)p Fs(\))396 1645 y Fk(u)p 
Fs(\()p Fk(t)p Fs(\))475 1562 y Fb(\025)506 1621 y Fm(\000)548 
1562 y Fb(\022)587 1596 y Fk(N)5 b Fs(\()p Fk(q)q(;)i(\022)q 
Fs(\))588 1645 y Fk(D)q Fs(\()p Fk(q)q(;)g(\022)q Fs(\))724 
1562 y Fb(\023)762 1621 y Fk(x)p Fs(\()p Fk(t)p Fs(\)][)p 
Fm(\001)p Fs(])881 1604 y Fc(T)-111 1773 y Fs(with)20 
b Fk(x)p Fs(\()p Fk(t)p Fs(\))j(=)207 1757 y Fr(1)p 145 
1764 142 2 v 145 1788 a Fc(D)172 1792 y Fa(x)190 1788 
y Fr(+)p Fc(C)r(N)267 1792 y Fa(x)291 1773 y Fk(r)q Fs(\()p 
Fk(t)p Fs(\))e(where)h Fk(G)539 1779 y Fc(x)583 1773 
y Fs(:=)g Fk(N)682 1779 y Fc(x)704 1773 y Fk(=D)759 1779 
y Fc(x)800 1773 y Fs(is)f(an)-111 1823 y(auxiliary)12 
b(mo)q(del)g(that)i(is)g(stabilized)g(b)o(y)f Fk(C)s 
Fs(.)-111 1898 y(The)h(iden)o(ti\014ed)g(plan)o(t)g(mo)q(del)e(is)i 
(obtained)f(through)316 2003 y(^)306 2013 y Fk(G)p Fs(\()p 
Fk(q)q Fs(\))f(=)464 1975 y(^)452 1985 y Fk(N)5 b Fs(\()p 
Fk(q)q Fs(\))p 452 2004 91 2 v 463 2037 a(^)453 2048 
y Fk(D)q Fs(\()p Fk(q)q Fs(\))547 2013 y Fk(:)-111 2152 
y Fs(By)23 b(using)f(a)g(normalization)e(pro)q(cedure,)k(and)e(a)h 
(common)-111 2202 y(denominator)16 b(parametrization)h(in)g(the)i(iden) 
o(ti\014cation,)d(the)-111 2251 y(mo)q(del)d(order)j(of)180 
2241 y(^)171 2251 y Fk(G)e Fs(will)f(b)q(e)j(equal)e(to)h(the)g(maxim)n 
(um)10 b(mo)q(del)-111 2301 y(order)15 b(of)57 2291 y(^)45 
2301 y Fk(N)k Fs(and)187 2291 y(^)177 2301 y Fk(D)r Fs(.)-111 
2376 y(A)13 b(quic)o(k-start)f(option)g(is)h(a)o(v)n(ailable)d(for)i 
(the)i(iden)o(ti\014cation)d(of)-111 2426 y(an)17 b(auxiliary)e(plan)o 
(t)i(mo)q(del)e Fk(G)396 2432 y Fc(x)434 2426 y Fs(that)i(is)g(used)h 
(to)f(construct)-111 2476 y(the)d(auxiliary)f(signal)f 
Fk(x)p Fs(.)-111 2525 y(Iden)o(ti\014cation)i(of)f(unstable)h(mo)q 
(dels)f(is)h(p)q(ossible.)-111 2654 y(4.5)20 b Fq(Dual-Y)m(oula/Kuc)n 
(er)n(a)15 b(metho)n(d)-111 2754 y Fs(A)g(particular)g(closed-lo)q(op)g 
(transfer)i(function)e(is)g(estimated,)-111 2804 y(and)h(b)o(y)f(using) 
h(kno)o(wledge)g(of)f(the)i(con)o(troller)f(an)f(op)q(en-lo)q(op)987 
116 y(plan)o(t)g(mo)q(del)e(is)i(reconstructed.)j(The)d(plan)o(t)f(mo)q 
(del)g(is)h(guar-)987 166 y(an)o(teed)j(to)f(b)q(e)g(stabilized)g(b)o 
(y)g(the)g(implemen)o(ted)e(con)o(troller.)987 216 y(This)f(metho)q(d)f 
(is)h(a)g(generalization)f(of)g(the)i Fq(Indir)n(e)n(ct)f(metho)n(d)p 
Fs(.)987 290 y(The)i(con)o(troller)g Fk(C)i Fs(is)e(required)g(to)g(b)q 
(e)g(kno)o(wn)f(in)g(a)g(coprime)987 340 y(factor)g(represen)o(tation)i 
Fk(C)f Fs(=)d Fk(N)1504 346 y Fc(c)1522 340 y Fk(=D)1577 
346 y Fc(c)1594 340 y Fs(,)h(as)h(w)o(ell)f(as)h(an)o(y)g(auxil-)987 
390 y(iary)f(system)f Fk(G)1242 396 y Fc(x)1274 390 y 
Fs(=)f Fk(N)1351 396 y Fc(x)1373 390 y Fk(=D)1428 396 
y Fc(x)1462 390 y Fs(that)i(is)g(stabilized)g(b)o(y)f 
Fk(C)s Fs(.)987 465 y Ft(Estimation)e Fs(\(in)j(SITB\))987 
515 y(P)o(arameters)g(are)h(estimated)e(according)h(to)1170 
622 y(^)1166 633 y Fk(\022)1185 639 y Fc(N)1229 633 y 
Fs(=)e(arg)7 b(min)1364 660 y Fc(\022)1428 604 y Fs(1)p 
1419 623 38 2 v 1419 661 a Fk(N)1484 581 y Fc(N)1469 
593 y Fb(X)1472 681 y Fc(t)p Fr(=1)1529 633 y Fs([)p 
Fk(z)r Fs(\()p Fk(t)p Fs(\))i Fm(\000)g Fk(R)p Fs(\()p 
Fk(q)q(;)e(\022)q Fs(\))p Fk(x)p Fs(\()p Fk(t)p Fs(\)])1865 
615 y Fr(2)1884 633 y Fk(;)987 773 y Fs(with)1103 844 
y Fk(z)r Fs(\()p Fk(t)p Fs(\))i(=)1318 816 y(1)p 1225 
834 206 2 v 1225 872 a Fk(D)1259 878 y Fc(c)1286 872 
y Fs(+)g Fk(G)1360 878 y Fc(x)1381 872 y Fk(N)1414 878 
y Fc(c)1436 844 y Fs([)p Fk(y)q Fs(\()p Fk(t)p Fs(\))h 
Fm(\000)g Fk(G)1601 850 y Fc(x)1621 844 y Fs(\()p Fk(q)q 
Fs(\))p Fk(u)p Fs(\()p Fk(t)p Fs(\)])55 b(and)1101 931 
y Fk(x)p Fs(\()p Fk(t)p Fs(\))8 b(=)g([)p Fk(D)1266 937 
y Fc(x)1296 931 y Fs(+)i Fk(C)s(N)1404 937 y Fc(x)1425 
931 y Fs(])1437 914 y Fi(\000)p Fr(1)1481 931 y Fk(r)q 
Fs(\()p Fk(t)p Fs(\))p Fk(:)987 1011 y Fs(A)k(plan)o(t)g(mo)q(del)e(is) 
i(obtained)f(through)1371 1110 y(^)1362 1120 y Fk(G)o 
Fs(\()p Fk(q)q Fs(\))f(=)1507 1092 y Fk(N)1540 1098 y 
Fc(x)1570 1092 y Fs(+)e Fk(D)1646 1098 y Fc(c)1672 1082 
y Fs(^)1663 1092 y Fk(R)p 1507 1111 189 2 v 1507 1155 
a(D)1541 1161 y Fc(x)1571 1155 y Fm(\000)g Fk(N)1646 
1161 y Fc(c)1672 1144 y Fs(^)1663 1155 y Fk(R)987 1259 
y Fs(The)18 b(mo)q(del)e(order)i(of)1375 1249 y(^)1365 
1259 y Fk(G)f Fs(will)f(generically)h(b)q(e)h(equal)f(to)g(the)987 
1309 y(sum)c(of)h(the)g(mo)q(del)e(orders)j(of)f Fk(G)1523 
1315 y Fc(x)1543 1309 y Fs(,)g Fk(C)i Fs(and)1705 1299 
y(^)1696 1309 y Fk(R)p Fs(.)987 1384 y(A)d(quic)o(k-start)g(option)f 
(is)g(a)o(v)n(ailable)f(for)h(the)h(iden)o(ti\014cation)f(of)987 
1434 y(an)k(auxiliary)d(mo)q(del)h Fk(G)1379 1440 y Fc(x)1400 
1434 y Fs(,)g(used)j(in)e(the)h(construction)g(of)f(the)987 
1484 y(auxiliary)d(signals)i Fk(x)f Fs(and)h Fk(z)r Fs(.)1238 
1633 y(5.)20 b(MODEL)14 b(EV)-5 b(ALUA)m(TION)987 1733 
y(Once)19 b(a)e(mo)q(del)f(is)h(estimated)g(and)g(made)f(a)o(v)n 
(ailable)g(on)h(the)987 1783 y(mo)q(del)f(b)q(oard,)g(sev)o(eral)i(op)q 
(en-lo)q(op)e(and)h(closed-lo)q(op)g(mo)q(del)987 1832 
y(prop)q(erties)12 b(can)e(b)q(e)h(ev)n(aluated.)e(This)h(is)g(done)h 
(using)f(the)g(sev)o(en)987 1882 y Ft(Mo)q(del)16 b(ev)m(aluation)d 
Fs(options)h(at)h(the)g(b)q(ottom)e(of)h(the)h(main)987 
1932 y Ft(Closid)d Fs(windo)o(w:)1001 2007 y(\(1\))21 
b Ft(closed-lo)q(op)9 b(transfer)f Fs(functions.)i(The)g(frequency)i 
(re-)1075 2057 y(sp)q(onses)f(of)e(the)g(four)g(transfer)i(functions)e 
(from)e Fk(col)q Fs(\()p Fk(r)1914 2063 y Fr(2)1933 2057 
y Fk(;)g(r)1971 2063 y Fr(1)1989 2057 y Fs(\))1075 2106 
y(to)18 b Fk(col)q Fs(\()p Fk(y)q(;)7 b(u)p Fs(\),)18 
b(are)h(sho)o(wn)f(in)g(a)g(separate)h(windo)o(w,)e(us-)1075 
2156 y(ing)e(the)h(curren)o(t)h(mo)q(dels)d(from)g(the)i(mo)q(del)e(b)q 
(oard)h(and)1075 2206 y(the)f(curren)o(t)h(con)o(troller)e 
Fk(C)j Fs(from)c(the)h(con)o(troller)h(b)q(oard.)1075 
2256 y(In)i(the)h(windo)o(w)f(the)g(amplitude)f(of)g(the)i(frequency)h 
(re-)1075 2306 y(sp)q(onses)d(are)g(sho)o(wn,)e(see)i(Figure)f(5.)1001 
2355 y(\(2\))21 b Ft(closed-lo)q(op)11 b(p)q(oles)p Fs(.)f(When)j(clic) 
o(king)e(this)h(option,)f(the)1075 2405 y(p)q(oles)i(of)f(the)h 
(closed-lo)q(op)g(transfer)g(functions)g(are)g(plot-)1075 
2455 y(ted)j(in)e(a)h(separate)h(windo)o(w,)e(also)g(sho)o(wing)g(the)i 
(stabil-)1075 2505 y(it)o(y)11 b(region)g(\(unit)g(circle\).)h(Th)o(us) 
f(the)h(\(in\)stabilit)o(y)e(of)h(the)1075 2555 y(closed-lo)q(op)j 
(system)f(can)h(simply)e(b)q(e)j(c)o(hec)o(k)o(ed.)1001 
2604 y(\(3\))21 b Ft(input/out)o(pu)o(t)7 b(sim)o(ulation)o 
Fs(.)f(Using)j(the)h(a)o(v)n(ailable)d(ref-)1075 2654 
y(erence)16 b(signal\(s\))d(in)g(the)h(curren)o(t)h(data)f(set,)g(a)f 
(plan)o(t)g(in-)1075 2704 y(put)d(signal)f Fk(u)g Fs(and)h(plan)o(t)f 
(output)h(signal)f Fk(y)j Fs(are)e(sim)o(ulated)1075 
2754 y(\(noisefree\),)16 b(emplo)o(ying)d(the)j(curren)o(t)g(mo)q(del)e 
(and)h(con-)1075 2804 y(troller.)9 b(These)i(sim)o(ulated)d(signals)h 
(are)h(plotted)g(together)p eop 
%%Page: 6 6 
6 5 bop -111 938 a Fs(Fig.)13 b(5.)g(Closed-lo)q(op)g(frequency)i(resp) 
q(onses)-23 1037 y(with)h(the)h(actual)f(\(measured\))h(input)f(and)h 
(output)f(sig-)-23 1087 y(nals)d(from)f(the)j(curren)o(t)g(data)f(set.) 
-97 1137 y(\(4\))21 b Ft(correlation)7 b(test)p Fs(.)h(The)h(sample)f 
(cross-co)o(v)n(ariance)j(func-)-23 1187 y(tion)h(is)h(sho)o(wn)g(b)q 
(et)o(w)o(een)h(the)f(external)h(reference)h(signal)-23 
1236 y Fk(r)21 b Fs(in)f(the)i(curren)o(t)g(data)e(set,)h(and)g(the)g 
(output)g(sim)o(u-)-23 1286 y(lation)d(error)i(\(top\))f(and)g(the)h 
(input)g(sim)o(ulation)c(error)-23 1336 y(\(b)q(ottom\).)c(This)i(test) 
i(indicates)e(whether)i(there)g(is)e(still)-23 1386 y(reference)19 
b(signal)d(information)e(in)j(the)g(output)g(and/or)-23 
1436 y(input)c(residual,)h(see)h(Figure)f(6.)-111 2295 
y(Fig.)f(6.)g(Closed-lo)q(op)g(correlation)h(test)-97 
2405 y(\(5\))21 b Ft(step)f(resp)q(onses)p Fs(.)c(Step)j(resp)q(onses)i 
(are)e(displa)o(y)o(ed)e(of)-23 2455 y(the)9 b(four)g(closed-lo)q(op)g 
(transfer)i(functions)e(from)e Fk(col)q Fs(\()p Fk(r)837 
2461 y Fr(2)856 2455 y Fk(;)g(r)894 2461 y Fr(1)912 2455 
y Fs(\))-23 2505 y(to)18 b Fk(col)q Fs(\()p Fk(y)q(;)7 
b(u)p Fs(\),)18 b(for)g(the)h(curren)o(t)g(mo)q(dels)f(on)g(the)g(mo)q 
(del)-23 2555 y(b)q(oard)d(and)h(the)h(curren)o(t)g(con)o(troller)f(on) 
f(the)i(con)o(troller)-23 2604 y(b)q(oard.)-97 2654 y(\(6\))k 
Ft(op)q(en-lo)q(op)d(transfer)p Fs(.)e(The)j(\(op)q(en-lo)q(op\))f(Bo)q 
(de)h(dia-)-23 2704 y(gram)d(is)i(displa)o(y)o(ed)f(of)h(the)g(curren)o 
(t)i(plan)o(t)d(mo)q(dels)g(on)-23 2754 y(the)12 b(mo)q(del)f(b)q 
(oard.)h(This)g(re\015ects)i(the)f(estimated)e(trans-)-23 
2804 y(fer)j(function)f(b)q(et)o(w)o(een)j(plan)o(t)d(input)h 
Fk(u)f Fs(and)h(output)g Fk(y)q Fs(.)1001 118 y(\(7\))21 
b Ft(p)q(ole-zero)15 b(plot)e Fs(of)h(the)h(estimated)f(transfer)i 
(function)1075 168 y(b)q(et)o(w)o(een)f(the)g(plan)o(t)e(input)h 
Fk(u)f Fs(and)h(output)g Fk(y)q Fs(.)987 243 y(Selecting)21 
b(one)f(or)f(sev)o(eral)i(of)e(these)i(ev)n(aluation)d(to)q(ols)i(will) 
987 293 y(op)q(en)13 b(a)f(\014gure)h(with)f(a)h(plot)f(of)f(the)i(ev)n 
(aluation)e(result)j(for)e(the)987 342 y(curren)o(t)17 
b(mo)q(dels)d(from)f(the)j(mo)q(del)d(b)q(oard;)i(where)h(appropri-)987 
392 y(ate)g(the)f(curren)o(t)h(data)f(and)g(curren)o(t)h(con)o(troller) 
f(will)e(also)i(b)q(e)987 442 y(emplo)o(y)o(ed.)d(A)i(zo)q(om)f(option) 
g(is)h(a)o(v)n(ailable)d(in)j(eac)o(h)g(\014gure.)1353 
592 y(6.)20 b(SUMMAR)m(Y)987 691 y(A)c Fp(Ma)m(tlab)i 
Fs(to)q(olb)q(o)o(x)d(has)h(b)q(een)h(presen)o(ted)h(for)e(closed-lo)q 
(op)987 741 y(system)e(iden)o(ti\014cation)g(on)g(the)h(basis)f(of)g 
(time)f(domain)f(data.)987 791 y(It)e(has)g(b)q(een)h(designed)g(as)f 
(an)f(add-on)h(to)f(Math)o(w)o(orks')h(System)987 841 
y(Iden)o(ti\014cation)18 b(T)m(o)q(olb)q(o)o(x)e(\(SITB\).)i(A)g 
(graphical)f(user)i(in)o(ter-)987 890 y(face)h(with)g(a)f(la)o(y-out)g 
(similar)e(to)i(the)i(SITB)f(supp)q(orts)h(the)987 940 
y(user,)h(and)g(facilitates)f(exc)o(hange)h(of)f(mo)q(dels)f(b)q(et)o 
(w)o(een)j(the)987 990 y(SITB)e(and)g(the)g(curren)o(t)h(to)q(olb)q(o)o 
(x.)d(In)i(its)f(curren)o(t)i(v)o(ersion)987 1040 y(the)c(graphical)e 
(user)i(in)o(terface)f(supp)q(orts)h(the)g(iden)o(ti\014cation)987 
1090 y(of)e(SISO)h(mo)q(dels;)e(the)j(pro)o(vided)e Fp(Ma)m(tlab)i 
Fs(m-\014les)d(are)i(im-)987 1139 y(plemen)o(ted)d(to)g(handle)f(also)h 
(m)o(ultiv)n(ari)o(able)d(mo)q(dels.)1242 1289 y(A)o(CKNO)o 
(WLEDGEMENTS)987 1389 y(The)f(authors)g(ac)o(kno)o(wledge)f(con)o 
(tributions)g(of)g(P)o(eter)h(Bongers,)987 1438 y(Ruud)j(Sc)o(hrama)g 
(and)g(Dou)o(w)o(e)g(de)g(V)m(ries)h(to)f(the)h(researc)o(h)h(and)987 
1488 y(the)g(soft)o(w)o(are)f(implemen)o(tatio)o(ns)e(in)o(v)o(olv)o 
(ed)g(in)i(this)g(pro)r(ject.)1347 1638 y(REFERENCES)987 
1712 y(Ljung,)h(L.)g(\(1987\).)f Fq(System)j(Identi\014c)n(ation:)f 
(The)n(ory)g(for)g(the)1029 1762 y(User.)d Fs(Pren)o(tice-Hall,)h 
(Englew)o(o)q(o)q(d)f(Cli\013s,)g(NJ.)987 1812 y(Ljung,)k(L.)g 
(\(1995\).)f Fq(System)j(Identi\014c)n(aiton)g(T)m(o)n(olb)n(ox)f 
(User's)1029 1862 y(Guide)p Fs(,)9 b(V)m(ersion)g(4.0,)f(The)i(Math)o 
(w)o(orks,)f(Inc.,)f(Natic)o(k,)h(Mass.,)1029 1912 y(1995.)987 
1961 y(S\177)-21 b(oderstr\177)g(om,)13 b(T.)g(and)g(P)m(.)g(Sto)-5 
b(\177)-16 b(\020ca)13 b(\(1989\).)f Fq(System)j(Identi\014c)n(a-)1029 
2011 y(tion)p Fs(.)e(Pren)o(tice-Hall,)h(Hemel)f(Hempstead,)g(U.K.)987 
2061 y(V)m(an)e(den)i(Hof,)d(P)m(.M.J.)g(and)i(R.J.P)m(.)e(Sc)o(hrama)g 
(\(1995\).)g(Iden)o(ti-)1029 2111 y(\014cation)15 b(and)g(con)o(trol)f 
(-)h(closed-lo)q(op)g(issues.)h Fq(A)o(utomatic)n(a)p 
Fs(,)1029 2161 y Ft(31)p Fs(,)d(1751-1770.)987 2210 y(V)m(an)c(den)h 
(Hof,)e(P)m(.M.J.)g(\(1997\).)h(Closed-lo)q(op)f(issues)j(in)d(system) 
1029 2260 y(iden)o(ti\014cation.)k Fq(Pr)n(o)n(c.)i(11th)g(IF)l(A)o(C)g 
(Symp.)h(System)f(Identi-)1029 2310 y(\014c)n(ation)p 
Fs(,)g(F)m(ukuok)n(a,)e(Japan.)p eop 
%%Trailer 
end 
userdict /end-hook known{end-hook}if 
%%EOF