Lecture notes for E211 System Identification Fal99/00 Professor Jonathan P. How Copyright 1999 by Professor Jonathan How
sYsT∈ M TDENTIFICATION o DEVELO PING AN APP Ro PRI ATE MoDEL oF A OYu AMIC SYSTEM US(AG oBSERVED DATA CoMBINEO W(Tk: BASIC MECHANICS AND OYNAMICS PRIOR KNoWLEOGE oF RELATIoN SHIPs BETWEEN SIGNALS → INPUT/ OUT PUT M0ELs TN0sτ o BE VERY ExP∈ RIMENTAL/ HEUAIST WE WILL TRY To DEVELOP THE TOOLS REQUIRE O To PERFoRM THE ASk BUT IT WILL TAKE MANY MORE TRIES(YEARs?) T0EvEL0P佣∈工川TutT0 N UECESSARy T0G氏TG00,L0山- RDER MOr0ELs →NEED个0W0 RK WITH REAL0Tq AS MUCH AS POSSI BLE
WHY DO SYSTEM T0 7 ALLoWs US To DEVELoP MODELs FoR sysT∈ MS WITH VERY C。 MPLEx0 YN AMICS AND/oR SYSTEMS WITH UNKNOWN PHY SICAL PARAMETE R VALVES 今 REALLY SHoUL0E0ME工 N PARALLEL vwτ0EVEL0 PMENT of丹 N ANALYTIC MODEL(WFF PUR POseS OF IDENTIFI CATIo N →KYPo( NT IS TH肝EM00 EL ACCURACY REQUIREMENTS ARE A STRONG FUNCTIoN oF THE DESIRED APPLICATIoN CONTROL ESTIMATIoN ( oF STATES NOT AVAILABLE PREDICTION (OF RESPoNSE To DIFFERENT INPUTS)
1-3 SYSTEM TDENTIFICATION PRocEss Desig ·CL∈RRLY Data 工 TERATIVe, BUT AT I Choos MANY LEUELS Criterion I Calculate model Model Revise OK: Use it! The System Identification Loop 壬 XPERIMENT- NEED T0 DESIGN EXPT.心ELTo G∈TG0o00AT MODEL STRUCTURE -MANY CHoICES, PICK BASED ON OUR UNDERSTANDING of SYSTEM DYNAMICS FIT MODEL OfTIMIZATioN E小乱 UATION VALlOATE MoDEL To MAE SURE THE FIT TS REASONA BLE
Choose Model Set Model Not OK: OK: Use it! Prior Knowledge Experiment Choose Criterion Calculate Model Data Validate Revise The System Identification Loop. Design of Fit
-4 EXPERIMENTs oPEN-LooP OR CLoSED-LooP D千 TEN No CHoiCe.BuT CLP INTRO DUCES MANY CoMPLICAT INE FACTORs. WHAT Is THE IVPdT SEQUENCE 2 FREQUENCY CONTENT & BIG IMPACT! ACTUAToR LIMITS ( SLEWRATES s航 PLING RATE/0A升 LENGTH MEMORY SISO/SIMO/ MIMO SYSTEM DATA fILTERIN G DRiFTs bIAsEs OUTLIERS NOISE ATTENVATION MODEL STRUCTURE NON- PA RAMETRIC TRANSFER FUN CTION PLOT 工 MPuLSE REsP0AsE 代4 RAMETRIC CAPTURe DYNAMIcs IN t SIPLE STRUCTURE G(s)=S+∝ s2+P5+B2 LINEAR/NONLINEAR MODEL SIZE ( POLES, ZERos)
F ITTING THE MODEL · BIG TRADE-FFB∈ TWEEN 兵 CCURACY E5E0FS。LTN DEGREE OF USER INPUT REQUIRED? △6E5 THE PRocEss ALWAYs woRK? NALI DATIoN PREOICTION AND SIMULATION DIFFERE NT DATA SETS TIME FRE& DOMAIN ANALysIS OF THE ERRoR STOCHA6Tw升LYsS0F佣ERE510 uAL ERRoR D0EsR∈ SULT IMPLY THAT山SH0L0MRE CHANGES To: MODEL CHOICE ( ORDER,WP∈…) EXPT (INPUT SEQVENCE 0B5∈crv∈FNf0RFT ∪AL(0ATEA0 FFERENT DAT升mHA7 HAT USED To MAKE THE MopEL
LECTURE世5 Ezl TRANSFER FUACTIONS ETFE+PRf∈RTEs SMoOTHING ∈ XAMPLE L63,5.2,b4,6.5,6.6 Copyright 1999 by Professor Jonathan How. DATA 千 RANS FER FUNCTION EST I MATE TME DOMAIN CURVE 工 NSIGHTS FT心G R工 TERATE!
LECTURE 5 ME ASPECTs0F0sR∈T∈LM∈m SYSTEM DYNAMICS IMPUSE RESPONSE MODE LING/ESTIMATIoN DIScRETE STATE SPACE SYSTEMS SYSTEM REALIzATIo THEDRy
⊥ NEAR SYST∈As 0ua0AT井 WILL TYPICALLY& E COLLECT∈0 FRoM只 EAL SY5TEMS 015CQET∈0ATA DISCRETE AODELS ·C0S(0ERT1SSC∈AARD: G yt T RESPONSE GIVEN8￥ K INTEGER Y(K CONVOLUTON INTEGRAL )(t-y) TYPICALLy AsSUME THAT (T)=o y ro g(r)DEfINES THE CAUSAL RELATIONSHIf 6ET心ETHe工NPUT0(+)400rPT9) CALLED THE IMPULSE RESPONSE COULD MODEL THE SYSTEM VERY WELL 工 F WE COULD FIND9比t)
ONE PROBLEM: MUST WoRK IN DISCRETETIME SLIGHTL-Y0 FFERENT工 uPULS日 RESPONSE SAMPLE REsPo心sEAT△ SCRETE TIMES七=kT KT= 3(n)以(KT-T) T0 SIMPLIfY AN升LYss,升550 ME THAT THE工Puru(t) Ts PlECE-川 ISE COWSTAAT (OUPUT of ult)APPLIEO TO A zoH →以(七)以K甘 kT么七<(K+)T NOT ALWAYS VALID MT NoW GET CKT)= 2 T)以(kTT)中 (M-T CONSTANT R K T alr)dy 工 MPVLSE RE5oNsE m-小)T F A SAMPLED-DATA SYST∈M CAN WE MEASURE THIS DIRECTLY