State Feedback Control Block Diagram

Transcription

1 State Feedback Cotrol Block Dagra r B C -K lt-it I Ste t Cotrollablt:,B cotrollable ff rakp, P[B B - B]: Pck -learl deedet col of P gog fro left to rght ad rearrage a b b b b b : col of B Potve teger o fod are called cotrollablt dee

2 State Traforato to I Cotrollable For ICF Partto - : ew tate Note: j B, j < T 3 I Cotrollable For Detal Trafor te b To ICF B B b B, 3 Note: b ad b j, j <

3 ICF Sbte,,,, dt d O O where ad are row vector, ad [ ] -th locato State Feedback Cotrol of I Ste. Trafor to ICF. Fd K c to lace ole of c B c K c 3. Set ga to KK c T for orgal te Note: Feedback ga ot qe Otato oble

4 ICF State-Sace Eq c B c O c, O O :CCF O O B c O Fleble Ste Eale K5 Deg tate feedback cotroller to lace ole at,,5 ± j

5 State odel P B B B B [ ] P Cotrollablt atr: earl Ideedet Traforato atr Cotrollablt dee:, T

6 ICF: Cotrol law: ICF atrce c B c K c r 5 5 c, B c 5 5 K k k k 3 k 4 k k k 3 k 4 Cloed-oo Ste Cloed-oo ICF: c B c K B c 5 k c B c K c k 5 k 3 k 4 5 k k 5 k 3 k 4 t leat oble olto: Two block trctre: Sgle block trctre: k 5, k 3 5, k k 4 k 3 k 5, k 4 k

7 -Block Strctre Cloed-loo atr: c B K c c 5 k k 5 k 3 k 4 de de K T 5 5 Sgle-Block Strctre Cloed-loo atr: c BcKc 5 k Dered Char. Eq. k 5 k 3 k 4 de Ga: k 995, k 344, k 3 433, k 4 34 K K c 5 T

8 atlab Solto Ste atrce [ ; ;-5 5 ;5-5 ]; B[ ; ; ; -]; C[ ; ]; Dero,; Dered ole Pd[-;-;-5*qrt*j;-5*qrt*-j]; Klace,B,Pd; K Cotat Ott/Dtrbace Reglato Plat: B w dtrbace C Cotrol: K r Cloed-loo Ste: d cotatrcotat, d cotat d BK d Br w d C d BK Br w C d C BK Br w

9 Dered Referece It Dered referece t: r G d C BK w, G C BK B Provded the cloed-loo ga G vertble. Iractcal Solto: Need eact odel of te ad dtrbace Itegral Cotrol Cotrol law: K t K I et dt d K B C lat Itegral cotroller K toatcall geerate referece t r

10 Cloed-oo Itegral Cotrol Ste Plat: Cotrol: B w C t K K I et dt, e d Itegral tate: e d Cloed-loo te I t d dt I C I B I w [ K K ] I d Stead State Error Obervato: If the cotrol ga are choe ch that the cloed-loo te atotcall table, the all the tate varable t reach a cotat vale ce the t w ad d are cotat. Th l t et

11 Pole-Placeet wth Itegral Cotrol Need to fd K[K K I ] to lace the egevale of B K C, B B atlab: K lace,b,p d Fleble Ste Eale k Paraeter: Kg. K5 N/ Deg a tegral cotroller that lace the ole at,, 5,5 ± j

12 atlab Solto Ste atrce [ ; ;-5 5 ;5-5 ]; B[;;;]; C[ ]; D; Dered Pole Pd[-5;-;-;-5*qrt*j;-5*qrt*-j]; Itegral Cotrol Deg bar[ ero4,;c ]; Bbar[B;]; Bwbar[;;;;-]; Cbar[C ]; Kackerbar,Bbar,Pd; clbar-bbar*k,bwbar,cbar,d; tecl,[:.:]; Ste Reoe Ste Reoe Te ec

13 State Oberver State varable are ofte earable State of obervable te ca be detered fro t ad ott Oberver ca atotcall etate tate fro t ad ott State Feedback Cotrol Block Dagra Ste B C Oberver

14 Plat: eberger Oberver Oberver: B C ˆ ˆ B Cˆ Cloed-loo Ste: C, ˆ If egevale of -C are HP the l ~ t ˆ t t a t t Oberver Pole Placeet Proble Chooe the oberver feedback ga to lace the cloed-loo oberver ole,.e., Egevale of : C t ecfed locato de, de, K Slar to tate feedback ole laceet Oberver ole are choe fater tha cotroller ole

15 Oberver Pole Placeet Procedre Cotroller-Oberver Dalt: e.v. C e.v. C T e.v. T C T T Oberver ole laceet eqvalet to ole laceet BK wth ~ T, B~C T, ad -K T. atlab: acker,c,pd or lace,c,pd Ba-Gra Forla for SISO Ste Charactertc eqato: I a a a Dered Charactertc Eqato: de de de a de a de a T - * de a a a a a Q de N N a a de, a a Q: Obervablt atr

16 Oberver Trafer Fcto Oberver C B ˆ ˆ ˆ Oberver State Eqato: Trafer Fcto: I G C B I G Y G U G X, ˆ Clacal Oberver Eale Veloct etato baed o oto ad accelerato eareet: State eqato: dt d * accelerato veloct, oto,

17 Veloct Oberver ˆ ˆ ˆ ˆ ˆ dt d Oberver: Cloed-loo oberver atr -C: [ ] C Chooe ga to et atral freqec ad dag rato Veloct Oberver Ga Selecto de Dered Charactertc Eqato: Cloed-loo Oberver Charactertc Eqato: I Oberver Ga:,

18 Oberver Trafer Fcto Trafer fcto, Xˆ Xˆ G U G Y G G Relt: I B I U X ˆ X ˆ U Y Y Etree Cae Cae Fat oberver: Y U X ˆ Y X ˆ U Y Y Cae Slow oberver: Y U X ˆ X ˆ U Y U U

19 Coet o Veloct Oberver Fat veloct oberver ~ dfferetator-- Setve to hgh freqec oe Slow veloct oberver ~ tegrator-- Setve to offet I geeral, oberver etate each tate b cobg fltered t ad ott. atlab Solto Ste atrce [ ; ]; B[;]; C[ ]; C[ ]; Oberver Dac eta.77; w; wdqrt-eta^*w; Kacker,C,[-eta*wj*wd;-eta*w-j*wd]; K ; Trafer Fcto VG*UG*Y G-*C,B,C,; G-*C,,C,; bodeg,g;

20 Bode Dagra Veloct Oberver Veloct Etate:.77 rad/ec X ˆ U Y Bode Dagra Phae deg; agtde db Freqec rad/ec