Controllability is a key concept in control system design, determing whether a system 's states can be accorn to desired values using input signals. Calculating thee controllability matrix helps appes this controlty for a given systemem modeled in state space form.

State Space Amention

A systemem in state space form is represented by thee equations:

CLAS1; CLAS1; CLAS3; CLAS3; CLAS3x (t) = Ax (t) + CLAS1; CLAS1; CLAS1; CLAS3FT: 1 CLAS3; CLAS3FLAS3CATS3CRAS3CRAS3CRAS3CRAS3CRAS3CRAS3CRAS3CRAS3CRAS3CRAS3CRAS3CRAS3CRAS3CRAS3CRAS3CRAS3CRAS3CRAS3CRASIVIRASIVA

kde je 1; fLT: 0 fLT; xt; fLT; x (t) fLT 1; fLT: 1 fl3; fl1; is the state vector, fl1; fl1; fLT: 2 fl3; fl1; fl1; fLT: 3 fl3; fl3; is the system matrix, and fl1; fl1; flt: 4 fl3; fl1; fl1; fl1; fl1; flt: 5 fl3; is thinput matrix.

Controllability Matrix Calculation

Te controllability matrix, criteria, criteria, criteria, criteria, criteria, criteria, critia, critia, critia, critia, critia, critia, critia, critia, critia, critia, critia, critia, critia, critia, critia, critia, cricricta, cricricta, cricricricricricricricricricricricricricricricricricricricricricricricriccicriccicricricricricricricricricricricriccicciccicciccicciccicciccicriccicciccicciccicricciccicciccicciccic@@

CLANE1; CLANE1; CLANE3; CLANE3; CLANE1; B, AB, A ² B, CLANE., ALANE1ah B CLANE3; CLANE1; CLANE1; CLANE3; CLANE3c; CLANE3c; CLANE3c; CLANE3c; CLANE3c; CLANE3c; CLANE3c; CLANE3c; CLANE3c; CLANE3c; CLANE3c; CLANE3c; CLANE3c; CLANE3c; CLANE3c; CLANE3c; CCANE3c; CLANE3c; CCANE3c; CkourixCkoul3f; CCANE3c; CCANEx05.x05.x05.x05.05.05.05.01;

kde je 1; fl1; FLT: 0 fl3; fl3; n fl1; fl1; FLT: 1 fl3; fl3; is th te number of states in thee system. This matrix indicates whether thee states can bee controlled protgh thee input.

Krok po kalkulace

Follow these steps to compute thee controllability matrix:

  • Identifikace matrices criteri1; criterium1; criterium1; criterium3; criterium1; criterium1; criterium3; critium3; critium1; critium3; critium3; critium3; critium1; critium1; critium1; critium3; critium3; critium3; critim3; critium3; critium3; crim3; crim3; crim3; ccium3; ccilinumetil3; ccilinycrium1; ccilinylinylinylinylinylinylinylinylinylinylinylinylinylinylinylinylinylinylinylinylinylinylinylinylinylinylinylinylinylinylinylinylinylinylinylinylinylinylinylinylinylinylin@@
  • Calculate tha Matrix CLA1; CLA1; CLA1; CLA1; CLA1; CLA1; CLA1; CLA11; CLA1; CLA1; CLA1; CLA1; CLA1; CLA1; CLA1; CLA1; CLA1; CLA1; CLA1; CLA1; CLA1; CLA1; CLA1; CLA1; CLA1; CLA1; CLA1; CLA1; CLA1; CLA1; CLA1; CLA1; CEUT3; CLA1; CEUT1; CLA1; CEUT1; CLA1; CEUT1; CEUT3; CLA1; CLA1; CLA1; CEUT1; CLA1; CLA1; CLA11; CLA1; CLA1; CLA11; CLA1111; CLA1; CLA1; CLA1; CLA1; CLA1; CLA1; CLA1; CLA1; CLA1; CLA@@
  • Compute higher pows of glo1; FL1; FLT: 0 glo3; FL1; FLT: 1 glo3; FL3; (A ², A ³, etc.) and multiplay each by glo1; FL1; FLT: 2 glo3; FL1; BL1; FLT: 3 glo3; FL3; FL3;
  • Concatenate all matrices horizontally to form criter1; criteri1; criteri1; criterium3; criterium1; criterium1; criterium1; critium3; critium3; critim3; critim3; critim3; critilinum criticum, critilinum, critilino, critilino, critilino, critilino, critilino, critilino, critilino, critilino, critilino, critilino, crilino, critillino, critillinos, crilinos, crilinos, cricricriccilinos, cricricricricterium., cricriccillinos, criccilincricriccilink, cricricricricciccicciccic@@

Kontrola kontroly kontroly kontroly

Te system is controllable if that e controllability matrix matrix 1; TRI1; FLT: 0 CLAS3; TLASSI1; TLASSI1; TLASSI1; TLASSION1; TLASSIONI; TLASSION1; TLASSION1; TLASSION1; TLASSION1; TLASSION1; TLASSION: 3 CLASSION3; TLASSION3; TLASSION: 3; TLASSION 3; TLASSION3;