State space representatios a mathematikal model model uded deskripbe shafoor of mekanicher system. Ini provide a framewors to analyze syemize dynammics using matric anvektors, making it requier to controllers and and and and realzle stability.

Basics of State Spacie Representation

Ini adalah contoh model yang mewakili sistem with pertama-tama dari perbedaan ekuasi. Ini tidak menggunakan status vector to encapsulate aly kebutuhan informasi abourt tersebut system 's condition.

Te general form is:

11; Syaria1; FLT: 0 Abo3; Syari3; = Ax (t) + Bu (t) 1; FLT: 1 Syari3; AF3;

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Periksa: Mass-Spring- Systems Dampe

Konsistensi sistem shape shape shape shape shape shape, fLT: 0: 33; m 1; FLT: 1: 1; FL3: 3 Koefisien, FL1; FLT; 3OP; 33O1gt; 3; 31gt; & lt; 313031gt; S31gt; S31gt; & lt; s; s; s; s; s; 31111123;

1f 1; 1f; FLT: 0 1f 3; m * x castquote; + c * x * x * x = k * u (t) 1; FLT: 1 1f 3; 1f 3;

Defining state variables as arias arif 1; FLT: 0: 33; xvo3; x = x = x1; FLT: 1: 1 1f 3; and 1; FLT: 2 MIS3; x = x Aver1; FL1; FLT: 3 MIS33D;, the states space becomets;

111; WAL1; FLT: 0 ASA3; AF3; ASAX = x ASA1; FLT: 1 JUGA; JUGA 3;

11; FLT: 0 = 03; Aver3. assax3. = - (k / m) * x / m- (c / m) * x jel + (1 / m) * u (t) 1; 1; FLT: 1: 1 MIL3; S3;;

Ini form matrix:

11; Syaria1; FLT: 0 Abo3; Syari3; Syarix (t) = A x (t) + B u (t) 1; FLT: 1 Syari3; Aver3;;

Where:

  • A = = 111; 13.0, 113;, 1f; - (k / m), - (c / m) 1f; 123; 1st;;
  • B = 111; 13.0;, 111; 1 / m 1st; 123;

Calculations and Analysis

Using that state state model, proceers cath cath cath arlity analytic, controllability, and obserbility assessments. Eigenvalues of matrix 1f; FLT: 0 43; A43; A Sys1; FL1; FLT: 1 313; incentate Systemm stabile stabile.

Controllability is checked by examing the controllabibility matrix:

111; WHI1; FLT: 0 AF3; Q = 1; B, AB AB3; WHI1; FLT: 1: 3; 13; 13;

If 1f; WHI1; FLT: 0 AF3; Q 1; WHI1; FLT: 1 ASA3; HAS FALI rank, the systems is controllaIIe.