nuous-time LTI (Linear Time Invariant) models in MatLab it is necessary to use operator ss . example,
sys = ss (A, B, C, D)
creates the state space of a continuous-time system.
Relationship between state space and transfer function description
The diagram explaining the relationship between the state space description and description with the transfer functions is represented in fig. 7. br/>
. 7
For the continuous case we have
.
In MatLab operator ss2tf carries out conversion from state space description to transfer functions. If output is a vector than numerator Num of the transfer function is a matrix, each row of which contains numerator polynomial coefficients of the corresponding transfer function (from input to the first, second and so on outputs). If it is necessary to define any concrete transfer function then it is necessary to take the corresponding row from the matrix Num , for example tf2 = tf (Num (2, :), Den). Denominator would be common for all transfer functions.
Program code:
[A0, B0, C0, D0] = tf2ss (n0, d0)
Results of the program:
A0 =
-60 -630
0 0
1 0 =
=
63.0000 630.0000 =
9) calculate the eigenvalues ​​of the uncompensated system;
Theoretical information:
Eigenvalues ​​
The eigenvalues ​​of the square matrix are the roots of the equation:, where is a unit matrix. The result of using the operator is a vector containing the eigenvalues ​​of the square matrix. p> Program code:
eigenvalues ​​= eig (Wclun)% task 1.9
Results of the program:
eigenvalues ​​=
.8199
.5901 + 6.4933i
.5901 - 6.4933i
10) calculate -norm of the uncompensated system.
Theoretical information:
Calculation of -norm
The-norm of a stable continuous system with a transfer function is a square root from average value of a square of impulse response of a system, and at conversion to Laplace transformation according ...
