ss2tf

Convert state-space representation to transfer function.

Syntax

• [b, a] = ss2tf(A, B, C, D)
• [b, a] = ss2tf(A, B, C, D, ni)

Input argument

• A (n x n) - Represents the system's state-transition matrix. It describes how the system's internal state evolves over time.
• B (n x m) - Describes the input-to-state mapping. It shows how control inputs affect the change in the system's state.
• C (p x n) - Represents the state-to-output mapping. It shows how the system's state variables are related to the system's outputs.
• D (p x m) - Describes the direct feedthrough from inputs to outputs. In many systems, this matrix is zero because there is no direct feedthrough.
• ni - Input index:integer scalar or 1 (default).

Output argument

• b - Transfer function numerator coefficients: vector or matrix.
• a - Transfer function denominator coefficients: vector.

Description

[b, a] = ss2tf(A, B, C, D) transforms a state-space representation of a system into an equivalent transfer function.

The function ss2tf returns the Laplace-transform transfer function for continuous-time systems and the Z-transform transfer function for discrete-time systems.

[b, a] = ss2tf(A, B, C, D, ni) computes the transfer function resulting from exciting the nith input of a system with multiple inputs using a unit impulse.

Example

Fs = 16;
dt = 1/Fs;
Ac = [0 1 0 0; -2 0 1 0; 0 0 0 1; 1 0 -2 0];
A = expm(Ac*dt);
Bc = [0 0; 1 0; 0 0; 0 1];
B = Ac\(A-eye(4))*Bc;
C = [-2 0 1 0; 1 0 -2 0];
D = eye(2);
[b, a] = ss2tf(A, B, C, D, 2)

See also

tf2ss, ss, tf.

History

Author

Allan CORNET