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# How do you represent transfer function in state-space?

## How do you represent transfer function in state-space?

To convert a transfer function into state equations in phase variable form, we first convert the transfer function to a differential equation by cross-multiplying and taking the inverse Laplace transform, assuming zero initial conditions.

## How do I transfer a transfer function to state space in Matlab?

[ A , B , C , D ] = tf2ss( b , a ) converts a continuous-time or discrete-time single-input transfer function into an equivalent state-space representation.

How do you find the state-space representation?

Key Concept: Defining a State Space Representation

1. q is nx1 (n rows by 1 column); q is called the state vector, it is a function of time.
2. A is nxn; A is the state matrix, a constant.
3. B is nxr; B is the input matrix, a constant.
4. u is rx1; u is the input, a function of time.
5. C is mxn; C is the output matrix, a constant.

### What is state space realization?

A state-space realization (A, B, C, D) of G(s) is said to be an MR of G(s) if the matrix A has the smallest possible dimension, that is, if (A′, B′, C′, D′) is any other realization of G(s), then the order of A′ is greater than or equal to the order of A.

### What are the types of transfer function?

Common transfer function families Butterworth filter – maximally flat in passband and stopband for the given order. Chebyshev filter (Type I) – maximally flat in stopband, sharper cutoff than a Butterworth filter of the same order.

What is the difference between transfer function and state space representation?

Note that although there are many state space representations of a given system, all of those representations will result in the same transfer function (i.e., the transfer function of a system is unique; the state space representation is not). Example: State Space to Transfer Function

## Is the state-space representation of the system unique?

State Transformation The state-space representation is NOT unique! ME 433 – State Space Control 38 We consider the linear, time-invariant, homogeneous system Time-invariant Dynamics: where Ais a constant n×nmatrix. The solution can be written as Solution of State Equation where We can note that Then, 5 ME 433 – State Space Control 39

## How to convert from state space to transfer function in MATLAB?

To make this task easier, MatLab has a command (ss2tf) for converting from state space to transfer function.

Does the transfer function depend on state choice?

We inverse Laplace transform to obtain where we have used that Solution of State Equation 8 ME 433 – State Space Control 45 The transfer function does NOT depend on the state choice because it represents the input-output relationship. Proof: In class State Transformation