How is the state space representation not unique?
Another important point is that the state space representation is not unique. As a simple example we could simply reorder the variables from the example above (the new state variables are labeled qnew ). This results in a new state space representation
Can you make new state variables in state space?
In the previous case careful examination of the original and modified state space system reveals that they represent the same system. However we can make entirely new state variables by forming linear combination of the original state variables in which this equality is not obvious. Consider the state variable qnew defined as follows:
How are transfer functions used in state space?
In some cases it is easier to develop a transfer function model and convert this to a state space model. Transfer functions are discussed elsewhere. The energy variables for rotating systems are potential energy stored in springs (½K r θ²) and kinetic energy stored in inertial elements (½Jω²).
Can a linear system be represented in state space?
The state space representation is not unique; many (actually an infinite number) of state space systems can be used to represent any linear physical system. Another, powerful, way to develop a state space model is directly from the free body diagrams.
Why is a state-space representation called a controllable form?
This state-space realization is called controllable canonical form because the resulting model is guaranteed to be controllable (i.e., because the control enters a chain of integrators, it has the ability to move every state). The transfer function coefficients can also be used to construct another type of canonical form
How are state variables related in a state space model?
A state-space model is a mathematical representation of a physical system as a set of input, output, and state variables related by first-order differential equations. The state variables define the values of the output variables.
Why are there more poles than zeros in the s-plane?
NOT to time continuous system and poles and zeros in the s-plane. A time discrete system with all zeroes and no poles is simply an FIR filter which is always stable and causal. A system with more zeros than poles can be easily split into a cascaded FIR and IIR filter where the excess zeros are end up in the FIR filter.
When to search for the Poles in the state space model?
If we want to find the poles, we search when the denominator ( D) is equal 0 and for the zeroes when the numerator ( N) is 0. My question is, if we want to define which part of the state space model influence whether the poles or the zeroes.