How is the state space model of a system derived?
The state space model of a continuous-time dynamic system can be derived either from the system model given in the time domain by a differential equation or from its transfer function representation. Both cases will be considered in this section.
How to write state space representation in canonical form?
State space representations in canonical forms Consider a system de\\fned by, y(n)+ a 1y(n 1)+ (+ a n 1y_ + any = b 0um)+ b 1u(m 1)+ + b m 1u_ + bmu where ’u’ is the input and ’y’ is the output. This equation can also be written as, Y (s) U(s)=
How are state variables defined in state space?
The state variables define a location in state space, a vector space of the same dimension as the order of the system. As a system changes state with time it follows a trajectorythrough state space. 12/29/10! M.
How does forcing function I affect state space?
The forcing function i in(t)and the initial state of the system determine how the system will move through state space and the state variables describe its position in state space as it follows that trajectory. 12/29/10! M.
How to obtain state space models from transfer functions?
The common procedure for obtaining state space models from transfer functions is performed with help of the so-called transfer function simulation diagrams. In the case of continuous-time systems, the simulation diagrams are elementary analog computers that solve differential equations describing systems dynamics.
When to use the state space approach in math?
The state space approach is very convenient for representation of high-order dimensional and complex systems, and extremely efficient for numerical calculations since many efficient and reliable numerical algorithms developed in mathematics, especially within the area of numerical linear algebra, can be used directly.