**Subject :**Advance Control System

## Alternative Representations in State Space

- System modeling in state space can take on many representations other than the phase-variable form.

- Although each of these models yields the same output for a given input, an engineer may prefer a particular one for several reasons.

- For example, one set of state variables, with its unique representation, can model actual physical variables of a system, such as amplifier and filter outputs.

- Another motive for choosing a particular set of state variables and state-space model is ease of solution.

- As we will see, a particular choice of state variables can decouple the system of simultaneous differential equations. Here each equation is written in terms of only one state variable, and the solution is affected by solving n first-order differential equations individually.

- Ease of modeling is another reason for a particular choice of state variables.

- Certain choices may facilitate converting the subsystem to the state-variable representation by using recognizable features of the model.

- The engineer learns quickly how to write the state and output equations and draw the signal-flow graph, both by inspection.

- These converted subsystems generate the definition of the state variables.

- In a state space system, the internal state of the system is explicitly accounted for by an equation known as the state equation.

- The system output is given in terms of a combination of the current system state, and the current system input, through the output equation.

- These two equations form a system of equations known collectively as state-space equations.

- The state-space is the vector space that consists of all the possible internal states of the system.

- Because the state-space must be finite, a system can only be described by state-space equations if the system is lumped.