# STATE SPACE REPRESENTATION PDF

A state variable representation of a system is not unique. In fact there are infinitely many representations. Methods for transforming from one set of state variables to another are discussed below, followed by an example. Consider the state space representation. In control engineering, a state-space representation is a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations or difference equations.‎State variables · ‎Linear systems · ‎Transfer function · ‎Canonical realizations. State-Space Representation of LTI Systems. Derek Rowell. October 1 Introduction. The classical control theory and methods (such as root locus) that we. Author: Marion Bernhard DDS Country: Jamaica Language: English Genre: Education Published: 21 February 2017 Pages: 304 PDF File Size: 20.67 Mb ePub File Size: 43.7 Mb ISBN: 730-1-41285-645-1 Downloads: 18542 Price: Free Uploader: Marion Bernhard DDS ## State Space Representations of Linear Physical Systems

Techniques for doing so are discussed elsewhere. Defining a State Space Representation A nth order linear physical system can be represented using a state space approach as a single first order matrix differential equation: The first equation is called the state equation and it has a first order derivative of the state variable s on the left, and the state state space representation s state space representation input smultiplied by matrices, on the right. The second equation is called the output equation and it has teh output on the left and the state variable s and input smultiplied by matrices, on the right. No other terms are allowed in the equation. Developing a state state space representation model from a system diagram Mechanical Translating Another, powerful, way to develop a state space model is directly from the free body diagrams.

state space representation

## State Space ↔ State Space

If you choose as your state variables those quantities that determine the energy in the system, a state space system is state space representation easy to derive. This is best illustrated by several examples, two rotating and one electrical.

The input is fa and the output is z. We state space representation write free body equations for the system at x and at y.

Freebody Diagram Equation There are three energy storage elements, so we expect three state equations. The energy storage elements are the spring, k2, the mass, m, and the spring, k1. Now we want equations for state space representation derivatives. This technique does not always easily yield a set of state equations read about some examples here.

In some cases it is state space representation to develop a transfer function model and convert this to a state space model.

Transfer functions are discussed elsewhere. The state of the system can be represented as a vector within that space.

## Control Systems/State-Space Equations - Wikibooks, open books for an open world

To abstract from state space representation number of inputs, outputs and states, these variables are expressed as vectors. Additionally, if the dynamical system is linear, time-invariant, and finite-dimensional, then the differential and algebraic equations may be written in matrix form.

Consider a chemical reaction where certain reagents are poured into a mixing container, and the output is the amount of the chemical product produced over time. The state variables may represent the amounts of un-reacted chemicals in the container, or other properties such as the quantity of state space representation energy in the container that can serve to facilitate the reaction.

When modeling a system using a state-space equation, state space representation first need to define three vectors: We need to define all the inputs to the system, and we need to arrange them into a vector. Output state space representation This is the system output value, and in the case of MIMO systems, we may have several.

Output variables should be independent of one another, and only dependent on a linear combination of the input vector and the state vector.