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A state variable is one of the set of variables that are used to describe the mathematical "state" of a dynamical system. Intuitively, the state of a system describes enough about the system to determine its future behaviour in the absence of any external forces affecting the system. Models that consist of coupled first-order differential equations are said to be in state-variable form.
- In mechanical systems, the position coordinates and velocities of mechanical parts are typical state variables; knowing these, it is possible to determine the future state of the objects in the system.
- In thermodynamics, a state variable is also called a state function. Examples include temperature, pressure, volume, internal energy, enthalpy, and entropy. In contrast heat and work are not state functions, but process functions.
- In electronic circuits, the voltages of the nodes and the currents through components in the circuit are usually the state variables.
- In ecosystem models, population sizes (or concentrations) of plants, animals and resources (nutrients, organic material) are typical state variables.
Control systems engineering
In control engineering and other areas of science and engineering, state variables are used to represent the states of a general system. The state variables can be used to describe the state space of the system. The equations relating the current state and output of a system to its current input and past states are called the state equations. The state equations for a linear time invariant system can be expressed using coefficient matrices:
- RN*N, RN*L, RM*N, RM*L,
where N, L and M are the dimensions of the vectors describing the state, input and output, respectively.
The state variable representing the current state of a discrete-time system (i.e. digital system) is , where n is the discrete point at which the system is being evaluated. The discrete-time state equations are
- , which describes the next state of the system (x[n+1]) with respect to current state and inputs u[n] of the system.
- , which describes the output y[n] with respect to current states and inputs u[n] to the system.
Continuous time systems
The state variable representing the current state of a continuous-time system (i.e. analog system) is , and the continuous time state equations are
- , which describes the next state of the system with respect to current state x(t) and inputs u(t) of the system.
- , which describes the output y(t) with respect to current states x(t) and inputs u(t) to the system.
- ^ William J. Palm III (2010). System Dynamics (2nd ed.). p. 225.
Intro to Control - 6.1 State-Space Model Basics
Explanation of state-space modeling of systems for controls.
Introduction to State Space (State Variable) Representation
Develops, by example, the state variable representation of a 3rd order LTI system, beginning with it's scalar differential equation, creating a signal block diagram, ...
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Lec-47 State-Variable Equations
Lecture Series on Control Engineering by Prof. S.D. Agashe, Department of Electrical Engineering,IIT Bombay. For more details on NPTEL visit ...
GATE 2013 ECE State Variable Analysis control systems
Proof: S (or Entropy) is a valid state variable
Prroof that S (or entropy) is a valid state variable. More free lessons at: http://www.khanacademy.org/video?v=sPz5RrFus1Q.
Synthesizers.com Q107 State Variable Filter
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State variable form extra example 2nd order
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11. Physics | Laws of Thermodynamics | State Variable & Path Variable | by Ashish Arora
http://www.physicsgalaxy.com State and path variables - difference between state and path variables, internal energy as state variable, work and heat as path ...
Mon, 02 Nov 2015 19:22:30 -0800
Tickets for the 2016 home game against Michigan are expected to cost a record $195 each under Ohio State's variable-pricing model, according to Columbus Business First. The Ohio State Board of Trustees will consider the athletic council's ...
Mon, 26 Oct 2015 09:52:30 -0700
The key state variable is the firm's asset base scaled by its instantaneous operating pro t, which increases monotonically with operating leverage. Firms inhabit different ranges of this state variable between their upper and lower scale adjustment ...
Fri, 13 Nov 2015 13:05:50 -0800
states are prioritized, so using a single AI state variable with a state stack is possible. multiple AI state variables (IE flags) is another approach. i started with a setstate/runstate type architecture with a single AI state variable. i've moved to ...
Thu, 29 Oct 2015 10:37:30 -0700
We also show that the bubble state variable calibrated on the Chinese market data corresponds well to the regimes when the market exhibits a strong price acceleration followed by clear change of price regimes. Our results suggest that SIN may ...
Mon, 15 Dec 2014 00:42:27 -0800
The usual schematic of a state-variable filter with two inverting integrators is well known. Curiously, the input signal is almost always connected to the minus input of U1. Figure 1 is an example with ω0 = 1kHz and Q = 5. Figure 1 Typical state ...
Wed, 25 Feb 2015 11:16:27 -0800
Introduced last year by Penn State, variable pricing determines individual game prices from many factors, including the expected demand for that game, and provides more pricing choices for Nittany Lion fans. Season tickets, which are on sale for the ...
Tue, 14 Jan 2014 12:08:49 -0800
UNIVERSITY PARK, Pa. - Penn State Athletics today announced variable pricing structure for its single game public football tickets during the 2014 season. Variable pricing determines individual game prices from many factors including expected demand ...
Fri, 12 Oct 2012 06:00:07 -0700
The KOMA Elektronik SVF-201 is a state variable filter for the Eurorack modular synthesizer system. Its filter circuit is built up with optical parts (Vactrols) therefore delivering excellent studio audio quality and an unique warm analogue sound. The ...
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