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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.
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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Here is a brief demonstration of the capabilities and sound of the Synthesizers.com state variable filter.
Tasker 101 Tutorials: Lesson 16b - Screen State Variable, SIMPLE Lock Screen, Addnl Lock Options
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MFOS Dual State Variable Filter
This is my customized design based on the Ray Wilson Music From Outer Space State Variable (Multimode) Filter. This combines two separate filters in one ...
state variable filter pcb
worked 1st try! holla!
Mon, 27 Jul 2015 08:56:15 -0700
where γ is the state variable, σ is the effective normal stress, A is a fault constitutive parameter and S is the coulomb stress function. The starting state variable is , where is the background stressing rate. The earthquake rate R at the midpoint of ...
Thu, 23 Jul 2015 03:41:15 -0700
Soil moisture is a primary state variable of hydrology and the water cycle on land, and is an initial or boundary condition of Earth science models. An assessment of surface soil moisture is necessary for applications such as weather forecasting ...
The National Law Review
Sun, 05 Jul 2015 09:30:00 -0700
The Board also noted that Gruse fails to disclose at least one state variable that identifies a location where a state of rights is tracked and associating the at least one state variable with the at least one right in the first location. The Petition ...
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 ...
Armed with Science
Armed with Science
Fri, 17 Jul 2015 04:50:56 -0700
Including electron spin as an additional state variable offers new prospects for information processing, enabling future non-volatile, reprogrammable devices beyond the current semiconductor technology roadmap. Silicon is an ideal host for such a spin ...
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 ...
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 ...
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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