Modern Control Theory
In contrast to the frequency domain analysis of the classical control theory, modern control theory utilizes the time-domain state space representation, a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations. To abstract from the number of inputs, outputs and states, the variables are expressed as vectors and the differential and algebraic equations are written in matrix form (the latter only being possible when the dynamical system is linear). The state space representation (also known as the "time-domain approach") provides a convenient and compact way to model and analyze systems with multiple inputs and outputs. With inputs and outputs, we would otherwise have to write down Laplace transforms to encode all the information about a system. Unlike the frequency domain approach, the use of the state space representation is not limited to systems with linear components and zero initial conditions. "State space" refers to the space whose axes are the state variables. The state of the system can be represented as a vector within that space.
Read more about this topic: Control Theory
Famous quotes containing the words modern, control and/or theory:
“A building is akin to dogma; it is insolent, like dogma. Whether or no it is permanent, it claims permanence, like a dogma. People ask why we have no typical architecture of the modern world, like impressionism in painting. Surely it is obviously because we have not enough dogmas; we cannot bear to see anything in the sky that is solid and enduring, anything in the sky that does not change like the clouds of the sky.”
—Gilbert Keith Chesterton (1874–1936)
“When a book, any sort of book, reaches a certain intensity of artistic performance it becomes literature. That intensity may be a matter of style, situation, character, emotional tone, or idea, or half a dozen other things. It may also be a perfection of control over the movement of a story similar to the control a great pitcher has over the ball.”
—Raymond Chandler (1888–1959)
“A theory of the middle class: that it is not to be determined by its financial situation but rather by its relation to government. That is, one could shade down from an actual ruling or governing class to a class hopelessly out of relation to government, thinking of gov’t as beyond its control, of itself as wholly controlled by gov’t. Somewhere in between and in gradations is the group that has the sense that gov’t exists for it, and shapes its consciousness accordingly.”
—Lionel Trilling (1905–1975)