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:
“These modern ingenious sciences and arts do not affect me as those more venerable arts of hunting and fishing, and even of husbandry in its primitive and simple form; as ancient and honorable trades as the sun and moon and winds pursue, coeval with the faculties of man, and invented when these were invented. We do not know their John Gutenberg, or Richard Arkwright, though the poets would fain make them to have been gradually learned and taught.”
—Henry David Thoreau (1817–1862)
“Time in the hand is not control of time,
Nor shattered fragments of an instrument
A proof against the wind; the wind will rise,
We can only close the shutters.”
—Adrienne Rich (b. 1929)
“No one thinks anything silly is suitable when they are an adolescent. Such an enormous share of their own behavior is silly that they lose all proper perspective on silliness, like a baker who is nauseated by the sight of his own eclairs. This provides another good argument for the emerging theory that the best use of cryogenics is to freeze all human beings when they are between the ages of twelve and nineteen.”
—Anna Quindlen (20th century)