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Q. What do you mean by Superposition and linearity?
Mathematically a function is said to be linear if it satisfies two properties: homogeneity (proportionality or scaling) and additivity (superposition),
f (Kx) = Kf (x) (homogeneity)
where K is a scalar constant, and
f (x1 + x2) = f (x1) + f (x2) (additivity)
Linearity requires both additivity and homogeneity. For a linear circuit or system in which excitations x1 and x2 produce responses y1 and y2, respectively, the application of K1x1 and K2x2 together (i.e., K1x1 + K2x2) results in a response of (K1y1 + K2y2), where K1 and K2 are constants. With the cause-and-effect relation between the excitation and the response, all linear systems satisfy the principle of superposition. A circuit consisting of independent sources, linear dependent sources, and linear elements is said to be a linear circuit. Note that a resistive element is linear. Capacitors and inductors are also circuit elements that have a linear input-output relationship provided that their initial stored energy is zero. Nonzero initial conditions are to be treated as independent sources.
Q. Explain Digital control systems? Significant progress has been made in recent years in discrete-data and digital control systems because of the advancesmade in digital compu
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