By Shlomo Engelberg

ISBN-10: 1860945708

ISBN-13: 9781860945700

Impressive a cautious stability among mathematical rigor and engineering-oriented purposes, this textbook goals to maximise the readers' figuring out of either the mathematical and engineering elements of keep an eye on concept. The bedrock parts of classical regulate conception are comprehensively coated: the Routh–Hurwitz theorem and functions, Nyquist diagrams, Bode plots, root locus plots, the layout of controllers (phase-lag, phase-lead, lag-lead, and PID), and 3 additional complicated subject matters: non-linear keep watch over, smooth regulate and discrete-time regulate. A Mathematical creation to regulate conception could be a useful booklet for junior and senior point collage scholars in engineering, relatively electric engineering. scholars with an exceptional wisdom of algebra and complicated variables also will locate many attention-grabbing functions during this quantity.

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**Extra resources for A Mathematical Introduction to Control Theory (Series in Electrical and Computer Engineering)**

**Example text**

Thus: I(c)K ' 500 A - (s + 200)(s + 800) , s + 200 B s + 800' Multiplying the fractions by (s + 200)(s + 800), we find that: 500 = A(s + 800) + B(s + 200) =» A = 5/6, B = -5/6. We find that the solution of the equation is: i(t) = | ( e - 2 0 O t - e - 8 0 0 t ) « ( * ) where the current is measured in amperes. A Look at Resonance^—An Example Consider the equation satisfied by a spring-mass system with an m Kg mass and a spring whose spring constant is k N/M that is being excited by a sinusoidal force of amplitude A newtons and angular frequency Q, rad/sec.

E. Iog10(x)—as opposed to the natural logarithm, ln(x) = log e (z). 4 Named after their inventor, Hendrik Bode (pronounced bode—with a hard o and a hard e). Bode invented the Bode plots in 1938 while employed by the Bell Telephone Laboratories [Lew92]. Transfer Functions 41 phase plot of the combined system we also need only add the phase plots of the separate systems. We scale the frequency logarithmically because of the fact that our transfer functions generally behave like powers of s. Consider (jui)n measured in dB.

7 Exercises (1) Find the Laplace transform of: (a) cos(ut)u(t), u) > 0 Note that u(u>t) = u(t) if u> > 0. (b) f(t) = te-1 cos{t)u(t) (c) f(t) = Pe-tuit) (d) f(t) = e"* sm(2t)u{i) (2) Find the function whose Laplace transform is: Mathematical Preliminaries 33 (a) F(8) - 1±1 (b) (c) (d) (e) Do each problem both "by hand" and using MATLAB'S residue command. (3) Use the Laplace transform to solve the differential equation: y"(t) + 5y'(t) + Ay(t) = 1 subject to the initial conditions: 1,(0) = j/(0) = 0 (4) Use the Laplace transform to solve the integral equation: / y(r) dr = -y(t) + u(t) Jo where u{t) is the unit step function.

### A Mathematical Introduction to Control Theory (Series in Electrical and Computer Engineering) by Shlomo Engelberg

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