Dorf Solution Manual
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Modern control systems 13th edition dorf solutions manual.1.open−loopclosed−loopyModern Control Systems 13th Edition Dorf SOLUTIONS MANUALFull download:H A P T E R 2Mathematical Models of SystemsExercisesE2.1 We have for the open-loopy = r2and for the closed-loope = r − y and y = e2.So, e = r − e2 and e2 + e − r = 0.1510500 1 2 3 4 5 6rFIGURE E2.1Plot of open-loop versus closed-loop.For example, if r = 1, then e2 + e − 1 = 0 implies that e = 0.618. Thus,y = 0.382. A plot y versus r is shown in Figure E2.1.22.Spring breaksSpring compressese∂T ◦−Force(n)Exercises 23E2.2 Definef(T ) = R = R0−0.1TandThen,∆R = f(T ) − f(T0), ∆T = T − T0.∂fwhere∆R = f(T ) − f(T0) =∂fT =T0=20−0.1T0∆T + ∂T= 0.1R0 e◦= −135,T =T0=20when R0 = 10, 000Ω. Thus, the linear approximation is computed byconsidering only the first-order terms in the Taylor series expansion, andis given by∆R = −135∆T.E2.3 The spring constant for the equilibrium point is found graphically byestimating the slope of a line tangent to the force versus displacementcurve at the point y = 0.5cm, see Figure E2.3.
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