Chap2_2
E2.12 Off-road vehicles experience many disturbance inputs as they traverse over rough roads. An active suspension system can be controlled by a sensor that looks “ahead” at the road conditions. An example of a simple suspension system that can accommodate the bumps is shown in Fig. E2.12. Find the appropriate gain K1 so that the vehicle does not bounce when the desired deflection is R(s)=0 and the disturbance is D(s).
E(s)
P2.1 An electric circuit is shown in Fig. P2.1. Obtain a set of simultaneous integrodifferential equations representing the network.
P2.2 A dynamic vibration absorber is shown in Fig. P2.2. This system is representative of many situations involving the vibration of machines containing unbalanced components. The parameters M2 and k12 may be chosen so that the main mass M1 does not vibrate in the steady-state when
F(t)?asin?0t. Obtain the differential equations describing the system.
P2.3 A couple spring-mass system is shown in Fig. P2.3. The masses and springs are assumed to be equal. Obtain the differential equations describing the system.
P2.7 Obtain the transfer function of the differentiating circuit shown in Fig P2.7.
P2.13 A electromechanical open-loop control system is shown in Fig. P2.13. The generator, driven at a constant speed, provides the field voltage for the motor. The motor has an inertia Jm and bearing friction bm. Obtain the transfer function ?L(s)/Vf(s), and draw a block diagram of the system. The generator voltage, vg, can be assumed to be proportional to the field current, if.
P2.17 A mechanical system is shown in Fig. P2.17, which is subjected to a known displacement x3(t) with respect to the reference.
a) Determine the two independent equations of motion.
b) Obtain the equations of motion in terms of the Laplace transform, assuming that the initial
conditions are zero.
c) Sketch a signal-flow graph representing the system of equations.
d) Obtain the relationship between X1(s) and X3(s), T13(s), by using Mason’s signal-flow gain
formula. Compare the work necessary to obtain T13(s) by matrix methods to that using
Mason’s signal-flow gain formula.
P2.34 Find the transfer function for Y(s)/R(s) for the idle speed control system for a fuel injected engine as shown in Fig. P2.34.
P2.34 Find the transfer function for Y(s)/R(s) for the idle P2.35 The suspension system for one wheel of an old-fashioned pickup truck is illustrated in
Fig. P2.35. The mass of the vehicle is m1 and the mass of the wheel is m2. The suspension spring has a spring constant k1, and the tire has a spring constant k2. The damping constant of the shock absorber is b. Obtain the transfer function Y1(s)/X(s), which represents the vehicle response to bumps in the road.
y1k1y2m1bm2k2 xP2.47 A load added to a truck results in a force F on the support spring, and the tire flexes as shown in Fig. P2.47(a). The model for the tire movement is shown in Fig. P2.47(b). Determine the transfer function X1(s)/F(s).
控制系统第2章部分练习（英语）
