Dynamic Modeling and Control of Engineering Systems 3rd. Edition by Bohdan T. Kulakowski, John F. Gardner, J. Lowen Shearer | 9780521864350 | 0521864356 | Holooly

Dynamic Modeling and Control of Engineering Systems [EXP-11549]

81 SOLVED PROBLEMS

Question: 7.3

(a) Write the state-variable equations based on the energy-storage elements L and C for the circuit shown in Fig. 7.13(a). (b) Linearize these equations for small perturbations of all variables. (c) Combine to eliminate the unwanted variable and obtain the input–output system differential equation

Verified Answer:

(a) In general, the state-variable for a capacitor...

Question: 2.4

A mass m, supported only by a bearing having a pressurized film of viscous fluid, undergoes translation (i.e., motion along a straight line in the x direction) as the result of having a time-varying input force Fi applied to it, as shown in Fig. 2.10. The object is to develop a mathematical model

Verified Answer:

Newton’s second law applied to the mass m yields [...

Question: 10.2

A permanent magnet dc motor is being used to drive a mechanical load consisting of a load inertia j1 and load damping B1 as shown in Fig. 10.10. Develop the system differential input–output equation relating the output speed _ to the input voltage ei.

Verified Answer:

Asimplified schematic of the dc motor is shown in ...

Question: 7.5

A time-varying inductor in series with a voltage source and a fixed resistor is being used as part of a moving-metal detector. The circuit diagram for this system is shown in Fig. 7.25. Derive the state-variable equations for the circuit.

Verified Answer:

Use Kirchhoff’s voltage law to write

e_{s} ...

Question: 10.3

A variable-displacement hydraulic motor supplied with a constant flow source is used to vary the output speed of an inertia-damper load, as shown in Fig. 10.13. The displacement of the motor Dm is proportional to the stroke lever angle Ψ , and the motor has leakage resistance Rf, rotor inertia Jm,

Verified Answer:

The detailed symbolic diagram for this system is s...

Question: 9.2

A variable-orifice NLR is being used to modulate the flow rate QNLR and control the pressure P2r in the simple fluid control system shown in Fig. 9.10. The flow equation for the orifice is QNLR = Cl Ao(P2r)^0.5. Develop the input–output differential equation relating small changes in the output pres

Verified Answer:

The elemental equations for small perturbations in...

Question: 14.4

Although the previous example portrays the manner in which control systems are often designed in practice, the heuristic nature of the approach is unsatisfying for a number of reasons. In particular, because there are three different parameters to adjust, each of which has a unique contribution,

Verified Answer:

In this example, the problem of Example 14.3 is so...

Question: 12.1

An electric motor operating at a constant speed of 1000 rpm is generating a vertical vibratory force Fm that is due to an imbalance in its rotating elements. The amplitude of force Fm is 400N. To absorb the vibration, the motor is supported by rubber shock mounts of stiffness k = 50,000 N/m and

Verified Answer:

The basic equation of motion for the vertical moti...

Question: 8.1

As advances in microelectronic circuits have allowed continual miniaturization of digital circuits, the issue of cooling has become more important. If you open the PC on your desktop, you will find that the central processing unit (CPU) has a large black metal piece attached to it. This piece, the

Verified Answer:

The first step of the solution is to use the Biot ...

Question: 14.1

Consider a heating system for a one-room sealed-up house, shown schematically in Fig. 14.5. The house is modeled as a lumped system having contents of mass m and average specific heat c. The rate of heat supplied by an electric heater is Q_in(t). The spatial average temperature inside the house is

Verified Answer:

The heat balance equation is

mc\frac{dT_{1...

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