System Dynamics 2nd. Edition by William John Palm | 9780073529271 | 0073529273 | Holooly

Control Systems

System Dynamics

293 SOLVED PROBLEMS

Question: 9.4.1

Estimating Capacitance from the Free Response Commercially available resistors are marked with a color code that indicates their resistance value. Suppose that the resistance in the circuit of Figure 9.4.1a is 10^5 Ω . A voltage is applied to the circuit for t < 0 and then is suddenly removed at ...

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The circuit model may be derived from Kirchhoff’s ...

Question: 8.5.2

Identifying a Second-Order System Measured response data are shown by the small circles in Figure 8.5.2. Determine the transfer function ...

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After drawing the asymptotes shown by the dashed l...

Question: 8.4.4

Response to Nonsinusoidal Inputs An engine valve train can be modeled as an equivalent mass, equivalent damping, and two stiffnesses, one due to the valve spring and one due to the elasticity of the push rod (Figure 8.4.5). The equation of motion is Io /a² x + ce x + (k1 + k2 a²/b² )x = a/b k2 y(t) ...

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The transfer function is

T (s) = \frac{X(s)...

Question: 8.4.3

Superposition and Forced Response The model of a series RC circuit is RCv + v = vs Suppose the input voltage is the following sum of a constant and two sine waves. vs(t) = 10 + 5 sin t + 3 sin 6t Obtain the expression for the steady-state response if the time constant is τ = RC = 0.5 s. ...

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The total forced response at steady state is the s...

Question: 8.4.1

Bandwidth of a First-Order Model Consider the model τv + v = f (t), for which M = V /F = 1 /√1 + ω²τ² Obtain an expression for the bandwidth in terms of τ and interpret its significance ...

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The peak in M occurs at ω = 0 and is

M_{\te...

Question: 13.2.2

Isolation of a Motor Often motors are mounted to a base with an isolator consisting of an elastic pad. The pad serves to reduce the motor’s rotating unbalance force transmitted to the base. A particular motor weighs 10 lb and runs at 3200 rpm. Neglect damping in the pad and calculate the pad ...

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A 90% force reduction corresponds to a transmissib...

Question: 10.7.2

Design of a PD Control System For the system shown in Figure 10.7.1, we are given that I = 10 and c = 2. The dominant time constant τ is specified to be 2 s, and the damping ratio is specified to be ζ = 1. a. Compute the required values for KP and K D. Evaluate the steady-state command error and ...

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a. From the figure we obtain the following output,...

Question: 10.7.1

PD Control of a Neutrally Stable Second-Order Plant PD control of a neutrally stable second-order plant is shown in Figure 10.7.1. Investigate its performance for step and ramp inputs for c ≥ 0. ...

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The output equation is

\Theta(s) = \frac{K_...

Question: 10.6.4

Use of Internal Feedback Suppose the plant to be controlled is G p(s) = 1/I s + c where I = 5 and c = 2. Figure 10.6.6 shows a proposed alternative to PI control for this plant. It uses an internal feedback loop to adjust the output of the controller. The dominant time constant is specified to be ...

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a. From the figure, we obtain the output equation ...

Question: 10.6.3

Computing PI Gains A PI control system is shown in Figure 10.6.2. Suppose the plant has the parameter values I = 5 and c = 2. The dominant time constant is specified to be 0.5 s. a. Compute the required values for KP and KI for each of the following three cases: (1) ζ = 0.707, (2) ζ = 1, and (3) ...

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From the block diagram we obtain the following out...

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