Modeling and Analysis of Dynamic Systems 3rd. Edition by Ramin S. Esfandiari, Bei Lu | 9781351751650 | 1351751654 | Holooly

Control Systems

Modeling and Analysis of Dynamic Systems

174 SOLVED PROBLEMS

Question: 7.4

A Single-Tank Liquid-Level System with a Pump Consider the single-tank liquid-level system shown in Figure 7.11, where a pump is connected to the bottom of the tank through a valve of linear resistance R. The inlet to the pump is open to the atmosphere, and the pressure of the fluid increases by Δp ...

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We begin by applying the law of conservation of ma...

Question: 6.14

A Series RLC Circuit Consider the series RLC circuit shown in Figure 6.57, where R = 1 Ω, L = 1 H, and C = 0.5 F. When the switch is closed at 1 second, the circuit is driven by a 24 V DC voltage source. Assume that all initial conditions are zero. a. Build a Simscape model of the physical system ...

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a. The Simscape block diagram corresponding to the...

Question: 5.12b

A Lever Mechanism Consider the system shown in Figure 5.77, in which a lever arm has a force applied on one side and a spring–damper combination on the other side with a suspended mass. When θ = 0 and f = 0, the system is at static equilibrium. Assume that the lever arm can be approximated as a ...

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This is a mixed system with two masses. The suspen...

Question: 5.12a

A Pure Rolling Disk Consider the system shown in Figure 5.60a, in which a uniform disk of mass m and radius r rolls on a horizontal surface. A translational spring of stiffness k is attached to the disk. Assuming that there is no slipping between the disk and the surface, derive the differential ...

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The free-body diagram of the system is shown in Fi...

Question: 5.5

A Two-Degree-of-Freedom Quarter-Car Model Consider a quarter-car model shown in Figure 5.34a, where m1 is the mass of one-fourth of the car body and m2 is the mass of the wheel–tire–axle assembly. The spring k1 represents the elasticity of the suspension and the spring k2 represents the elasticity ...

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a. We choose the displacements of the two masses [...

Question: 5.18

A Cart–Inverted-Pendulum System (Energy Method) Reconsider the mechanical system, as shown in Figure 5.79. Derive the equations of motion of the system by using Lagrange’s equations. ...

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As shown in Figure 5.88a, the motion of the cart i...

Question: 10.26

Control of a Single-Degree-of-Freedom Mass–Spring–Damper System Consider a single-degree-of-freedom mass–spring–damper system as shown in Figure 5.29, where m = 2 kg, b = 2 N s/m, and k = 50 N/m. A PD controller, f = −kpx − kDx , is designed to adjust the input force f, so that the mass block can ...

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a. The dynamics of the plant is described by [late...

Question: 10.25

Full-State Feedback Control of a Direct Current Motor–Driven Cart Consider the full-state feedback control system discussed in Example 10.24, in which the state-space representation of the plant is x =[0 1 0 -16.883]x +[0 3.778]u y=[1 0]uand the mathematical model of the controller is u = −Kx with ...

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There are two ways to construct a Simulink block d...

Question: 10.24

Full-State Feedback Control Design Consider the DC motor–driven cart discussed in Example 10.13, in which a PD controller was designed to satisfy the requirements: overshoot Mp < 10% and rise time tr < 0.15 s. a. Find a full-state feedback controller such that the closed-loop system meets the same ...

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a. The transfer function of the cart is given by [...

Question: 10.23

Controllability and Observability Determine the controllability and observability of the two second-order systems given in Example 10.22. ...

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For the system in Part (a), the controllability ma...

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