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Mechanics Dynamics
Modeling and Analysis of Dynamic Systems
173 SOLVED PROBLEMS
Question: 10.24
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 be ...
Verified Answer:
a. The dynamics of the plant is described by [late...
Question: 10.23
Full-State Feedback Control of a DC Motor–Driven Cart Consider the full-state feedback control system discussed in Example 10.22, in which the statespace representation of the plant is x = [0 1 0 -16.883]x + [0 3.778 ]u, y = [1 0]x, and the mathematical model of the controller is u = −Kx with ...
Verified Answer:
There are two ways to construct a Simulink block d...
Question: 10.22
Full-State Feedback Control Design Consider the DC motor–driven cart discussed in Example 10.12, in which a PD controller was designed to achieve 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 achieves the ...
Verified Answer:
a. The transfer function of the cart is given by [...
Question: 10.21
Controllability and Observability Determine the controllability and observability for the second-order systems given in Example 10.20. ...
Verified Answer:
For the system in Part (a), the controllability ma...
Question: 10.20
Controllability and Observability Consider a dynamic system described by G(s) = 2/(s + 4), which can be converted to state-space form as x1 = -4×1+2u, y = x1. a. A new state is added and the resulting state-space equation is x1 = -4×1 + 2u, x2 = -x2, y = x1 +3×2. Determine the transfer function ...
Verified Answer:
a. The system matrices
\mathbf{A}, \mathbf{...
Question: 10.19
Stability Analysis in State Space a. Compute the poles of the system described by x = [0 1 0 -16.883]x + [0 3.778] u, y = [1 0]x. b. Verify the results by converting the state-space representation to a transfer function and then identifying the poles of the transfer function. ...
Verified Answer:
a. The characteristic equation is
|s \math...
Question: 10.18
Proportional Control Design Using a Bode Plot Design a proportional controller for the cart system in Example 10.12 using the Bode plot technique. ...
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The Bode plot for the open-loop transfer function ...
Question: 10.17
Stability Analysis Using a Bode Plot Consider the feedback control system in Figure 10.63, where KG(s) = K 100/s(s+5)(s+20) ,and K is assumed to be 1. Plot the Bode magnitude and phase curves using MATLAB. Give comments on the stability of the closed-loop system. ...
Verified Answer:
Note that the Bode plot is drawn based on the loop...
Question: 10.16
Bode Plot Sketching Plot the Bode magnitude and phase for the system with the transfer function KG(s) = K s+2/s(s²+8s+400) , where K = 1. ...
Verified Answer:
Step 1: Convert the transfer function to the frequ...
Question: 10.15
Proportional Control Design Using Root Locus Design a proportional controller for the cart system in Example 10.12 using the root locus technique. ...
Verified Answer:
For proportional feedback control of the DC motor-...
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