Control Systems Engineering
7th Edition
ISBN: 9781118170519
Author: Norman S. Nise
Publisher: WILEY
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Question
Chapter 7, Problem 3P
To determine
The steady state error of unity feedback system for the given input.
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##### For the attached electropneumatic circuit, design where and how a counter should be attached so that a part is counted for each cycle
If you have a spring mass damper system, given by m*x_double_dot + c*x_dot + kx = 0 where m, c, k (all positive scalars) are the mass, damper coefficient, and spring coefficient, respectively. x ∈ R represents the displacement of the mass.
Let us then discuss the stability of the system by using Lyapunov stability theorem. Consider the system energy as a candidate Lyapunov function shown in the image.
Discuss the positive definiteness of V (x, x_dot).
Derive the Lyapunov rate of this system (i.e., V_dot ), and discuss the stability property of thesystem based on the information we gain from ̇V_dot .
In class, two approaches—Theorems 1 and 2 below—are discussed to prove asymptotic stability of asystem when ̇V = 0.
Show the asymptotic stability of the system given in Eq. (1) by applying Theorem 1.
Show the asymptotic stability of the system given in Eq. (1) by applying Theorem 2.
Chapter 7 Solutions
Control Systems Engineering
Ch. 7 - Prob. 1RQCh. 7 - A position control, tracking with a constant...Ch. 7 - Name the test inputs used to evaluate steady-state...Ch. 7 - Prob. 4RQCh. 7 - Increasing system gain has what effect upon the...Ch. 7 - Prob. 6RQCh. 7 - Prob. 7RQCh. 7 - Prob. 8RQCh. 7 - Prob. 9RQCh. 7 - The forward transfer function of a control system...
Ch. 7 - Prob. 11RQCh. 7 - Prob. 12RQCh. 7 - Is the forward-path actuating signal the system...Ch. 7 - Prob. 14RQCh. 7 - Prob. 15RQCh. 7 - Name two methods for calculating the steady-state...Ch. 7 - Prob. 1PCh. 7 - Figure P7.2 shows the ramp input r(t) and the...Ch. 7 - Prob. 3PCh. 7 - Prob. 4PCh. 7 - Prob. 5PCh. 7 - Prob. 6PCh. 7 - Prob. 7PCh. 7 - Prob. 8PCh. 7 - A system has Kp = 4. What steady-state error can...Ch. 7 - Prob. 10PCh. 7 - Prob. 11PCh. 7 - Prob. 12PCh. 7 - For the system shown in Figure P7.4. [Section:...Ch. 7 - Prob. 14PCh. 7 - 1515. Find the system type for the system of...Ch. 7 - Prob. 16PCh. 7 - Prob. 17PCh. 7 - Prob. 18PCh. 7 - Prob. 19PCh. 7 - Given the system of Figure P7.8, design the value...Ch. 7 - Prob. 21PCh. 7 - Prob. 22PCh. 7 - Prob. 23PCh. 7 - Prob. 24PCh. 7 - Prob. 25PCh. 7 - Prob. 26PCh. 7 - Prob. 27PCh. 7 - Prob. 28PCh. 7 - Prob. 29PCh. 7 - Prob. 30PCh. 7 - Prob. 31PCh. 7 - Prob. 32PCh. 7 - Given the system in Figure P7.9, find the...Ch. 7 - Repeat Problem 33 for the system shown in Figure...Ch. 7 - Prob. 36PCh. 7 - Prob. 37PCh. 7 - Prob. 38PCh. 7 - Design the values of K1and K2in the system of...Ch. 7 - Prob. 41PCh. 7 - For each system shown in Figure P7.17, find the...Ch. 7 - For each system shown in Figure P7.18, find the...Ch. 7 - Prob. 44PCh. 7 - 45. For the system shown in Figure P7.20,...Ch. 7 - Prob. 47PCh. 7 - Prob. 48PCh. 7 - Prob. 49PCh. 7 - Prob. 50PCh. 7 - Prob. 51PCh. 7 - Prob. 52PCh. 7 - Prob. 53PCh. 7 - Prob. 54PCh. 7 - Prob. 55PCh. 7 - Prob. 58PCh. 7 - Prob. 59PCh. 7 - Prob. 62PCh. 7 - Prob. 63PCh. 7 - Prob. 64PCh. 7 - Prob. 65PCh. 7 - Prob. 66PCh. 7 - Prob. 67PCh. 7 - Prob. 68P
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