Control Systems Engineering
7th Edition
ISBN: 9781118170519
Author: Norman S. Nise
Publisher: WILEY
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 6, Problem 4RQ
Why are marginally stable systems considered unstable under the BIBO definition of stability?
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A linear, time-invariant system is marginally stable if the natural response:
oscillates as time approaches infinity
grows without bound as time approaches infinity
approaches zero as time approach infinity
approaches infinity as time approach infinity
1. Verify Eqs. 1 through 5.
Figure 1: mass spring damper
In class, we have studied mechanical systems of this
type. Here, the main results of our in-class analysis are
reviewed. The dynamic behavior of this system is deter-
mined from the linear second-order ordinary differential
equation:
where
(1)
where r(t) is the displacement of the mass, m is the
mass, b is the damping coefficient, and k is the spring
stiffness. Equations like Eq. 1 are often written in the
"standard form"
ď²x
dt2
r(t) =
= tan-1
d²r
dt2
m.
M
+25wn +wn²x = 0
(2)
The variable wn is the natural frequency of the system
and is the damping ratio.
If the system is underdamped, i.e. < < 1, and it has
initial conditions (0) = zot-o = 0, then the solution
to Eq. 2 is given by:
IO
√1
x(1)
T₁ =
+b+kr = 0
dt
2π
dr.
dt
ل لها
-(wat sin (wat +)
and
is the damped natural frequency.
In Figure 2, the normalized plot of the response of this
system reveals some useful information. Note that the
amount of time Ta between peaks is…
The Routh-Hurwitz criterion to be used to determine the stability of a system with a characteristic equation given by
85 + 2s4 + 2s3 + 4s² + 11s + 10
Comment on the stability of the system.
Neutral
Stable
Unstable
Chapter 6 Solutions
Control Systems Engineering
Ch. 6 - Prob. 1RQCh. 6 - Prob. 2RQCh. 6 - What would happen to a physical system chat...Ch. 6 - Why are marginally stable systems considered...Ch. 6 - Prob. 5RQCh. 6 - Prob. 6RQCh. 6 - Prob. 7RQCh. 6 - Prob. 8RQCh. 6 - Prob. 9RQCh. 6 - Why do we sometimes multiply a row of a Routh...
Ch. 6 - Prob. 11RQCh. 6 - Prob. 12RQCh. 6 - 13. Does the presence of an entire row of zeros...Ch. 6 - Prob. 14RQCh. 6 - Prob. 15RQCh. 6 - Prob. 16RQCh. 6 - Tell how many roots of the following polynomial...Ch. 6 - Tell how many roots of the following polynomial...Ch. 6 - Using the Routh table, tell how many poles of the...Ch. 6 - Prob. 4PCh. 6 - Determine how many closed-loop poles lie in the...Ch. 6 - Determine how many closed-loop poles lie in the...Ch. 6 - MATLAB ML 7. Use MATLAB to find the pole location...Ch. 6 - Symbolic Math SM 8. Use MATLAB and the Symbolic...Ch. 6 - Determine whether the unity feedback system of...Ch. 6 - Use MATLAB to find the pole locations for the...Ch. 6 - Consider the unity feedback system of Figure P6.3...Ch. 6 - In the system of Figure P6.3, let Gs=Ks+1ss2s+3...Ch. 6 - Given the unity feedback system of Figure P6.3...Ch. 6 - Using the Routh-Hurwitz criterion and the unity...Ch. 6 - Given the unity feedback system of Figure P6.3...Ch. 6 - Repeat Problem 15 using MATLAB.Ch. 6 - Prob. 17PCh. 6 - For the system of Figure P6.4, tell how many...Ch. 6 - Using the Routh-Hurwitz criterion, tell how many...Ch. 6 - Determine if the unity feedback system of Figure...Ch. 6 - For the unity feedback system of Figure P6.3 with...Ch. 6 - In the system of Figure P6.3, let Gs=Ksassb Find...Ch. 6 - For the unity feedback system of Figure P63 with...Ch. 6 - Find the range of K for stability for the unity...Ch. 6 - For the unity feedback system of Figure P6.3 with...Ch. 6 - find the range of K for stability. [Section: 6.41]...Ch. 6 - Find the range of gain, K, to ensure stability in...Ch. 6 - Using the Routh-Hurwitz criterion, find the value...Ch. 6 - Use the Routh-Hurwitz criterion to find the range...Ch. 6 - Prob. 32PCh. 6 - Given the unity feedback system of Figure P63 with...Ch. 6 - Repeat Problem 33 for [Section: 6.4]...Ch. 6 - For the system shown in Figure P6.8, find the...Ch. 6 - Given the unity feedback system of Figure P6.3...Ch. 6 - For the unity feedback system of Figure P6.3 with...Ch. 6 - For the unity feedback system of Figure P6.3 with...Ch. 6 - Given the unity feedback system of Figure P6.3...Ch. 6 - Using the Routh-Hurwitz criterion and the unity...Ch. 6 - Find the range of K to keep the system shown in...Ch. 6 - Prob. 43PCh. 6 - The closed-loop transfer function of a system is...Ch. 6 - Prob. 45PCh. 6 - Prob. 46PCh. 6 - An interval polynomial is of the form...Ch. 6 - A linearized model of a torque-controlled crane...Ch. 6 - The read/write head assembly arm of a computer...Ch. 6 - A system is represented in state space as...Ch. 6 - State Space SS 52. The following system in state...Ch. 6 - Prob. 54PCh. 6 - A model for an airplane’s pitch loop is shown in...Ch. 6 - Prob. 57PCh. 6 - Prob. 58PCh. 6 - Prob. 59PCh. 6 - Prob. 60PCh. 6 - Prob. 61PCh. 6 - Look-ahead information can be used to...Ch. 6 - Prob. 63PCh. 6 - It has been shown (Pounds, 2011) that an unloaded...Ch. 6 - Prob. 65PCh. 6 - The system shown in Figure P6.16 has G1s=1/ss+2s+4...Ch. 6 - Prob. 67PCh. 6 - Prob. 68PCh. 6 - Hybrid vehicle. Figure P6.l8 shows the HEV system...Ch. 6 - Prob. 70P
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- The Gilles & Retzbach model of a distillation column, the system model includes the dynamics of a boiler, is driven by the inputs of steam flow and the flow rate of the vapour side stream, and the measurements are the temperature changes at two different locations along the column. The state space model is given by: x = 0 00 -30.3 0.00012 -6.02 0 0 0 -3.77 00 0 -2.80 0 0 Is the system?: a. unstable b. C. not unstable x+ 6.15 0 0 0 0 3.04 0 0.052 not asymptotically stable d. asymptotically stable -1 u y = 0 0 0 0 -7.3 0 0 -25.0 Xarrow_forwardWhat is the minimum dampening ratio for an underdamped system such that its overshoot is limited to 10%? This image is my scratch work based of an in-class problem. I'm unsure of the steps and the final equation for Zeta. It also puts out a different number that my professor wrote…arrow_forwardA system has the following characteristic equation: s+ s+ 3s+ 2s + 2 = 0 Using the Routh-Hurwitz method, checka. How many roots are to the right of the imaginary axis?b. Is the system stable?.arrow_forward
- Classify the structures for Stability and determinacy , if unstable state why, if indeterminate state the degree of indeterminacyarrow_forwardCharacteristic equation of a system is given by: C = s³ + 4s² + 25s + K = 0 %3D determine the range of values of K for which the system is stable. Use Roth Hurwitz stability criteria.arrow_forwardConclusion on observable Canonical Form and Observer Design in control engineeringarrow_forward
- (b) For the configuration shown below. Write the finite difference equation under steady state conditions for node (m, n). Ay I m, n + 1 m, n-1 <- Ax Ax- Material A KA m+1, n Ay Material B kąarrow_forwardThe response of a system under arbitrary force can be determined by summing the responses resulting from several elementary impulses. Choose an option: RealFalsearrow_forwardSummarize five key steps involved in defining a system using state-space approach.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning
Principles of Heat Transfer (Activate Learning wi...
Mechanical Engineering
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Cengage Learning
Introduction to Kinematics; Author: LearnChemE;https://www.youtube.com/watch?v=bV0XPz-mg2s;License: Standard youtube license