Control Systems Engineering
7th Edition
ISBN: 9781118170519
Author: Norman S. Nise
Publisher: WILEY
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Chapter 1, Problem 9P
The human eye has a biological control system that varies the pupil diameter to mamtain constant light intensity to the retina. As the light intensity increases, the optical nerve sends a signal to the brain, which commands internal eye muscles to decrease the pupil's eye diameter. When the light intensity decreases, the pupil diameter increases.
- Draw a functional block diagram of the light-pupil system indicating the input, output, and intermediate signals; the sensor, the controller; and the actuator. (Section 1.4: Introduction to a Case Study]
- Under normal conditions the incident light will be larger than the pupil. If the incident light is smaller than the diameter of the pupil, the feedback path is broken (Beehhoefer. 2005). Modify your block diagram from Part a. to show where the loop is broken. What will happen if the narrow beam of light varies in intensity, such as in a sinusoidal fashion?
- It has been found (Bechhuefer. 2005) that it takes the pupil about 300 milliseconds to react to achongc in the incident light. If light shines off center to the retina, describe the response of the pupil with delay present and then without delay present
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Problem 2 (55 pts). We now consider the FEM solution of Problem 1.(a) [5pts] Briefly describe the 4 steps necessary to obtain the approximate solution of thatBVP using the Galerkin FEM. Use the minimum amount of math necessary to supportyour explanations.(b) [20pts] Derive the weak form of the BVP.(c) [10pts] Assuming a mesh of two equal elements and linear shape functions, sketch byhand how you expect the FEM solution to look like. Also sketch the analytical solutionfor comparison. In your sketch, identify the nodal degrees of freedom that the FEMsolution seeks to find.(d) [10pts] By analogy with the elastic rod problem and heat conduction problem considered in class, write down the stiffness matrix and force vector for each of the twoelements considered in (c).(e) [10pts] Assemble the global system of equations, and verbally explain how to solve it.
An aluminum rod of length L = 1m has mass density ρ = 2700 kgm3 andYoung’s modulus E = 70GPa. The rod is fixed at both ends. The exactnatural eigenfrequencies of the rod are ωexactn =πnLqEρfor n=1,2,3,. . . .1. What is the minimum number of linear elements necessary todetermine the fundamental frequency ω1 of the system? Discretizethe rod in that many elements of equal length, assemble the globalsystem of equations KU = ω2MU, and find the fundamentalfrequency ω1. Compute the relative error e1 = (ω1 − ωexact1)/ωexact1.Sketch the fundamental mode of vibration.
Chapter 1 Solutions
Control Systems Engineering
Ch. 1 - Prob. 1RQCh. 1 - Prob. 2RQCh. 1 - Prob. 3RQCh. 1 - Prob. 4RQCh. 1 - State one condition under which the error signal...Ch. 1 - Prob. 6RQCh. 1 - Name two advantages of having a computer in the...Ch. 1 - Name the three major design criteria for control...Ch. 1 - Prob. 9RQCh. 1 - Physically, what happens to a system that is...
Ch. 1 - Instability is attributable to what pan of the...Ch. 1 - Describe a typical control system analy sis task.Ch. 1 - Describe a typical control system design task.Ch. 1 - Prob. 14RQCh. 1 - Name three approaches to the mathematical modeling...Ch. 1 - Briefly describe each of your answers to Question...Ch. 1 - Prob. 1PCh. 1 - Prob. 2PCh. 1 - An aircraft's attitude varies in roll, pitch, and...Ch. 1 - We can build a control system that will...Ch. 1 - Prob. 5PCh. 1 - During a medical operation an anesthesiologist...Ch. 1 - Prob. 7PCh. 1 - Prob. 8PCh. 1 - The human eye has a biological control system that...Ch. 1 - A Segway ®5 Personal Transporter (PT) (Figure Pl...Ch. 1 - In humans, hormone levels, alertness, and core...Ch. 1 - Tactile feedback is an important component in the...Ch. 1 - Prob. 13PCh. 1 - Moored floating platforms are subject to external...Ch. 1 - In the Case Study of Section 1.4. an antenna...Ch. 1 - Figure Pl.5 shows the topology of a photo-voltaic...Ch. 1 - Prob. 17PCh. 1 - Prob. 18PCh. 1 - Prob. 19PCh. 1 - Prob. 20PCh. 1 - Prob. 21PCh. 1 - Contol of HIV/AIDS. As of 2012. the number of...Ch. 1 - Prob. 23PCh. 1 - Parabolic trough collector. A set of parabolic...
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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
- Problem 1 (65 pts, suggested time 50 mins). An elastic string of constant line tension1T is pinned at x = 0 and x = L. A constant distributed vertical force per unit length p(with units N/m) is applied to the string. Under this force, the string deflects by an amountv(x) from its undeformed (horizontal) state, as shown in the figure below.The PDE describing mechanical equilibrium for the string isddx Tdvdx− p = 0 . (1)(a) [5pts] Identify the BCs for the string and identify their type (essential/natural). Writedown the strong-form BVP for the string, including PDE and BCs.(b) [10pts] Find the analytical solution of the BVP in (a). Compute the exact deflectionof the midpoint v(L/2).(c) [15pts] Derive the weak-form BVP.(d) [5pts] What is the minimum number of linear elements necessary to compute the deflection of the midpoint?(e) [15pts] Write down the element stiffness matrix and the element force vector for eachelement.arrow_forwardProblem 1 (35 pts). An elastic string of constant line tension1 T is pinned at x = 0 andx = L. A constant distributed vertical force per unit length p (with units N/m) is appliedto the string. Under this force, the string deflects by an amount v(x) from its undeformed(horizontal) state, as shown in the figure below.Force equilibrium in the string requires thatdfdx − p = 0 , (1)where f(x) is the internal vertical force in the string, which is given byf = Tdvdx . (2)(a) [10pts] Write down the BVP (strong form) that the string deflection v(x) must satisfy.(b) [2pts] What order is the governing PDE in the BVP of (a)?(c) [3pts] Identify the type (essential/natural) of each boundary condition in (a).(d) [20pts] Find the analytical solution of the BVP in (a).arrow_forwardProblem 2 (25 pts, (suggested time 15 mins). An elastic string of line tension T andmass per unit length µ is pinned at x = 0 and x = L. The string is free to vibrate, and itsfirst vibration mode is shown below.In order to find the frequency of the first mode (or fundamental frequency), the string isdiscretized into a certain number of linear elements. The stiffness and mass matrices of thei-th element are, respectivelyESMi =TLi1 −1−1 1 EMMi =Liµ62 11 2 . (2)(a) [5pts] What is the minimum number of linear elements necessary to compute the fundamental frequency of the vibrating string?(b) [20pts] Assemble the global eigenvalue problem and find the fundamental frequency ofvibration of the stringarrow_forward
- I need part all parts please in detail (including f)arrow_forwardProblem 3 (10 pts, suggested time 5 mins). In class we considered the mutiphysics problem of thermal stresses in a rod. When using linear shape functions, we found that the stress in the rod is affected by unphysical oscillations like in the following plot E*(ux-a*T) 35000 30000 25000 20000 15000 10000 5000 -5000 -10000 0 Line Graph: E*(ux-a*T) MULT 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Arc length (a) [10pts] What is the origin of this issue and how can we fix it?arrow_forwardanswer the questions and explain all of it in words. Ignore where it says screencast and in class explanationarrow_forward
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