Problem 1. (2 points) Consider the magnetic levitation system in Fig. 1. The equation of motion...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Problem 1. (2 points) Consider the magnetic levitation system in Fig. 1. The equation of motion for the levitated ball is: m Light Source d²w(t). dt² Lens. where w(t) is the position of the ball measured from the bottom of the coil to the top of the ball, i(t) is the coil current, m is the ball's mass, g is the gravitational constant, and a is a constant determined via experiments. Let the state vector of the nonlinear system be given by z(t) = and the output be w(1). Coil i(t) mgaw (1) Ball = Photosensor Array Figure 1. Schematic of a magnetic levitation system. ż (t) = a) (0.5 point) Verify that the nonlinear state equation is Z₂ (t) [₂00] [w] w (1) g output. Where are the poles and zeros located? 1 m , the input be v(t) = i(t), v² (t) a²z²(t), b) (1 point) Determine a linear state space representation of the nonlinear system that approximates the dynamics of the magnetic levitation system when the ball is 0.01 meter below the coil and it remains at that position. c) (0.5 point) Determine the transfer function of the linearized system. Clearly explain what are its input and Problem 1. (2 points) Consider the magnetic levitation system in Fig. 1. The equation of motion for the levitated ball is: m Light Source d²w(t). dt² Lens. where w(t) is the position of the ball measured from the bottom of the coil to the top of the ball, i(t) is the coil current, m is the ball's mass, g is the gravitational constant, and a is a constant determined via experiments. Let the state vector of the nonlinear system be given by z(t) = and the output be w(1). Coil i(t) mgaw (1) Ball = Photosensor Array Figure 1. Schematic of a magnetic levitation system. ż (t) = a) (0.5 point) Verify that the nonlinear state equation is Z₂ (t) [₂00] [w] w (1) g output. Where are the poles and zeros located? 1 m , the input be v(t) = i(t), v² (t) a²z²(t), b) (1 point) Determine a linear state space representation of the nonlinear system that approximates the dynamics of the magnetic levitation system when the ball is 0.01 meter below the coil and it remains at that position. c) (0.5 point) Determine the transfer function of the linearized system. Clearly explain what are its input and
Expert Answer:
Related Book For
Posted Date:
Students also viewed these electrical engineering questions
-
Write the general equation of motion for a mass that is on a horizontal frictionless surface and is connected to a spring at equilibrium (a) If the mass is initially pulled in the axis from the...
-
Derive the differential equation of motion for the system shown in terms of the variable x 1 . Neglect friction and the mass of the linkage. >x1 k1 C1 www X2 k2 m2 C2 B
-
A point mass m is located a distance D from the nearest end of a thin rod of mass M and length L along the axis of the rod. Find the gravitational force exerted on the point mass by the rod.
-
A construction company is considering taking on a new project. The total project cost is $5 million, and there is a 70% chance that the project will be completed on time and within budget, resulting...
-
Calculate the normal time for each of the workelements. Mean Performance Rating Factor 0.95 0.85 1.10 1.10 Work Observed Time Element (minutes) 1.20 1.00 0.80 0.90
-
At a time when demand for ready-to-eat cereal was stagnant, a spokesperson for the cereal maker Kelloggs was quoted as saying, . . . for the past several years, our individual company growth has...
-
A 1.2-lb kite with an area of \(6 \mathrm{ft}^{2}\) flies in a \(20-\mathrm{ft} / \mathrm{s}\) wind such that the weightless string makes an angle of \(55^{\circ}\) relative to the horizontal. If the...
-
Refer to Figure which shows the computer solution THE MANAGEMENT SCIENTIST SOLUTION FOR THE INVESTMENT ADVISORS PROBLEM a. How much would the return for U.S. Oil have to increase before it would be...
-
Coronado, Inc., manufactures clamps used in the overhead bin latches of several leading airplane models. Brian Lee, president of Coronado, Inc., has gathered the following cost information from the...
-
Use the data set GPA1 to answer this question. It was used in Computer Exercise C13 in Chapter 3 to estimate the effect of PC ownership on college GPA. (i) Run the regression colGPA on PC, hsGPA, and...
-
A company owns two identical apartment buildings. Both buildings were built at the same time. The first building was acquired by the company ten years ago. The second building was acquired by the...
-
What mechanisms can be implemented to address latent conflicts within organizational structures, preempting escalation into overt confrontations that undermine productivity and cohesion ?
-
Blossom Company must perform an impairment test on its equipment. The equipment will produce the following cash flows: Year 1, $37,000; Year 2, $40,000; Year 3, $64,500. The discount rate is 12%....
-
How do conflict resolution professionals navigate ethical dilemmas when mediating disputes between stakeholders with competing interests, balancing impartiality with the pursuit of equitable outcomes?
-
What role does emotional intelligence play in the resolution of high-stakes conflicts within cross-functional teams, particularly in environments characterized by interdependence and ambiguity?
-
Cameron Cookiest produces gourmet cookies, which sell for $16 a basket. Variable costs per basket are $6 and fixed costs are $5,000 per month. If the company expects to sell 1,500 baskets of cookies,...
-
What is the acetate ion concentration, [CH3O2] of a 100mL of calcium acetate solution, Ca(C2H3O2)2, with 25.0g dissolved Ca(CH3O2)2?
-
The graph of an equation is given. (a) Find the intercepts. (b) Indicate whether the graph is symmetric with respect to the x-axis, the y-axis, or the origin. -3 6 -6 3 x
-
The experimental values in Table 3 were obtained for the Young modulus E and the shear modulus G of steel: The formula (E/2G) ? 1 = v was then used to calculate the Poisson ratio v. Find v and...
-
A capacitor C, which may be considered to be loss-free, is connected with an inductor to form a closed loop. The inductor behaves as a pure inductance L in series with a resistor R. If, when the...
-
The distance between an object and its real image, formed by a converging lens, is held fixed. Show that there are two possible positions for the lens, and that the size of the object is given by...
-
Repeat Exercise 13.3, but this time work on the assumption that non-current assets that had originally cost :30,000, with accumulated depreciation of :12,000, had been sold during the year ended 31...
-
Study Figure 13.6. Write a short report on Bayers management of its cash flows over the period reported. Figure 13.6 Bayer Group's consolidated statement of cash flows Income after taxes Income taxes...
-
Expenses and revenues are subjective; cash flows are facts. Therefore cash flow statements cannot mislead. Discuss.
Study smarter with the SolutionInn App